Ready for TAKS? Benchmark Tests for Grade 9€¦ ·  · 2014-05-01Pre-Test TAKS Obj 10, (8.16)(B)...

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Transcript of Ready for TAKS? Benchmark Tests for Grade 9€¦ ·  · 2014-05-01Pre-Test TAKS Obj 10, (8.16)(B)...

Holt Math

Ready for TAKS?

Benchmark Tests for

Grade 9

3 R D P R I N T

Copyright © by Holt, Rinehart and Winston

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ISBN 0-03-092160-0

1 2 3 4 5 862 10 09 08 07 06

3 R D P R I N T

Copyright © by Holt, Rinehart and Winston. iii Holt Mathematics Grade 9All rights reserved.

Directions for Administering Tests. . vii

Reference to Other Materials . . . . . viii

Diagnosis and Prescription: Student Mastery Charts . . . . . . . . . ix

Reports . . . . . . . . . . . . . . . . . . . . . . . . xi

Answer Sheets . . . . . . . . . . . . . . . . xxvi

Pre-Test TAKS Obj 1, (A.1)(A) . . . . . . . . 1

Pre-Test TAKS Obj 1, (A.1)(B) . . . . . . . . 2

Pre-Test TAKS Obj 1, (A.1)(C) . . . . . . . 3

Pre-Test TAKS Obj 1, (A.1)(D) . . . . . . . 4

Pre-Test TAKS Obj 1, (A.1)(E) . . . . . . . . 5

Pre-Test TAKS Obj 2, (A.2)(A) . . . . . . . . 6

Pre-Test TAKS Obj 2, (A.2)(B) . . . . . . . . 7

Pre-Test TAKS Obj 2, (A.2)(C) . . . . . . . 8

Pre-Test TAKS Obj 2, (A.2)(D) . . . . . . . 9

Pre-Test TAKS Obj 2, (A.3)(A) . . . . . . . 10

Pre-Test TAKS Obj 2, (A.3)(B) . . . . . . . 11

Pre-Test TAKS Obj 2, (A.4)(A) . . . . . . . 12

Pre-Test TAKS Obj 2, (A.4)(B) . . . . . . . 13

Pre-Test TAKS Obj 2, (A.4)(C) . . . . . . . 14

Pre-Test TAKS Obj 3, (A.5)(A) . . . . . . . 15

Pre-Test TAKS Obj 3, (A.5)(C) . . . . . . 16

Pre-Test TAKS Obj 3, (A.6)(A) . . . . . . . 17

Pre-Test TAKS Obj 3, (A.6)(B) . . . . . . . 18

Pre-Test TAKS Obj 3, (A.6)(C) . . . . . . 19

Pre-Test TAKS Obj 3, (A.6)(D) . . . . . . 20

Pre-Test TAKS Obj 3, (A.6)(E) . . . . . . . 21

Pre-Test TAKS Obj 3, (A.6)(F) . . . . . . . 22

Pre-Test TAKS Obj 3, (A.6)(G) . . . . . . 23

Pre-Test TAKS Obj 4, (A.7)(A) . . . . . . . 24

Pre-Test TAKS Obj 4, (A.7)(B) . . . . . . . 25

Pre-Test TAKS Obj 4, (A.7)(C) . . . . . . 26

Pre-Test TAKS Obj 4, (A.8)(A) . . . . . . . 27

Pre-Test TAKS Obj 5, (A.9)(C) . . . . . . 28

Pre-Test TAKS Obj 5, (A.11)(A) . . . . . . 29

Pre-Test TAKS Obj 6, (8.6)(A) . . . . . . . 30

Pre-Test TAKS Obj 6, (8.6)(B) . . . . . . . 31

Pre-Test TAKS Obj 6, (8.7)(D) . . . . . . . 32

Pre-Test TAKS Obj 7, (8.7)(A) . . . . . . . 33

Pre-Test TAKS Obj 7, (8.7)(B) . . . . . . . 34

Pre-Test TAKS Obj 7, (8.7)(C) . . . . . . . 35

Pre-Test TAKS Obj 8, (8.8)(A) . . . . . . . 36

Pre-Test TAKS Obj 8, (8.8)(B) . . . . . . . 37

Pre-Test TAKS Obj 8, (8.8)(C) . . . . . . . 38

Pre-Test TAKS Obj 8, (8.9)(A) . . . . . . . 39

Pre-Test TAKS Obj 8, (8.9)(B) . . . . . . . 40

Pre-Test TAKS Obj 8, (8.10)(A) . . . . . . 41

Pre-Test TAKS Obj 8, (8.10)(B) . . . . . . 42

Pre-Test TAKS Obj 9, (8.1)(B) . . . . . . . 43

Pre-Test TAKS Obj 9, (8.3)(B) . . . . . . . 44

Pre-Test TAKS Obj 9, (8.11)(A) . . . . . . 45

Pre-Test TAKS Obj 9, (8.11)(B) . . . . . . 46

Pre-Test TAKS Obj 9, (8.12)(A) . . . . . . 47

Pre-Test TAKS Obj 9, (8.12)(C) . . . . . . 48

Pre-Test TAKS Obj 9, (8.13)(B) . . . . . . 49

Pre-Test TAKS Obj 10, (8.14)(A) . . . . . 50

Pre-Test TAKS Obj 10, (8.14)(B) . . . . . 51

Pre-Test TAKS Obj 10, (8.14)(C) . . . . . 52

Pre-Test TAKS Obj 10, (8.15)(A) . . . . . 53

Pre-Test TAKS Obj 10, (8.16)(A) . . . . . 54

Pre-Test TAKS Obj 10, (8.16)(B) . . . . . 55

Post-Test TAKS Obj 1, (A.1)(A) . . . . . . 56

Post-Test TAKS Obj 1, (A.1)(B) . . . . . . 57

Post-Test TAKS Obj 1, (A.1)(C) . . . . . . 58

Post-Test TAKS Obj 1, (A.1)(D) . . . . . . 59

Post-Test TAKS Obj 1, (A.1)(E) . . . . . . 60

Post-Test TAKS Obj 2, (A.2)(A) . . . . . . 61

Post-Test TAKS Obj 2, (A.2)(B) . . . . . . 62

Post-Test TAKS Obj 2, (A.2)(C) . . . . . . 63

Post-Test TAKS Obj 2, (A.2)(D) . . . . . . 64

Post-Test TAKS Obj 2, (A.3)(A) . . . . . . 65

CONTENTS

3 R D P R I N T

CONTENTS, CONTINUED

Copyright © by Holt, Rinehart and Winston. iv Holt Mathematics Grade 9All rights reserved.

Post-Test TAKS Obj 2, (A.3)(B) . . . . . . 66

Post-Test TAKS Obj 2, (A.4)(A) . . . . . . 67

Post-Test TAKS Obj 2, (A.4)(B) . . . . . . 68

Post-Test TAKS Obj 2, (A.4)(C) . . . . . . 69

Post-Test TAKS Obj 3, (A.5)(A) . . . . . . 70

Post-Test TAKS Obj 3, (A.5)(C) . . . . . . 71

Post-Test TAKS Obj 3, (A.6)(A) . . . . . . 72

Post-Test TAKS Obj 3, (A.6)(B) . . . . . . 73

Post-Test TAKS Obj 3, (A.6)(C) . . . . . . 74

Post-Test TAKS Obj 3, (A.6)(D) . . . . . . 75

Post-Test TAKS Obj 3, (A.6)(E) . . . . . . 76

Post-Test TAKS Obj 3, (A.6)(F). . . . . . . 77

Post-Test TAKS Obj 3, (A.6)(G) . . . . . . 78

Post-Test TAKS Obj 4, (A.7)(A) . . . . . . 79

Post-Test TAKS Obj 4, (A.7)(B) . . . . . . 80

Post-Test TAKS Obj 4, (A.7)(C) . . . . . . 81

Post-Test TAKS Obj 4, (A.8)(A) . . . . . . 82

Post-Test TAKS Obj 5, (A.9)(C) . . . . . . 83

Post-Test TAKS Obj 5, (A.11)(A) . . . . . 84

Post-Test TAKS Obj 6, (8.6)(A). . . . . . . 85

Post-Test TAKS Obj 6, (8.6)(B). . . . . . . 86

Post-Test TAKS Obj 6, (8.7)(D). . . . . . . 87

Post-Test TAKS Obj 7, (8.7)(A). . . . . . . 88

Post-Test TAKS Obj 7, (8.7)(B). . . . . . . 89

Post-Test TAKS Obj 7, (8.7)(C). . . . . . . 90

Post-Test TAKS Obj 8, (8.8)(A). . . . . . . 91

Post-Test TAKS Obj 8, (8.8)(B). . . . . . . 92

Post-Test TAKS Obj 8, (8.8)(C). . . . . . . 93

Post-Test TAKS Obj 8, (8.9)(A). . . . . . . 94

Post-Test TAKS Obj 8, (8.9)(B). . . . . . . 95

Post-Test TAKS Obj 8, (8.10)(A). . . . . . 96

Post-Test TAKS Obj 8, (8.10)(B). . . . . . 97

Post-Test TAKS Obj 9, (8.1)(B). . . . . . . 98

Post-Test TAKS Obj 9, (8.3)(B). . . . . . . 99

Post-Test TAKS Obj 9, (8.11)(A). . . . . 100

Post-Test TAKS Obj 9, (8.11)(B). . . . . 101

Post-Test TAKS Obj 9, (8.12)(A). . . . . 102

Post-Test TAKS Obj 9, (8.12)(C). . . . . 103

Post-Test TAKS Obj 9, (8.13)(B). . . . . 104

Post-Test TAKS Obj 10, (8.14)(A). . . . 105

Post-Test TAKS Obj 10, (8.14)(B). . . . 106

Post-Test TAKS Obj 10, (8.14)(C). . . . 107

Post-Test TAKS Obj 10, (8.15)(A). . . . 108

Post-Test TAKS Obj 10, (8.16)(A). . . . 109

Post-Test TAKS Obj 10, (8.16)(B). . . . 110

Pre-Test TAKS Obj 1, (A.1)(A) Answers/TAKS DOCTOR . . . . . . . . 111

Pre-Test TAKS Obj 1, (A.1)(B) Answers/TAKS DOCTOR . . . . . . . . 112

Pre-Test TAKS Obj 1, (A.1)(C) Answers/TAKS DOCTOR . . . . . . . . 113

Pre-Test TAKS Obj 1, (A.1)(D) Answers/TAKS DOCTOR . . . . . . . . 114

Pre-Test TAKS Obj 1, (A.1)(E) Answers/TAKS DOCTOR . . . . . . . . 115

Pre-Test TAKS Obj 2, (A.2)(A) Answers/TAKS DOCTOR . . . . . . . . 116

Pre-Test TAKS Obj 2, (A.2)(B) Answers/TAKS DOCTOR . . . . . . . . 117

Pre-Test TAKS Obj 2, (A.2)(C) Answers/TAKS DOCTOR . . . . . . . . 118

Pre-Test TAKS Obj 2, (A.2)(D) Answers/TAKS DOCTOR . . . . . . . . 119

Pre-Test TAKS Obj 2, (A.3)(A) Answers/TAKS DOCTOR . . . . . . . . 120

Pre-Test TAKS Obj 2, (A.3)(B) Answers/TAKS DOCTOR . . . . . . . . 121

Pre-Test TAKS Obj 2, (A.4)(A) Answers/TAKS DOCTOR . . . . . . . . 122

Pre-Test TAKS Obj 2, (A.4)(B) Answers/TAKS DOCTOR . . . . . . . . 123

Pre-Test TAKS Obj 2, (A.4)(C) Answers/TAKS DOCTOR . . . . . . . . 124

3 R D P R I N T

Copyright © by Holt, Rinehart and Winston. v Holt Mathematics Grade 9All rights reserved.

Pre-Test TAKS Obj 3, (A.5)(A) Answers/TAKS DOCTOR . . . . . . . . 125

Pre-Test TAKS Obj 3, (A.5)(C) Answers/TAKS DOCTOR . . . . . . . . 126

Pre-Test TAKS Obj 3, (A.6)(A) Answers/TAKS DOCTOR . . . . . . . . 127

Pre-Test TAKS Obj 3, (A.6)(B)) Answers/TAKS DOCTOR . . . . . . . . 128

Pre-Test TAKS Obj 3, (A.6)(C) Answers/TAKS DOCTOR . . . . . . . . 129

Pre-Test TAKS Obj 3, (A.6)(D) Answers/TAKS DOCTOR . . . . . . . . 130

Pre-Test TAKS Obj 3, (A.6)(E) Answers/TAKS DOCTOR . . . . . . . . 131

Pre-Test TAKS Obj 3, (A.6)(F) Answers/TAKS DOCTOR . . . . . . . . 132

Pre-Test TAKS Obj 3, (A.6)(G) Answers/TAKS DOCTOR . . . . . . . . 133

Pre-Test TAKS Obj 4, (A.7)(A) Answers/TAKS DOCTOR . . . . . . . . 134

Pre-Test TAKS Obj 4, (A.7)(B) Answers/TAKS DOCTOR . . . . . . . . 135

Pre-Test TAKS Obj 4, (A.7)(C) Answers/TAKS DOCTOR . . . . . . . . 136

Pre-Test TAKS Obj 4, (A.8)(A) Answers/TAKS DOCTOR . . . . . . . . 137

Pre-Test TAKS Obj 5, (A.9)(C) Answers/TAKS DOCTOR . . . . . . . . 138

Pre-Test TAKS Obj 5, (A.11)(A) Answers/TAKS DOCTOR . . . . . . . . 139

Pre-Test TAKS Obj 6, (8.6)(A) Answers/TAKS DOCTOR . . . . . . . . 140

Pre-Test TAKS Obj 6, (8.6)(B) Answers/TAKS DOCTOR . . . . . . . . 141

Pre-Test TAKS Obj 6, (8.7)(D) Answers/TAKS DOCTOR . . . . . . . . 142

Pre-Test TAKS Obj 7, (8.7)(A) Answers/TAKS DOCTOR . . . . . . . . 143

Pre-Test TAKS Obj 7, (8.7)(B) Answers/TAKS DOCTOR . . . . . . . . 144

Pre-Test TAKS Obj 7, (8.7)(C) Answers/TAKS DOCTOR . . . . . . . . 145

Pre-Test TAKS Obj 8, (8.8)(A) Answers/TAKS DOCTOR . . . . . . . . 146

Pre-Test TAKS Obj 8, (8.8)(B) Answers/TAKS DOCTOR . . . . . . . . 147

Pre-Test TAKS Obj 8, (8.8)(C) Answers/TAKS DOCTOR . . . . . . . . 148

Pre-Test TAKS Obj 8, (8.9)(A) Answers/TAKS DOCTOR . . . . . . . . 149

Pre-Test TAKS Obj 8, (8.9)(B) Answers/TAKS DOCTOR . . . . . . . . 150

Pre-Test TAKS Obj 8, (8.10)(A) Answers/TAKS DOCTOR . . . . . . . . 151

Pre-Test TAKS Obj 8, (8.10)(B) Answers/TAKS DOCTOR . . . . . . . . 152

Pre-Test TAKS Obj 9, (8.1)(B) Answers/TAKS DOCTOR . . . . . . . . 153

Pre-Test TAKS Obj 9, (8.3)(B) Answers/TAKS DOCTOR . . . . . . . . 154

Pre-Test TAKS Obj 9, (8.11)(A) Answers/TAKS DOCTOR . . . . . . . . 155

Pre-Test TAKS Obj 9, (8.11)(B) Answers/TAKS DOCTOR . . . . . . . . 156

Pre-Test TAKS Obj 9, (8.12)(A) Answers/TAKS DOCTOR . . . . . . . . 157

Pre-Test TAKS Obj 9, (8.12)(C) Answers/TAKS DOCTOR . . . . . . . . 158

Pre-Test TAKS Obj 9, (8.13)(B) Answers/TAKS DOCTOR . . . . . . . . 159

Pre-Test TAKS Obj 10, (8.14)(A) Answers/TAKS DOCTOR . . . . . . . . 160

Pre-Test TAKS Obj 10, (8.14)(B) Answers/TAKS DOCTOR . . . . . . . . 161

Pre-Test TAKS Obj 10, (8.14)(C) Answers/TAKS DOCTOR . . . . . . . . 162

CONTENTS, CONTINUED

3 R D P R I N T

Copyright © by Holt, Rinehart and Winston. vi Holt Mathematics Grade 9All rights reserved.

CONTENTS, CONTINUED

Pre-Test TAKS Obj 10, (8.15)(A) Answers/TAKS DOCTOR . . . . . . . . 163

Pre-Test TAKS Obj 10, (8.16)(A) Answers/TAKS DOCTOR . . . . . . . . 164

Pre-Test TAKS Obj 10, (8.16)(B) Answers/TAKS DOCTOR . . . . . . . . 165

Answer Key Post Tests . . . . . . . . . . 166

3 R D P R I N T

Copyright © by Holt, Rinehart and Winston. vii Holt Mathematics Grade 9All rights reserved.

Using the Ready for TAKS? Benchmark Tests and Ready for TAKS? Intervention in Your ClassThe Ready for TAKS? Benchmark Tests will help you diagnose and assess the diverse skill levels of the students in your class, and will help you better prepare students for the TAKS tests.

Administering the Ready for TAKS? Benchmark Tests

Prepare a copy of the appropriate multiple-choice test and answer sheet in this book for each student who will take the test. Provide students with scratch paper. Use the TAKS Benchmark Pre-Tests to diagnose whether students are having difficulty and require Intervention. Use the TAKS Benchmark Post-Tests to assess whether students have made progress after they have had Intervention.

Scoring and Reports

When students have finished, collect all the tests and use the answer key to score them. For the TAKS Benchmark Pre-Tests, use the TAKS Doctor to diagnose errors. Record the scores on the Student Benchmark Test Profile and Class Benchmark Test Profile reports. Use these reports to keep track of students having difficulty on particular TEKS. Use the Class Benchmark Test Recording Sheet, and Student Intervention Plan to determine the steps needed to address problem areas, and to organize appropriate Intervention resources.

Intervention

The Diagnosis and Prescription: Student Mastery Chart indicates the Intervention resources for the TEKS. When more review is necessary, provide students with the appropriate TAKS Mini-Review to help them prepare for the TAKS tests.

3 R D P R I N T

Copyright © by Holt, Rinehart and Winston. viii Holt Mathematics Grade 9All rights reserved.

Other Materials Available for TAKS Test Preparation• Ready for TAKS? Benchmark Tests are available in different formats:

Ready for TAKS Intervention for Grades 6 through Exit Exam [CD-ROMs]—allows teachers to assign the TAKS Benchmark Pre- and Post-Tests to whole classes or individual students. The Reports show which students are having difficulty on particular TEKS. Teachers can choose to have interactive Intervention materials automatically assigned to students requiring help.

Ready for TAKS Intervention Online for Grades 6 through Exit Exam—provides diagnostic assessment and interactive Intervention and Practice. The TAKS Benchmark Pre-Test Reports show which students are having difficulty on particular TEKS. Teachers can choose to have the interactive Intervention materials automatically assigned to students requiring help. Once students have completed the Intervention, the system automatically assigns the appropriate TAKS Benchmark Post-Tests. The TAKS Benchmark Post-Test Reports show which students are proficient and which students need more help.

• TAKS Prep Workbook—provides extra practice for students by using alternative strategies to reteach skills that are tested on the TAKS.

• Countdown to TAKS Transparencies—provides practice on skills that are tested on the TAKS. The Transparencies can be used as lesson warm ups, or as daily or weekly quizzes.

3 R D P R I N T

Copyright © by Holt, Rinehart and Winston. ix Holt Mathematics Grade 9All rights reserved.

Ready for TAKS? Benchmark Tests

Diagnosis and PrescriptionDIAGNOSIS AND PRESCRIPTION: STUDENT MASTERY

The Benchmark Tests can be used to inform instructional planning, chart student progress, and provide individual and group snapshots of math concepts and skills proficiency.

TAKS/TEKS Ready for TAKS? Benchmark Pre-Test

Ready for TAKS? Benchmark Post-Test

Ready for TAKS? Intervention

TAKS Mini-Review

Objective 1 Foundations for Functions

(A.1)(A) Items 1–5 Items 1–5 (A.1)(A) Obj. 1

(A.1)(B) Items 1–5 Items 1–5 (A.1)(B) Obj. 1

(A.1)(C) Items 1–5 Items 1–5 (A.1)(C) Obj. 1

(A.1)(D) Items 1–5 Items 1–5 (A.1)(D) Obj. 1

(A.1)(E) Items 1–5 Items 1–5 (A.1)(E) Obj. 1

Objective 2 Foundations for Functions

(A.2)(A) Items 1–5 Items 1–5 (A.2)(A) Obj. 2, Part 1

(A.2)(B) Items 1–5 Items 1–5 (A.2)(B) Obj. 2, Part 1

(A.2)(C) Items 1–4 Items 1–4 (A.2)(C) Obj. 2, Part 1

(A.2)(D) Items 1–5 Items 1–5 (A.2)(D) Obj. 2, Part 1

(A.3)(A) Items 1–5 Items 1–5 (A.3)(A) Obj. 2, Part 2

(A.3)(B) Items 1–5 Items 1–5 (A.3)(B) Obj. 2, Part 2

(A.4)(A) Items 1–6 Items 1–6 (A.4)(A) Obj. 2, Part 2

(A.4)(B) Items 1–6 Items 1–6 (A.4)(B) Obj. 2, Part 2

(A.4)(C) Items 1–5 Items 1–5 (A.4)(C) Obj. 2, Part 2

Objective 3 Linear Functions

(A.5)(A) Items 1–4 Items 1–4 (A.5)(A) Obj. 3

(A.5)(C) Items 1–5 Items 1–5 (A.5)(C) Obj. 3

(A.6)(A) Items 1–5 Items 1–5 (A.6)(A) Obj. 3

(A.6)(B) Items 1–5 Items 1–5 (A.6)(B) Obj. 3

(A.6)(C) Items 1–5 Items 1–5 (A.6)(C) Obj. 3

(A.6)(D) Items 1–5 Items 1–5 (A.6)(D) Obj. 3

(A.6)(E) Items 1–5 Items 1–5 (A.6)(E) Obj. 3

(A.6)(F) Items 1–5 Items 1–5 (A.6)(F) Obj. 3

(A.6)(G) Items 1–5 Items 1–5 (A.6)(G) Obj. 3

Objective 4 Linear Functions

(A.7)(A) Items 1–5 Items 1–5 (A.7)(A) Obj. 4

(A.7)(B) Items 1–5 Items 1–6 (A.7)(B) Obj. 4

(A.7)(C) Items 1–5 Items 1–5 (A.7)(C) Obj. 4

(A.8)(A) Items 1–5 Items 1–5 (A.8)(A) Obj. 4

Objective 5 Quadratic and Other Nonlinear Functions

(A.9)(C) Items 1–5 Items 1–5 (A.9)(C) Obj. 5

(A.11)(A) Items 1–5 Items 1–5 (A.11)(A) Obj. 5

3 R D P R I N T

Copyright © by Holt, Rinehart and Winston. x Holt Mathematics Grade 9All rights reserved.

Ready for TAKS? Benchmark Tests

Diagnosis and PrescriptionDIAGNOSIS AND PRESCRIPTION: STUDENT MASTERY

The Benchmark Tests can be used to inform instructional planning, chart student progress, and provide individual and group snapshots of math concepts and skills proficiency.

TAKS/TEKS Ready for TAKS? Benchmark Pre-Test

Ready for TAKS? Benchmark Post-Test

Ready for TAKS? Intervention

TAKS Mini-Review

Objective 6 Geometry and Spatial Reasoning

(8.6)(A) Items 1–5 Items 1–5 (8.6)(A) Obj. 6

(8.6)(B) Items 1–5 Items 1–5 (8.6)(B) Obj. 6

(8.7)(D) Items 1–5 Items 1–5 (8.7)(D) Obj. 6

Objective 7 Geometry and Spatial Reasoning

(8.7)(A) Items 1–5 Items 1–5 (8.7)(A) Obj. 7

(8.7)(B) Items 1–5 Items 1–5 (8.7)(B) Obj. 7

(8.7)(C) Items 1–4 Items 1–4 (8.7)(C) Obj. 7

Objective 8 Measurement

(8.8)(A) Items 1–5 Items 1–5 (8.8)(A) Obj. 8

(8.8)(B) Items 1–5 Items 1–5 (8.8)(B) Obj. 8

(8.8)(C) Items 1–5 Items 1–5 (8.8)(C) Obj. 8

(8.9)(A) Items 1–5 Items 1–5 (8.9)(A) Obj. 8

(8.9)(B) Items 1–5 Items 1–5 (8.9)(B) Obj. 8

(8.10)(A) Items 1–5 Items 1–5 (8.10)(A) Obj. 8

(8.10)(B) Items 1–5 Items 1–5 (8.10)(B) Obj. 8

Objective 9 Number, Operations, and Quantitative Reasoning

(8.1)(B) Items 1–5 Items 1–5 (8.1)(B) Obj. 9, Part 1

Objective 9 Patterns, Relationships, and Algebraic Thinking

(8.3)(B) Items 1–5 Items 1–5 (8.3)(B) Obj. 9, Part 1

Objective 9 Probability and Statistics

(8.11)(A) Items 1–5 Items 1–5 (8.11)(A) Obj. 9, Part 1

(8.11)(B) Items 1–5 Items 1–5 (8.11)(B) Obj. 9, Part 1

(8.12)(A) Items 1–5 Items 1–5 (8.12)(A) Obj. 9, Part 2

(8.12)(C) Items 1–4 Items 1–4 (8.12)(C) Obj. 9, Part 2

(8.13)(B) Items 1–4 Items 1–4 (8.13)(B) Obj. 9, Part 2

Objective 10 Underlying Processes and Mathematical Tools

(8.14)(A) Items 1–5 Items 1–5 (8.14)(A) Obj. 10

(8.14)(B) Items 1–5 Items 1–5 (8.14)(B) Obj. 10

(8.14)(C) Items 1–5 Items 1–5 (8.14)(C) Obj. 10

(8.15)(A) Items 1–5 Items 1–5 (8.15)(A) Obj. 10

(8.16)(A) Items 1–5 Items 1–5 (8.16)(A) Obj. 10

(8.16)(B) Items 1–5 Items 1–5 (8.16)(B) Obj. 10

3 R D P R I N T

Copyright © by Holt, Rinehart and Winston. xi Holt Mathematics Grade 9All rights reserved.

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hm

ark

Tests R

ec

ord

ing

Sh

ee

t

Check off the appropriate box w

hen a student has difficulty on the Ready for TA

KS

? Benchm

ark Tests for Grade 9.

Use the R

eady for TAK

S? Intervention for G

rade 9 to help the student.

Stu

de

nt N

am

e

TA

KS

/TE

KS

Ob

jective 1: Th

e stud

ent w

ill describ

e fun

ction

al relation

ship

s in a variety o

f ways.

Fo

un

datio

ns fo

r Fu

nctio

ns

(A.1)(A

)(A

.1)(B)

(A.1)(C

)(A

.1)(D)

(A.1)(E

)

3 R D P R I N T

Copyright © by Holt, Rinehart and Winston. xii Holt Mathematics Grade 9All rights reserved.

Cla

ss B

en

ch

ma

rk T

est

s R

ec

ord

ing

Sh

ee

t

Che

ck o

ff th

e ap

prop

riate

box

whe

n a

stud

ent

has

diffi

culty

on

the

Rea

dy fo

r TA

KS

? B

ench

mar

k Te

sts

for

Gra

de 9

.U

se t

he R

eady

for

TAK

S?

Inte

rven

tion

for

Gra

de 9

to

help

the

stu

dent

.

Stu

de

nt

Na

me

TA

KS

/TE

KS

Ob

ject

ive

2: T

he

stu

den

t w

ill d

emo

nst

rate

an

un

der

stan

din

g o

f th

e p

rop

erti

es a

nd

att

ribu

tes

of

fun

ctio

ns.

Fo

un

dat

ion

s fo

r F

un

ctio

ns

(A.2

)(A

)(A

.2)(

B)

(A.2

)(C

)(A

.2)(

D)

(A.3

)(A

)(A

.3)(

B)

(A.4

)(A

)(A

.4)(

B)

(A.4

)(C

)

3 R D P R I N T

Copyright © by Holt, Rinehart and Winston. xiii Holt Mathematics Grade 9All rights reserved.

Cla

ss Be

nc

hm

ark

Tests R

ec

ord

ing

Sh

ee

t

Check off the appropriate box w

hen a student has difficulty on the Ready for TA

KS

? Benchm

ark Tests for Grade 9.

Use the R

eady for TAK

S? Intervention for G

rade 9 to help the student.

Stu

de

nt N

am

e

TA

KS

/TE

KS

Ob

jective 3: Th

e stud

ent w

ill dem

on

strate an u

nd

erstand

ing

of lin

ear fun

ction

s.

Lin

ear Fu

nctio

ns

(A.5)(A

)(A

.5)(C)

(A.6)(A

)(A

.6)(B)

(A.6)(C

)(A

.6)(D)

(A.6)(E

)(A

.6)(F)

(A.6)(G

)

3 R D P R I N T

Copyright © by Holt, Rinehart and Winston. xiv Holt Mathematics Grade 9All rights reserved.

Cla

ss B

en

ch

ma

rk T

est

s R

ec

ord

ing

Sh

ee

t

Che

ck o

ff th

e ap

prop

riate

box

whe

n a

stud

ent

has

diffi

culty

on

the

Rea

dy fo

r TA

KS

? B

ench

mar

k Te

sts

for

Gra

de 9

.U

se t

he R

eady

for

TAK

S?

Inte

rven

tion

for

Gra

de 9

to

help

the

stu

dent

.

Stu

de

nt

Na

me

TA

KS

/TE

KS

Ob

ject

ive

4: T

he

stu

den

t w

ill f

orm

ula

te a

nd

use

lin

ear

equ

atio

ns

and

ineq

ual

itie

s.

Lin

ear

Fu

nct

ion

s

(A.7

)(A

)(A

.7)(

B)

(A.7

)(C

)(A

.8)(

A)

3 R D P R I N T

Copyright © by Holt, Rinehart and Winston. xv Holt Mathematics Grade 9All rights reserved.

Cla

ss Be

nc

hm

ark

Tests R

ec

ord

ing

Sh

ee

t

Check off the appropriate box w

hen a student has difficulty on the Ready for TA

KS

? Benchm

ark Tests for Grade 9.

Use the R

eady for TAK

S? Intervention for G

rade 9 to help the student.

Stu

de

nt N

am

e

TA

KS

/TE

KS

Ob

jective 5: Th

e stud

ent w

ill dem

on

strate an u

nd

erstand

ing

of q

uad

ratic and

oth

er no

nlin

ear fun

ction

s.

Qu

adratic an

d O

ther N

on

linear F

un

ction

s

(A.9)(C

)(A

.11)(A)

3 R D P R I N T

Copyright © by Holt, Rinehart and Winston. xvi Holt Mathematics Grade 9All rights reserved.

Cla

ss B

en

ch

ma

rk T

est

s R

ec

ord

ing

Sh

ee

t

Che

ck o

ff th

e ap

prop

riate

box

whe

n a

stud

ent

has

diffi

culty

on

the

Rea

dy fo

r TA

KS

? B

ench

mar

k Te

sts

for

Gra

de 9

.U

se t

he R

eady

for

TAK

S?

Inte

rven

tion

for

Gra

de 9

to

help

the

stu

dent

.

Stu

de

nt

Na

me

TA

KS

/TE

KS

Ob

ject

ive

6: T

he

stu

den

t w

ill d

emo

nst

rate

an

un

der

stan

din

g o

f g

eom

etri

c re

lati

on

ship

s an

d s

pat

ial r

easo

nin

g.

Geo

met

ric

and

Sp

atia

l Rea

son

ing

(8.6

)(A

)(8

.6)(

B)

(8.7

)(D

)

3 R D P R I N T

Copyright © by Holt, Rinehart and Winston. xvii Holt Mathematics Grade 9All rights reserved.

Cla

ss Be

nc

hm

ark

Tests R

ec

ord

ing

Sh

ee

t

Check off the appropriate box w

hen a student has difficulty on the Ready for TA

KS

? Benchm

ark Tests for Grade 9.

Use the R

eady for TAK

S? Intervention for G

rade 9 to help the student.

Stu

de

nt N

am

e

TA

KS

/TE

KS

Ob

jective 7: Th

e stud

ent w

ill dem

on

strate an u

nd

erstand

ing

of tw

o- an

d th

ree-dim

ensio

nal rep

resentatio

ns o

f g

eom

etric relation

ship

s and

shap

es.

Geo

metric an

d S

patial R

eason

ing

(8.7)(A)

(8.7)(B)

(8.7)(C)

3 R D P R I N T

Copyright © by Holt, Rinehart and Winston. xviii Holt Mathematics Grade 9All rights reserved.

Cla

ss B

en

ch

ma

rk T

est

s R

ec

ord

ing

Sh

ee

t

Che

ck o

ff th

e ap

prop

riate

box

whe

n a

stud

ent

has

diffi

culty

on

the

Rea

dy fo

r TA

KS

? B

ench

mar

k Te

sts

for

Gra

de 9

.U

se t

he R

eady

for

TAK

S?

Inte

rven

tion

for

Gra

de 9

to

help

the

stu

dent

.

Stu

de

nt

Na

me

TA

KS

/TE

KS

Ob

ject

ive

8: T

he

stu

den

t w

ill d

emo

nst

rate

an

un

der

stan

din

g o

f th

e co

nce

pts

an

d u

ses

of

mea

sure

men

t an

d s

imila

rity

.

Mea

sure

men

t

(8.8

)(A

)(8

.8)(

B)

(8.8

)(C

)(8

.9)(

A)

(8.9

)(B

)(8

.10)

(A)

(8.1

0)(B

)

3 R D P R I N T

Copyright © by Holt, Rinehart and Winston. xix Holt Mathematics Grade 9All rights reserved.

Cla

ss Be

nc

hm

ark

Tests R

ec

ord

ing

Sh

ee

t

Check off the appropriate box w

hen a student has difficulty on the Ready for TA

KS

? Benchm

ark Tests for Grade 9.

Use the R

eady for TAK

S? Intervention for G

rade 9 to help the student.

Stu

de

nt N

am

e

TA

KS

/TE

KS

Ob

jective 9: Th

e stud

ent w

ill dem

on

strate an u

nd

erstand

ing

of p

ercents, p

rop

ortio

nal relatio

nsh

ips, p

rob

ability, an

d

statistics in ap

plicatio

n p

rob

lems.

Nu

mb

er, Op

eration

s, and

Qu

antitative R

eason

ing

; Pattern

s, Relatio

nsh

ips, an

d A

lgeb

raic Th

inkin

g;

Pro

bab

ility and

Statistics

(8.1)(B)

(8.3)(B)

(8.11)(A)

(8.11)(B)

(8.12)(A)

(8.12)(C)

(8.13)(B)

3 R D P R I N T

Copyright © by Holt, Rinehart and Winston. xx Holt Mathematics Grade 9All rights reserved.

Cla

ss B

en

ch

ma

rk T

est

s R

ec

ord

ing

Sh

ee

t

Che

ck o

ff th

e ap

prop

riate

box

whe

n a

stud

ent

has

diffi

culty

on

the

Rea

dy fo

r TA

KS

? B

ench

mar

k Te

sts

for

Gra

de 9

.U

se t

he R

eady

for

TAK

S?

Inte

rven

tion

for

Gra

de 9

to

help

the

stu

dent

.

Stu

de

nt

Na

me

TA

KS

/TE

KS

Ob

ject

ive

10: T

he

stu

den

t w

ill d

emo

nst

rate

an

un

der

stan

din

g o

f th

e m

ath

emat

ical

pro

cess

es a

nd

to

ols

use

d in

p

rob

lem

so

lvin

g.

Un

der

lyin

g P

roce

sses

an

d M

ath

emat

ical

To

ols

(8.1

4)(A

)(8

.14)

(B)

(8.1

4)(C

)(8

.15)

(A)

(8.1

6)(A

)(8

.16)

(B)

3 R D P R I N T

Copyright © by Holt, Rinehart and Winston. xxi Holt Mathematics Grade 9All rights reserved.

Student Intervention Plan

Student Name ______________________________________________________________________

Class ________________________________ Teacher __________________________________

Date __________________________________

TAKS/TEKS Steps Taken to Address Reteaching/Intervention Problem Area Processes

3 R D P R I N T

TAKS BENCHMARK PRE-TESTS BENCHMARK POST-TESTS

Objective TEKS Number % Intervention Number % Proficient? Correct Correct Needed? Correct Correct Yes/No Yes/No

3 (A.5)(A) /4 /4

3 (A.5)(C) /5 /5

3 (A.6)(A) /5 /5

3 (A.6)(B) /5 /5

3 (A.6)(C) /5 /5

3 (A.6)(D) /5 /5

3 (A.6)(E) /5 /5

3 (A.6)(F) /5 /5

3 (A.6)(G) /5 /5

TAKS BENCHMARK PRE-TESTS BENCHMARK POST-TESTS

Objective TEKS Number % Intervention Number % Proficient? Correct Correct Needed? Correct Correct Yes/No Yes/No

2 (A.2)(A) /5 /5

2 (A.2)(B) /5 /5

2 (A.2)(C) /4 /4

2 (A.2)(D) /5 /5

2 (A.3)(A) /5 /5

2 (A.3)(B) /5 /5

2 (A.4)(A) /6 /6

2 (A.4)(B) /6 /6

2 (A.4)(C) /5 /5

TAKS BENCHMARK PRE-TESTS BENCHMARK POST-TESTS

Objective TEKS Number % Intervention Number % Proficient? Correct Correct Needed? Correct Correct Yes/No Yes/No

1 (A.1)(A) /5 /5

1 (A.1)(B) /5 /5

1 (A.1)(C) /5 /5

1 (A.1)(D) /5 /5

1 (A.1)(E) /5 /5

Student Benchmark Test Profile

Student Name ______________________________________________________________________

Copyright © by Holt, Rinehart and Winston. xxii Holt Mathematics Grade 9All rights reserved.

Proficiency Levels

Advanced Learners 90% to 100%

On-Level Learners 70% to 89%

Learners Having Difficulty below 70%

3 R D P R I N T

TAKS BENCHMARK PRE-TESTS BENCHMARK POST-TESTS

Objective TEKS Number % Intervention Number % Proficient? Correct Correct Needed? Correct Correct Yes/No Yes/No

6 (8.6)(A) /5 /5

6 (8.6)(B) /5 /5

6 (8.7)(D) /5 /5

Copyright © by Holt, Rinehart and Winston. xxiii Holt Mathematics Grade 9All rights reserved.

Student Benchmark Test Profile

Student Name ______________________________________________________________________

TAKS BENCHMARK PRE-TESTS BENCHMARK POST-TESTS

Objective TEKS Number % Intervention Number % Proficient? Correct Correct Needed? Correct Correct Yes/No Yes/No

4 (A.7)(A) /5 /5

4 (A.7)(B) /6 /6

4 (A.7)(C) /5 /5

4 (A.8)(A) /5 /5

Proficiency Levels

Advanced Learners 90% to 100%

On-Level Learners 70% to 89%

Learners Having Difficulty below 70%

TAKS BENCHMARK PRE-TESTS BENCHMARK POST-TESTS

Objective TEKS Number % Intervention Number % Proficient? Correct Correct Needed? Correct Correct Yes/No Yes/No

5 (A.9)(C) /5 /5

5 (A.11)(A) /5 /5

TAKS BENCHMARK PRE-TESTS BENCHMARK POST-TESTS

Objective TEKS Number % Intervention Number % Proficient? Correct Correct Needed? Correct Correct Yes/No Yes/No

7 (8.7)(A) /5 /5

7 (8.7)(B) /5 /5

7 (8.7)(C) /4 /4

3 R D P R I N T

Copyright © by Holt, Rinehart and Winston. xxiv Holt Mathematics Grade 9All rights reserved.

Student Benchmark Test Profile

Student Name ______________________________________________________________________

TAKS BENCHMARK PRE-TESTS BENCHMARK POST-TESTS

Objective TEKS Number % Intervention Number % Proficient? Correct Correct Needed? Correct Correct Yes/No Yes/No

8 (8.8)(A) /5 /5

8 (8.8)(B) /5 /5

8 (8.8)(C) /5 /5

8 (8.9)(A) /5 /5

8 (8.9)(B) /5 /5

8 (8.10)(A) /5 /5

8 (8.10)(B) /5 /5

Proficiency Levels

Advanced Learners 90% to 100%

On-Level Learners 70% to 89%

Learners Having Difficulty below 70%

TAKS BENCHMARK PRE-TESTS BENCHMARK POST-TESTS

Objective TEKS Number % Intervention Number % Proficient? Correct Correct Needed? Correct Correct Yes/No Yes/No

9 (8.1)(B) /5 /5

9 (8.3)(B) /5 /5

9 (8.11)(A) /5 /5

9 (8.11)(B) /5 /5

9 (8.12)(A) /5 /5

9 (8.12)(C) /4 /4

9 (8.13)(B) /4 /4

TAKS BENCHMARK PRE-TESTS BENCHMARK POST-TESTS

Objective TEKS Number % Intervention Number % Proficient? Correct Correct Needed? Correct Correct Yes/No Yes/No

10 (8.14)(A) /5 /5

10 (8.14)(B) /5 /5

10 (8.14)(C) /5 /5

10 (8.15)(A) /5 /5

10 (8.16)(A) /5 /5

10 (8.16)(B) /5 /5

3 R D P R I N T

Copyright © by Holt, Rinehart and Winston. xxv Holt Mathematics Grade 9All rights reserved.

Cla

ss Be

nc

hm

ark

Test P

rofile

Class _____________________________________________________________________________

Stu

de

nt N

am

e

Pro

ficiency L

evels

Advanced Learners

90%

to 100%

On-Level Learners

70%

to 89%

Learners Having D

ifficulty

below 70%

Ben

chm

ark P

re-Test%

C

orrect

Interven

tion

N

eeded

?

Yes/No

Ben

chm

ark P

ost-Test

%

Co

rrectP

roficien

t? Yes/

No

3 R D P R I N T

Copyright © by Holt, Rinehart and Winston. xxvi Holt Mathematics Grade 9All rights reserved.

Ready for TAKS? Benchmark TestsAnswer Sheet

Student Name _______________________________________________________________________

Benchmark Pre-Test _____________________ Benchmark Post-Test ________________________

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Student Name _______________________________________________________________________

Benchmark Pre-Test _____________________ Benchmark Post-Test ________________________

1.

2.

3.

4.

5.

6.

7.

8.

9.

10. F G H J

A B C D

F G H J

A B C D

F G H J

A B C D

F G H J

A B C D

F G H J

A B C D

F G H J

A B C D

F G H J

A B C D

F G H J

A B C D

F G H J

A B C D

F G H J

A B C D

3 R D P R I N T

Copyright © by Holt, Rinehart and Winston. 1 Holt Mathematics Grade 9All rights reserved.

Name Date Class

Ready for TAKS?Benchmark Pre-Test (A.1)(A)1

OBJECTIVE

1. A relation exists between a sandwich shop’s profit and the number of sandwiches it sells. In this relation, what is the dependent variable?

A the shop’s profit

B the price of each sandwich

C the number of sandwiches sold

D the number of days the shop is open

2. The relation between the number of hours a student works, h, and the amount of money the student earns, m, is given by the function m � 8.50h. In this relation, what is the dependent variable?

F the hourly pay rate, $8.50

G the number of hours worked, h

H the number of days worked, d

J the amount of money earned, m

3. The table shows a relation between two variables, a and b. Which statement is the best description of the relationship between a and b?

a b

1 10

2 3

3 4

4 7

5 2

6 5

7 1

A As a increases, b increases.

B As a increases, b decreases.

C It does not appear that b is dependent on a.

D There is a linear relationship between a and b.

4. Which of the following relations is least likely to have an independent variable and a dependent variable?

F length of a side, area of a rectangle

G time spent studying for a test, grade on the test

H weight of a book, number of pages in the book

J number of square feet in a room, price per square foot of carpet

5. The graph shows a function in which y is the dependent variable. Which statement is the best description of the relation between x and y ?

y

x

20

18

16

14

12

10

8

6

4

2

–2

–2 2 4 6 8 10 12 14 16 18 20

A As x increases, y increases.

B As x increases, y decreases.

C As x increases, y increases at a constant rate.

D As x increases, y decreases at a constant rate.

AGA07_RTAKS09_001-005.indd 1AGA07_RTAKS09_001-005.indd 1 4/13/06 10:40:32 PM4/13/06 10:40:32 PM

3 R D P R I N T

Copyright © by Holt, Rinehart and Winston. 2 Holt Mathematics Grade 9All rights reserved.

Name Date Class

1OBJECTIVE

1. A high school is purchasing academic letters for their honor roll students. They were quoted the following prices for the letters.

Academic Letter Pricing

Number of letters, n

Total cost, c ($)

10 40

15 55

20 70

25 85

Which function represents the relationship between the total cost, c, and the number of academic letters, n?

A c � n � 15

B c � 3n � 10

C c � 4n

D c � 3n

2. The graph shows the relationship between two variables, t and h. Which function represents this relationship?

h

t

20

18

16

14

12

10

8

6

4

2

–2

–2 2 4 6 8 10 12 14 16 18 20

F h � 2t H h � t � 3

G h � 2t � 3 J h � 2 __ t � 3

3. Which function could be used to describe the data set shown?

{(�3, 0), (�1, 2), (1, 4), (3, 6)}

A y � x � 2

B y � x � 3

C y � x � 3

D y � 3x

4. Which function represents the data set shown?

Domain

�3

0

�2

2

Range

9

0

4

F y � �3x

G y � x � 6

H y � x 2

J y � � x 2

5. The total cost, c, paid for m miles driven in a rental car per day is shown in the table. Which function represents the relationship between the total amount paid and the number of miles driven?

Miles driven, m

Total cost, c ($)

25 25.00

35 29.00

45 33.00

55 37.00

A c � m

B c � m � 4

C c � 0.4m � 15

D c � 1.4m � 15

Ready for TAKS?Benchmark Pre-Test (A.1)(B)

AGA07_RTAKS09_001-005.indd 2AGA07_RTAKS09_001-005.indd 2 4/13/06 10:40:33 PM4/13/06 10:40:33 PM

3 R D P R I N T

Copyright © by Holt, Rinehart and Winston. 3 Holt Mathematics Grade 9All rights reserved.

Name Date Class

1OBJECTIVE

1. Mario opened a savings account with $50 that he received for his birthday. Each week, he deposits $5 of his allowance into the account. The table shows the balance in the account, b, after w weeks have passed since opening the account. Which equation best describes the balance?

Savings Account Balance

Number of weeks, w

Balance, b

1 $55

2 $60

3 $65

4 $70

A b � 50 � 5 � w

B b � 50 � 5w

C b � 50(5w)

D b � (50 � 5)w

2. A tee-shirt company charges $8.00 for a plain tee-shirt. If the customer wants to add iron-on decals to the shirt, the additional cost is $2.50 per decal. If the customer also wants words, the cost is $0.15 per letter. Which equation best expresses the total cost of the tee-shirt, c, in terms of the number of decals, d, and the number of letters, n?

F c � 2.50d � 0.15n

G c � 8.00 � 2.50n � 0.15d

H c � 8.00 � 2.50d � 0.15n

J c � 8(2.50d � 0.15n)

3. An interior decorating company is adding a chair rail to a room for a customer. The room is twice as long as it is wide. If the width of the room is w feet, and the chair rail costs $4 per foot, which equation describes the price, p, for adding the chair rail to the room?

A p � 6w

B p � 4(2 w 2 )

C p � 4(3w )

D p � 4(6w )

4. A furniture store charges a $150 fee to deliver a piece of furniture weighing up to 200 pounds. The store charges $2 extra for each additional pound over 200. Which equation best expresses the total delivery fee, f, in terms of the number of pounds, p?

F f � 150 � 2(p � 200)

G f � 150 � p � 200

_______ 2

H f � 150 � (p � 200)

J f � 150 � 2p

5. Mary has $20 to spend on art supplies. Art pencils cost $1.50 per pencil, including tax, and drawing pads cost $3.50 per pad, including tax. Which inequality best expresses the number of pencils, p, and drawing pads, d, that Mary is able to buy?

A p � d � 20

B p � d � 20

C 1.5p � 3.5d � 20

D 1.5p � 3.5d � 20

Ready for TAKS?Benchmark Pre-Test (A.1)(C)

AGA07_RTAKS09_001-005.indd 3AGA07_RTAKS09_001-005.indd 3 4/13/06 10:40:33 PM4/13/06 10:40:33 PM

3 R D P R I N T

Copyright © by Holt, Rinehart and Winston. 4 Holt Mathematics Grade 9All rights reserved.

Name Date Class

1OBJECTIVE

1. The function f (x) � {(�1, �2), (0, 0), (1, 2), (2, 4)} can be represented in a variety of different ways. Which of the following is NOT an accurate representation of f (x )?

A y � 2x with domain of {�1, 0, 1, 2}

B x � y __

2 with range of {�2, 0, 2, 4}

C y

x

6

4

2

–4

–6

–2–4–6 2 4 6

D Domain

�2

0

2

4

Range

�1

0

1

2

2. Which of the following does NOT represent a function?

F {(�2, 4), (�1, 1), (0, 0), (1, 1)}

G x �1 0 2 1

y 5 4 10 5

H 123

01

J y

x

6

4

2

–4

–6

–2–4–6 2 4 6

3. Which of the following equations does NOT represent a function?

A y � x � 1

B y � x 2 � 1

C x � y 2 � 1

D x � 2y � 1

4. Identify the graph that best represents the relationship between the number of hours a person works at $8.50 per hour and the person’s total pay.

F H

G J

5. A function is defined as follows: x is an integer between, but not including �5 and 0, and y is always 3 more than x. Which of the following is a correct representation of the function?

A y � x � 3 for �5 � x � 0

B f (x ) � {(�4, �1), (�3, 0), (�2, 1), (�1, 2)}

C x �1 0 1 2

y �4 �3 �2 �1

D y

x

6

4

2

–2

–6

–2–4–6 2 4 6

Ready for TAKS?Benchmark Pre-Test (A.1)(D)

AGA07_RTAKS09_001-005.indd 4AGA07_RTAKS09_001-005.indd 4 4/13/06 10:40:33 PM4/13/06 10:40:33 PM

3 R D P R I N T

Copyright © by Holt, Rinehart and Winston. 5 Holt Mathematics Grade 9All rights reserved.

Name Date Class

1OBJECTIVE

1. The table shows the approximate number of gallons of water used when doing laundry. Based on this data, what is the maximum number of whole loads of laundry a person is able to do and use less than 100 gallons of water?

Water Used per Load

Loads Gallons

1 40

2 80

3 120

4 140

A 1

B 2

C 3

D 4

2. The graph shows the total amount charged by an electrician who typically installs all the electrical outlets in a new home. If the materials for the job cost $52, what is the hourly rate charged by the electrician?

c

h

400

300

200

100

1 2 3 4 5 6 7 8 9

F $50 per hr

G $52 per hr

H $100 per hr

J $102 per hr

3. Which is always a correct conclusion about the quantities in the function y � x 2 , if x is an integer?

A As x increases, y increases.

B As x increases, y decreases.

C The variable y is always greater than or equal to the variable x.

D The variable y is always less than the variable x.

4. A pool cleaning service charges customers according to the formula c � 25 � 15h, where h represents the number of hours worked. The company supplies all the necessary chemicals to keep the water in the pool appropriately chlorinated. In the formula, 25 most likely represents

F the company’s hourly rate

G the number of hours it takes to clean an average-sized pool

H the cost of the chemicals

J the number of miles to the customer’s home

5. The Flyer, a local advertising mailer, sells “For Sale” ads according to the function c � 5 � 0.20(n � 10), where c represents the total charge for the ad and n represents the number of words in the ad. Which is the best interpretation of this function?

A The charge is $5.20 per word.

B The charge is $5 plus 20¢ per word.

C The charge is 20¢ plus $5 per word.

D The charge is $5 for the first 10 words plus 20¢ per word after 10.

Ready for TAKS?Benchmark Pre-Test (A.1)(E)

AGA07_RTAKS09_001-005.indd 5AGA07_RTAKS09_001-005.indd 5 4/13/06 10:40:34 PM4/13/06 10:40:34 PM

3 R D P R I N T

1. Which of the functions is NOT linear?

A 2y � 3 � x

B y � � 1 __ 2 x � 2

C y � 1 __ x � 3

D y � 2(x � 3) � 5

2. Which is the best representation of the function y � 2x ?

F

2

x

y

G

2 x

y

H

2x

y

J

2x

y

3. The graph of which function would pass through the points (�2, 12) and (2, 12)?

A y � �6x

B y � 6x

C y � 3 x 2

D y � 6 x 2

4. Which statement best describes the graph of y � � x 2 ?

F a line with a slope of �1

G a parabola whose vertex is at (0, �1)

H an upside-down parabola whose vertex is at (0, �1)

J an upside-down parabola whose vertex is at (0, 0)

5. The data in which table can be modeled using a linear function?

A x �2 0 1 2

y �3 3 6 9

B x �5 �2 0 3

y �1 2 3 7

C x 0 1 2 3

y �2 2 5 8

D x �1 0 1 2

y 1 0 1 4

Copyright © by Holt, Rinehart and Winston. 6 Holt Mathematics Grade 9All rights reserved.

Name Date Class

Ready for TAKS?Benchmark Pre-Test (A.2)(A)2

OBJECTIVE

AGA07_RTAKS09_006-014.indd 6AGA07_RTAKS09_006-014.indd 6 4/13/06 11:06:31 PM4/13/06 11:06:31 PM

3 R D P R I N T

Name Date Class

Copyright © by Holt, Rinehart and Winston. 7 Holt Mathematics Grade 9All rights reserved.

1. The pep club is raising money by washing cars. The function f (x ) � 5x describes the amount of money, in dollars, that the pep club will earn for washing x cars. What is the domain of the function?

A all real numbers

B all integers

C {0, 1, 2, 3, … }

D x > 0

2. The sum of the measures of the interior angles of a polygon with n sides is given by the function f (n ) � 180(n � 2). What is the domain of f (n )?

F all real numbers

G all integers

H all integers n � 0

J all integers n � 2

3. The perimeter of the rectangle is given by the function P � 2(2x � 5).

x � 3

x � 2

What is the most complete and reasonable domain for this function?

A x < 6

B x > 3

C x > 2

D x > 0

4. What is the domain of the function graphed?

y

x

5

5

F x � 0

G 0 � x � 9

H {0, 1, 2, 3}

J {0, 1, 4, 10}

5. What is the range of the function graphed?

y

x

�5

5

A y � �2

B y � �2

C x � �2

D { ... �4, �3, �2}

Ready for TAKS?Benchmark Pre-Test (A.2)(B)2

OBJECTIVE

AGA07_TAKs_WBK09_006-014.indd 7AGA07_TAKs_WBK09_006-014.indd 7 9/6/06 8:16:49 PM9/6/06 8:16:49 PM

3 R D P R I N T

1. The graph shows the fare to take a cab ride for m miles. Which statement is true?

Cab

Far

e ($

) 2.50

2.00

1.50

1.00

1 32 54Number of Miles

A The fare is $1.50 per mile.

B The fare is $1.50 per person.

C The minimum fare is $1.50.

D The rate of increase in the fare is $1.50 per mile.

2. Mr. Jones is choosing between two plumbers to install a new kitchen sink. The graph shows the relationship between the total cost for each plumber based on the number of hours to complete the job.

2

6050403020

4 6 8 10Hours

Rat

e ($

)

A

B

According to the graph, which statement is NOT true?

F Plumber A would cost less as long as the job takes no longer than 6 hours.

G The two plumbers would cost the same if the job takes 6 hours.

H Plumber B would cost less if the job takes more than 6 hours.

J Plumber A charges more than Plumber B for a job that takes 3 hours.

3. The graph shows how the number of baseball cards in John’s collection changed over time. Which statement is true?

Nu

mb

er o

f C

ard

s 250

200

150

100

50

1 32 5 64Number of Months

A John had 25 cards when he started his collection.

B John had 50 cards at the end of 4 months.

C John acquired 25 cards each month.

D John acquired 50 cards each month.

4. The graph shows the height, in feet, of a football t seconds after it is thrown. Which statement is true?

Hei

gh

t (f

t)

30

18

6

1 2 3 4Seconds

F The ball hits the ground at 4 seconds.

G The ball’s minimum height is 6 feet.

H The ball’s maximum height is 6 feet.

J The ball’s height increases for a total of 4 seconds.

Copyright © by Holt, Rinehart and Winston. 8 Holt Mathematics Grade 9All rights reserved.

Name Date Class

Ready for TAKS?Benchmark Pre-Test (A.2)(C)2

OBJECTIVE

AGA07_RTAKS09_006-014.indd 8AGA07_RTAKS09_006-014.indd 8 4/13/06 11:06:32 PM4/13/06 11:06:32 PM

3 R D P R I N T

Name Date Class

Copyright © by Holt, Rinehart and Winston. 9 Holt Mathematics Grade 9All rights reserved.

1. The graph shows the value of a certain stock during a period of several months. Which is a reasonable statement about the value of the stock during this time period?

Pri

ce P

er S

har

e ($

)

30

20

10

1 32 5 64Number of Months

A The stock lost value for the first three months.

B The stock experienced its most rapid increase in price between months 1 and 2.

C The stock only lost value between months 4 and 6.

D The value of the stock more than tripled in price by month 3.

2. The table shows the retail price of recliners based on the wholesale price.

Wholesale ($) Retail ($)

200 300

250 400

300 500

350 600

Use the data to predict the retail price of a recliner with a wholesale price of $500.

F $600 H $800

G $700 J $900

Use the scatter plot to answer questions 3�5.

Ask

ing

pri

ce in

tho

usa

nd

s ($

)

Age (years)

30

20

10

1 2 3 4 5 6 7 8

The scatter plot shows the asking price for a certain model of car based on the age of the car. The line of best fit for the data is also shown.

3. Predict the approximate asking price of a 7-year old car of the same model.

A $5,000 C $15,000

B $10,000 D $25,000

4. Which statement best describes the relationship between the asking price and the age of the car?

F As the age of the car increases, the asking price increases.

G As the age of the car increases, the asking price decreases.

H The age of the car does not affect the asking price.

J The asking price consistently decreased by $10,000 per year.

5. If the line of best fit is fairly accurate, even for a new car, what is the approximate value of a new car of this model?

A $10,000

B $20,000

C $25,000

D Cannot be determined.

Ready for TAKS?Benchmark Pre-Test (A.2)(D)2

OBJECTIVE

AGA07_TAKs_WBK09_006-014.indd 9AGA07_TAKs_WBK09_006-014.indd 9 9/6/06 8:16:50 PM9/6/06 8:16:50 PM

3 R D P R I N T

1. Which expression represents the change from a $20 bill when you purchase an item that costs d dollars?

A 20 � d

B 20 � d

C 20d

D 20 d

2. Mary has $220 in her purse. If she buys 4 items that each cost d dollars, which expression represents the new balance in Mary’s purse?

F 4d

G 220 � 4d

H 220 � 4d

J 220(4d )

3. The table shows the cost of buying DVDs at Movie Mania.

Number of DVDs

Total Cost ($)

1 15

2 30

3 45

4 60

Which equation represents the total cost, c, if a customer purchases n DVDs?

A c � 15

B c � 15 � n

C c � 15n

D c � 15 n

4. A typist began a big project with 420 pages of a novel to type. If she typed 18 pages per hour, which equation shows the number of pages, p, remaining after h hours?

F p � 420 � 18 � h

G p � 420 � 18h

H p � 420 � 18h

J p � 420 ____ 18h

5. A chemistry class is monitoring the temperature of a liquid. The initial temperature of the liquid is 72°F. The table shows the change in the temperature over time as the liquid is heated.

Number of minutes

Temperature (°F)

0 72

1 74

2 76

3 78

4 80

Which equation represents the temperature, t, after m minutes have passed?

A t � m � 2

B t � 2m

C t � 72 � m � 2

D t � 72 � 2m

Copyright © by Holt, Rinehart and Winston. 10 Holt Mathematics Grade 9All rights reserved.

Name Date Class

Ready for TAKS?Benchmark Pre-Test (A.3)(A)2

OBJECTIVE

AGA07_RTAKS09_006-014.indd 10AGA07_RTAKS09_006-014.indd 10 4/13/06 11:06:33 PM4/13/06 11:06:33 PM

3 R D P R I N T

Name Date Class

Copyright © by Holt, Rinehart and Winston. 11 Holt Mathematics Grade 9All rights reserved.

1. According to the pattern shown, if n is the number of sides that a polygon has, which expression represents the number of triangular regions that can be formed inside that polygon?

A n C n � 1

B n � 1 D n � 2

2. A small flight of stairs is constructed by stacking cement blocks. The pattern shows the number of blocks needed depending on how many steps are to be built.

Which statement accurately describes this pattern?

F The number of blocks needed is equal to the square of the number of steps.

G The number of blocks needed is 2 more than the number of the step.

H Except for the first step, the number of blocks needed is the number of the step minus one times 3.

J The increase in the number of blocks needed from one step to the next is equal to the number of the step.

3. The length of a rectangle is x � 5, and its width is x � 2. Which expression represents the area of the rectangle?

A 4x � 6 C x 2 � 3x � 10

B x 2 � 3x � 10 D x 2 � 10

4. A rectangle with an area of 4 x 2 � 14x � 6 is modeled below using algebra tiles.

Which expression gives the correct factorization for 4 x 2 � 14x � 6?

F (4x � 2)(x � 3)

G (4x � 3)(x � 2)

H (4x � 6)(x � 1)

J (2x � 2)(2x � 3)

5. The table shows the coordinates of several pairs of points.

x y

0 5

3 15

6 45

9 135

Which statement describes a pattern in the table?

A The y-value is 5 times the x-value.

B for every increase of 3 in the x-values, the y-value increases by 15.

C for every increase of 3 in the x-values, the y-value triples.

D The y-value is 3 raised to the x power.

Ready for TAKS?Benchmark Pre-Test (A.3)(B)2

OBJECTIVE

AGA07_RTAKS09_006-014.indd 11AGA07_RTAKS09_006-014.indd 11 2/27/07 9:57:41 AM2/27/07 9:57:41 AM

3 R D P R I N T

1. If f (x ) � x 2 � 4x � 5, what is f (�3)?

A 16

B 1

C �2

D �8

2. What is the missing value in the function table?

x f (x ) � 2 � 4x

�2 10

0 2

1 �2

? �14

F �4

G 2

H 3

J 4

3. What expression represents the perimeter of the equilateral triangle?

3x � 2

A (3x � 2 ) 3

B 9x � 2

C 3x � 6

D 9x � 6

4. What is the value of x in the equation 7x � 3 � �2x � 42?

F 39 ___ 9

G 5

H 9

J 36

5. Which equation shows the slope-intercept form of the linear equation 4x � 2y � 6?

A y � 2x � 6

B y � 2x � 3

C y � 2x � 3

D y � �2x � 3

6. The rectangle has an area of x 2 � 6x � 16.

x � 8

Which expression represents the width of the rectangle?

F x � 2

G x � 2

H x � 8

J x � 24

Copyright © by Holt, Rinehart and Winston. 12 Holt Mathematics Grade 9All rights reserved.

Name Date Class

Ready for TAKS?Benchmark Pre-Test (A.4)(A)2

OBJECTIVE

AGA07_RTAKS09_006-014.indd 12AGA07_RTAKS09_006-014.indd 12 4/13/06 11:06:33 PM4/13/06 11:06:33 PM

3 R D P R I N T

Name Date Class

Copyright © by Holt, Rinehart and Winston. 13 Holt Mathematics Grade 9All rights reserved.

1. Which real number property is illustrated by the equation 4x (3x � 7) � 12 x 2 � 28x ?

A Commutative Property of Addition

B Associative Property of Addition

C Distributive Property

D Multiplicative Identity Property of 1

2. Which real number property is illustrated by the equation (3 � 5x ) � 4x � 3 � (5x � 4x )?

F Commutative Property of Addition

G Associative Property of Addition

H Distributive Property

J Additive Identity Property of 0

3. Which expression is equivalent to 15 m 2 � 6( m 2 � 2m)?

A 9 m 2 � 2m

B 9 m 2 � 12m

C 9 m 2 � 12m

D 9 � 12m

4. Which expression is equivalent to 6 x 2 � 4x � 3 � 8x � 11 x 2 � 8?

F �5 x 2 � 12x � 5

G �5 x 2 � 12x � 11

H �5 x 2 � 12x � 5

J �5 x 4 � 12 x 2 � 11

5. What is the perimeter of the pentagon?

x

3x � 1

2x � 1

3x � 7

2x � 5

A 11x � 12

B 10x � 12

C 11 x 5 � 12

D 5(11x � 12)

6. The table shows the factored form and the simplified form for several products.

Factored form Simplified form

(x � 2)(x � 2) x 2 � 4

(x � 2)(x � 3) x 2 � x � 6

(x � 2 ) 2 x 2 � 4

(2x � 1)(2x � 1) 4x 2 � 1

Which product is NOT correctly simplified?

F (x � 2)(x � 2)

G (x � 2)(x � 3)

H (x � 2 ) 2

J (2x � 1)(2x � 1)

Ready for TAKS?Benchmark Pre-Test (A.4)(B)2

OBJECTIVE

AGA07_TAKs_WBK09_006-014.indd 13AGA07_TAKs_WBK09_006-014.indd 13 9/6/06 8:16:51 PM9/6/06 8:16:51 PM

3 R D P R I N T

1. Which function notation would represent the same relationship as the linear equation y � 3x � 2?

A f (x ) � x � 2 _____ 3

B f (x ) � 3x � 2

C 3f (x ) � x � 2

D f (x ) � 3(x � 2)

2. Which linear equation would represent the same relationship as the function f (x ) � �(x � 5)?

F y � 1 _____ x � 5

G y � x � 5

H y � x � 5

J y � �(x � 5)

3. The table shows several values generated by the function f (x ) � x 2 � 3.

x f (x )

�1 4

0 3

1 4

2 7

Which equation represents the same relationship?

A y � ��

x � 3

B y � (x � 3 ) 2

C y � x 2 � 3

D y 2 � x � 3

4. The line graphed is given by the

equation y � 1 __ 2

x � 1.

6

4

2

�2

�4

�6

�2�4�6 2 4 6 x

y

Which function would have the same graph?

F f (x ) � 1 __ 2

x � 1 G f (x ) � 2x � 1

H f (x ) � x � 1 __ 2

J f (x ) � 2(x � 1)

5. A chemistry class monitored the temperature of a substance being heated. The initial temperature of the liquid was 72°F and the temperature increased by 2 degrees every minute. The results can be represented by the function f (m ) � 72 � 2m, where m is the number of minutes that have passed. Which equation represents the temperature, t, after m minutes have passed?

A t � m � 2

B t � 2m

C t � 72 � m � 2

D t � 72 � 2m

Copyright © by Holt, Rinehart and Winston. 14 Holt Mathematics Grade 9All rights reserved.

Name Date Class

Ready for TAKS?Benchmark Pre-Test (A.4)(C)2

OBJECTIVE

AGA07_RTAKS09_006-014.indd 14AGA07_RTAKS09_006-014.indd 14 4/13/06 11:06:34 PM4/13/06 11:06:34 PM

3 R D P R I N T

Copyright © by Holt, Rinehart and Winston. 15 Holt Mathematics Grade 9All rights reserved.

Name Date Class

1. Which situation can best be described by a linear function?

A the total fee, f, for a painter who charges by the hour and the number of hours, h, that the painter worked

B the height of a pebble that is projected upward from ground level with an initial velocity of 45 ft/s

C the distance traveled by a person who walks quickly for 35 minutes then rests for 5 minutes before continuing on her walk for another 8 minutes

D the temperature in an oven as it is turned on and heated to 350° F and then kept at 400° F for 20 minutes

2. Which table below could represent a linear function?

F x 0 2 4 6

y �3 9 13 17

G x �2 2 5 9

y 4 4 4 4

H x 0 1 2 3

y 0 �2 2 �3

J x �2 4 9 16

y 1 2 3 4

3. Which of the following situations could be represented by the linear function shown?

y

x

(1, 3)

(2, 6)

8

7

6

5

4

3

2

1

1 2 3 4 5 6 7 8

A The area of a circle can be approximated using the formula A � 3r 2.

B Each month a company’s profits is $3 million greater than profits the previous year.

C The population of a certain kind of owl is decreasing at a rate of 3 thousand owls per year.

D The number of bacteria in a culture increases each day by three times the amount of the previous day’s increase.

4. Which linear function below includes the points (1, 2) and (�2, 5)?

F y � x 2 � 1

G y � 2x

H y � �x � 3

J y � x � 1

Ready for TAKS?Benchmark Pre-Test (A.5)(A)3

OBJECTIVE

AGA07_RTAKS09_015-023.indd 15AGA07_RTAKS09_015-023.indd 15 4/13/06 11:07:04 PM4/13/06 11:07:04 PM

3 R D P R I N T

1. What is the equation of the line shown?

6

4

2

�2

�4

�6

�2�4�6 2 4 6 x

y

A y � � 1 __ 3 x � 6 C y � 1 __

3 x � 6

B y � �3x � 6 D y � 3x � 6

2. The table shows several points that lie on a given line. Which of the following could be the equation of the line?

x �2 0 3

y 4 0 �6

F y � 2x G x � y � 0

H y � x � 6 J y � �2x

3. Which linear equation is equivalent to

the equation y � � 1 __ 2 x � 6?

A x � 2y � 6 � 0

B x � 2y � 12 � 0

C x � 2y � 12 � 0

D x � 2y � 12 � 0

4. Which linear equation represents the statement “the value of y is 3 less than twice the value of x”?

F y � 2x � 3

G y � 3 � 2x

H 2y � 3 � x

J 2y � x � 3

5. Which of the following is the graph of the equation 2x � y � 4?

A 5

3

1

�1

�3

�5

531�1�3�5 x

y

B 5

3

1

�1

�3

�5

531�1�3�5 x

y

C 5

3

1

�1

�3

�5

5 x

y

31�1�3�5

D 5

3

1

�1

�3

�5

531�1�3�5 x

y

Copyright © by Holt, Rinehart and Winston. 16 Holt Mathematics Grade 9All rights reserved.

Name Date Class

Ready for TAKS?Benchmark Pre-Test (A.5)(C)3

OBJECTIVE

AGA07_RTAKS09_015-023.indd 16AGA07_RTAKS09_015-023.indd 16 4/13/06 11:07:04 PM4/13/06 11:07:04 PM

3 R D P R I N T

Name Date Class

Copyright © by Holt, Rinehart and Winston. 17 Holt Mathematics Grade 9All rights reserved.

1. What is the slope of the line whose equation is 2y � �3x � 8?

A �3

B � 3 __ 2

C � 2 __ 3

D 4

2. What is the slope of the line whose equation is 3y � x � 4x � 6?

F 1

G 5 __ 3

H �2

J 3

3. What is the slope of the line whose graph is shown?

6

4

2

�2

�4

�6

�2�4�6 2 4 6 x

y

A �2 C 1 __ 2

B � 1 __ 2 D 2

4. Which graph shows a line with slope of �2?

F 5

3

1

�1

�3

�5

531�1�3�5 x

y

G 5

3

1

�1

�3

�5

531�1�3�5 x

y

H 5

3

1

�1

�3

�5

531�1�3�5 x

y

J 5

3

1

�1

�3

�5

531�1�3�5 x

y

5. Line a passes through each of the points in the table. What is the slope of line a ?

x �1 0 1

y 4 4 4

A 4 C 0

B �4 D undefined

Ready for TAKS?Benchmark Pre-Test (A.6)(A)3

OBJECTIVE

AGA07_TAKs_WBK09_015-023.indd 17AGA07_TAKs_WBK09_015-023.indd 17 9/6/06 8:17:07 PM9/6/06 8:17:07 PM

3 R D P R I N T

1. According to the graph, which statement best describes the relationship between x and y?

x

y

A As x increases, y remains constant.

B As y increases, x remains constant.

C As x increases, y increases.

D As x increases, y decreases.

2. The slopes of two equations are given. Which pair represents the slopes of parallel lines?

F 2; �2 H 2; 2

G 2; 1 __ 2 J 2; � 1 __

2

3. Which graph could represent a company’s profits over a year’s time if profits increased for a few months, then remained constant for a few months, then increased again?

A C

B D

4. Bob agreed to cut 24 lawns during 4 weeks in April. The graph shows how many lawns he had left to cut at the end of each week over the 4-week time period.

Week

Nu

mb

er

of

Law

ns

Lef

t to

Cu

t

3 421

24

Which statement is the best interpretation of the x-intercept?

F Bob finished cutting all the lawns by the end of the third week.

G Bob had 3 lawns left to cut at the end of the 4 weeks.

H It took Bob 3 months to cut all the lawns.

J Bob cut 3 lawns per week.

5. The graph shows how the number of figurines in Margaret’s collection changed in 2005.

Nu

mb

er o

fF

igu

rin

es

15

Months

Which statement is the best interpretation of the y-intercept?

A Mary had the most figurines at the end of 15 months.

B Mary acquired 15 new figurines each month.

C Mary had 15 figurines at the beginning of 2005.

D The most figurines Mary ever had was 15.

Copyright © by Holt, Rinehart and Winston. 18 Holt Mathematics Grade 9All rights reserved.

Name Date Class

Ready for TAKS?Benchmark Pre-Test (A.6)(B)3

OBJECTIVE

AGA07_RTAKS09_015-023.indd 18AGA07_RTAKS09_015-023.indd 18 4/13/06 11:07:05 PM4/13/06 11:07:05 PM

3 R D P R I N T

Name Date Class

Copyright © by Holt, Rinehart and Winston. 19 Holt Mathematics Grade 9All rights reserved.

1. The graphs of line n and line m are shown.

x

y6

4

2

–2

–4

–6

–6 –4 –2 2 4 6

Line n

x

y12

8

4

–4

–8

–12

–12 –8 –4 4 8 12

Line m

How does the graph of line n compare to the graph of line m ?

A The slope of n is less, but n ’s y-intercept is greater.

B The slope of n is less, and n ’s y-intercept is less.

C The slope of n is greater, and n ’s y-intercept is greater.

D The slope of n is greater, but n ’s y-intercept is less.

2. The graph of the function f (x ) � 2x � 5 is shown.

6

4

2

�2

�4

�6

�2�4�6 2 4 6 x

y

If the graph of f (x ) is shifted up 5 units, what would be the equation of the new function?

F f �(x ) � 2x H f �(x ) � 7x � 5

G f �(x ) � 2x � 10 J f �(x ) � 10x � 5

3. Line a is represented by the equation y � 2x � 5, and line b is represented by the equation y � 2x � 5. Which statement describes how line b is related to line a ?

A Line b is a reflection of line a across the x-axis.

B Line b is a reflection of line a across the y-axis.

C Line b is a translation of line a 10 units to the left.

D Line b is a translation of line a 10 units down.

4. Line a is represented by equation y � �2x � 3. Line b has the same slope as line a, but has a y-intercept of 1. Which statement below describes how line b is related to line a ?

F Line b is a translation of line a 2 units up.

G Line b is a translation of line a2 units down.

H Line b is a reflection of line a across the x-axis.

J Line b is a reflection of line a across the y-axis.

5. A line has the equation y � �2x � 3. If the slope of the line is tripled and 2 is subtracted from the y-intercept, which equation represents the new line?

A y � 3x � 2

B y � �4x � 9

C y � �6x � 1

D 3y � �2x � 1

Ready for TAKS?Benchmark Pre-Test (A.6)(C)3

OBJECTIVE

AGA07_RTAKS09_015-023.indd 19AGA07_RTAKS09_015-023.indd 19 4/13/06 11:07:05 PM4/13/06 11:07:05 PM

3 R D P R I N T

1. Which equation describes a line that passes through the point (–1, 3) and has a slope of –2?

A y = – 1 __ 2 x + 1

B y = –2x + 1

C y = –2x + 4

D y = –2x – 5

2. Which equation describes a line with a slope of 4 and a y-intercept of –3?

F 4x + y = –3

G 4x – y = –3

H 4x – y = 3

J 4x + y = 3

3. Which equation describes a line with ay-intercept of –5 and an x-intercept of 5?

A y – x = 5

B x – y = 5

C 5x – 5y = 0

D 5y – 5x = 1

4. Which equation describes the line whose graph is shown?

6

4

2

�2

�4

�6

�2�4�6 2 4 6 x

y

F y = 1 __ 2

x + 3 H y = 3 __ 2

x + 3

G y = x + 3 J y = 2x + 3

5. Which could NOT be the equation of the line whose graph is shown?

x

y

A y = 4 __ 5

x – 4

B y = x – 3.5

C x + y – 3 = 0

D x – y – 3 = 0

Copyright © by Holt, Rinehart and Winston. 20 Holt Mathematics Grade 9All rights reserved.

Name Date Class

Ready for TAKS?Benchmark Pre-Test (A.6)(D)3

OBJECTIVE

AGA07_RTAKS09_015-023.indd 20AGA07_RTAKS09_015-023.indd 20 4/13/06 11:07:06 PM4/13/06 11:07:06 PM

3 R D P R I N T

Name Date Class

Copyright © by Holt, Rinehart and Winston. 21 Holt Mathematics Grade 9All rights reserved.

1. If the line 4x � 3y � �12 were graphed, what would be the y-intercept?

A –4

B –3

C 0

D 4

2. If the line y � 2 __ 3 x � 8 were graphed,

what would be the x-intercept?

F �12

G 0

H 8

J 12

3. What is the x-intercept of the line graphed?

6

4

2

�2

�4

�6

�2�4�6 2 4 6 x

y

A 4

B –4

C 6

D 3 __ 2

4. The table below shows several points that lie on a line. What would be the coordinates of the y-intercept of this line?

x y

–4 5

–3 4

–2 3

F (1, 0)

G (0, 1)

H (0, 2)

J (2, 0)

5. A refrigerator company is testing a new refrigerator. The temperature inside the refrigerator, in degrees Fahrenheit, is recorded every hour, from the time the refrigerator is turned on. The table shows that the temperature decreases according to a linear relationship.

Time (h)

Temperature (°F)

0 72

1 60

2 48

3 36

Let x represent the time in hours and y represent the temperature in degree Fahrenheit. If the pattern continues and the linear relationship is graphed, what would be the x-intercept of the line?

A 4

B 5

C 6

D 7

Ready for TAKS?Benchmark Pre-Test (A.6)(E)3

OBJECTIVE

AGA07_RTAKS09_015-023.indd 21AGA07_RTAKS09_015-023.indd 21 4/13/06 11:07:06 PM4/13/06 11:07:06 PM

3 R D P R I N T

1. The graph of a line is shown below. If the slope is doubled and the y-intercept remains the same, which equation represents the new line?

12

8

4

�4

�8

�12

�4�8�12 4 8 12

y

x

A y � 1 __ 2 x � 12 C y � 2x � 6

B y � x � 6 D 2y � 1 __ 2 x � 6

2. Two start-up companies’ profits over a 6-month period of time are represented by the graphs. The units on the axes are the same.

Months

Pro

fits

Pro

fits

Months

Company A Company B

Which statement best describes the difference in the two companies’ profits?

F The two companies’ profits grew at the same rate since the slopes of the lines are the same.

G The two companies’ profits grew at the same rate since the y-intercepts of the lines are the same.

H Company A’s profits grew faster than company B’s since the slope of its line is greater.

J Company B’s profits grew faster than company A’s since the slope of its line is greater.

Use the information and the graph to answer questions 3–5.

A carpenter charges a flat fee of $40 plus an hourly rate to make a house call. The graph shows the total cost for a job based on the flat fee and the number of hours to complete the job.

21

(1, 65)

40

(2, 90)

Number of Hours

Co

st (

$)

3. If the carpenter changed his flat fee to $50, but kept his hourly rate the same, what would be the total charge for a job that took 2 hours?

A $75 C $100

B $90 D $140

4. If the carpenter left his flat fee at $40, but changed his hourly rate to $30, what would be the total charge for a job that took 2 hours?

F $70

G $90

H $100

J $130

5. If the carpenter changed his flat fee to $50 and changed his hourly rate to $30, what would be the total charge for a job that took 2 hours?

A $80 C $110

B $90 D $130

Copyright © by Holt, Rinehart and Winston. 22 Holt Mathematics Grade 9All rights reserved.

Name Date Class

Ready for TAKS?Benchmark Pre-Test (A.6)(F)3

OBJECTIVE

AGA07_RTAKS09_015-023.indd 22AGA07_RTAKS09_015-023.indd 22 4/13/06 11:07:06 PM4/13/06 11:07:06 PM

3 R D P R I N T

Name Date Class

Copyright © by Holt, Rinehart and Winston. 23 Holt Mathematics Grade 9All rights reserved.

1. A used car’s value decreases according to the age of the car. The table shows the value of the car depending on its age.

Age (yr) Value ($)

0 18,000

1 15,000

3 9,000

If the value of the car continues to decrease at the rate shown in the table, what will be the value of the car when it is 5 years old?

A $1,500 C $4,500

B $3,000 D $6,000

2. The force that must be applied to lift an object using a certain pulley system varies directly with the weight of the object. If a force of 0.75 pound is required to lift an object that weighs 30 pounds, how much force is required to lift an object that weighs 100 pounds?

F 25 lb

G 2.5 lb

H 0.25 lb

J 0.225 lb

3. Based on the given exchange rate for Mexican pesos on a certain day at the airport, Ms. Crawly purchased a 600-peso bottle of perfume for 50 US dollars. At this same rate, what would a 900-peso bottle of perfume cost in US dollars?

A $33 C $75

B $60 D $750

4. The U.S. bobsled team is practicing for the Winter Olympics. The coach recorded the following data during practice.

Time (s) Distance (m)

3.50 60

7.00 120

8.75 150

If the bobsled team continues to sled at the rate shown in the table, what is the approximate distance it will sled in 30 seconds?

F 400 m

G 450 m

H 514 m

J 600 m

5. The time it takes to hear thunder varies directly with a person’s distance from the lightning that precedes the thunder. The table shows the number of seconds between seeing lightning and hearing thunder for several times and distances.

Time (s) Distance (mi)

10 2

8 1.6

5 1

Based on the data in the table, how far is a person from lightning if it takes 7 seconds for him or her to hear the thunder?

A 1.2 mi

B 1.4 mi

C 14 mi

D 35 mi

Ready for TAKS?Benchmark Pre-Test (A.6)(G)3

OBJECTIVE

AGA07_RTAKS09_015-023.indd 23AGA07_RTAKS09_015-023.indd 23 4/13/06 11:07:07 PM4/13/06 11:07:07 PM

3 R D P R I N T

1. Mary Beth is exercising using a specific program in which the number of hours she runs each week, r, is 2 more than the number of hours she does aerobics, a. Which equation represents the relationship between the number of hours she runs each week and the number of hours she does aerobics?

A r � a � 2 B r � a � 2

C a � r � 2 D r � 2a

2. Jared has allotted a maximum of 60 minutes each day to work on exam practice sets. Each math question takes Jared approximately 3 minutes to complete. Each verbal question takes Jared approximately 2 minutes to complete. If m is the total number of math questions per set, and v is the total number of verbal questions per set, which of these best represents the time Jared can spend practicing a combination of math and verbal questions?

F m � v � 60

G 5(m � v) � 60

H 2m � 3v � 60

J 3m � 2v � 60

3. A toy rocket is launched from a platform that is 20 feet high. If the rocket rises at a constant rate of 15 feet per second for the first minute, which equation could be used to determine t, the time in seconds it will take the toy rocket to reach a height of 100 feet?

A 100 � 20 � 15t

B 100 � 15(t � 20)

C 100 � 20t � 15

D 100 � (20 � 15)t

4. Ms. Verde throws handfuls of bread crumbs to the ducks each day. The table shows the number of ducks that Ms. Verde saw compared to the number of handfuls of bread crumbs she threw.

Number of Ducks

Handfuls of Bread Crumbs

1 1

2 3

3 5

4 7

Which equation best describes the relationship between h, the number of handfuls of bread crumbs thrown, and d, the number of ducks seen?

F h � d H h � 2d � 1

G h � d � 1 J h � d � 1 _____ 2

� 1

5. The decoration committee for the spring dance has $250 to spend on streamers, flowers, and balloons. The table shows the price of each item.

Item Price

Streamers $2 per roll

Flowers $18 per vase

Balloons $3 per bag

Which inequality best describes the total numbers of rolls of streamers, s, vases of flowers, f, and bags of balloons, b, that can be purchased for $250 or less?

A s � f � b � 250

B sfb � 250

C 2s � 18f � 3b � 250

D 23(s � f � b) � 250

Copyright © by Holt, Rinehart and Winston. 24 Holt Mathematics Grade 9All rights reserved.

Name Date Class

Ready for TAKS?Benchmark Pre-Test (A.7)(A)4

OBJECTIVE

AGA07_RTAKS09_024-027.indd 24AGA07_RTAKS09_024-027.indd 24 4/13/06 11:19:46 PM4/13/06 11:19:46 PM

3 R D P R I N T

Name Date Class

Copyright © by Holt, Rinehart and Winston. 25 Holt Mathematics Grade 9All rights reserved.

1. A student is solving the equation 7 � x � 4x � x. Which of the following strategies would be the best way to start this problem?

A Divide both sides of the equation by 7.

B Divide both sides of the equation by 4.

C Subtract x from both sides of the equation.

D Add 7 to both sides of the equation.

2. What is the value of y if (5, y ) is a solution to the equation 4x � 3y � �10?

F �27

G �10

H 10 ___ 3

J 10

3. Each of the points on the line is a solution to the equation x � 2y � �2.

(2, y)(0, 1)

(–4, –1)

y

x

What is the missing value of y ?

A 1

B 1.5

C 2

D 2.5

4. The table shows several solutions to the equation 3x � 5y � 15.

x y

0 3

5 0

x �3

What is the missing value of x?

F 0

G 1

H 10

J 27

5. What is the the unknown number in the statement “the product of 5 and a number, decreased by 10, is 40?”

A 6

B 10

C 18

D 45

Ready for TAKS?Benchmark Pre-Test (A.7)(B)4

OBJECTIVE

AGA07_RTAKS09_024-027.indd 25AGA07_RTAKS09_024-027.indd 25 4/13/06 11:19:47 PM4/13/06 11:19:47 PM

3 R D P R I N T

1. The cost of renting a carpet cleaner at a certain store is described by the function f (x ) � 15x � 20 in which f (x ) is the cost and x is the time in days. If Mr. Hawthorne has $100 to spend, what is the maximum number of days that he can rent a carpet cleaner if tax is not considered?

A 4

B 5

C 6

D 7

2. The fund-raising committee at a local high school is trying to raise money for new band uniforms by holding a car wash each weekend in April and May. They decide to charge $15 per wash. If the committee wants to raise at least $2,500, what is the minimum number of cars it must wash?

F 100 cars

G 157 cars

H 167 cars

J 200 cars

3. Mark purchased x baseball cards at $3 each and y packs of gum at $1.50 each. He spent less than $20, not including tax. The number of items he purchased can be described by the linear inequality 3x � 1.5y < 20. If Mark purchased 4 baseball cards, what is the maximum number of packs of gums he could have purchased?

A 3

B 4

C 5

D 6

4. The graph of the linear inequality 4x � 3y � 12 is shown below.

12

8

4

�4

�8

�12

�4�8�12 4 8 12

y

x

Which point is in the solution set to the inequality 4x � 3y �12?

F (3, 1)

G (2, 3)

H (0, 5)

J (1, 2)

5. The graph of the linear equation

y � � 2 __ 3 x � 5 is shown below.

12

8

4

�4

�8

�12

�4�8�12 4 8 12

y

x

Which point is not in the solution set of

y � � 2 __ 3 x � 5?

A (1, 5) C (4, 2)

B (3, 2) D (9, �2)

Copyright © by Holt, Rinehart and Winston. 26 Holt Mathematics Grade 9All rights reserved.

Name Date Class

Ready for TAKS?Benchmark Pre-Test (A.7)(C)4

OBJECTIVE

AGA07_TAKs_WBK09_024-027.indd 26AGA07_TAKs_WBK09_024-027.indd 26 9/6/06 8:17:20 PM9/6/06 8:17:20 PM

3 R D P R I N T

Name Date Class

Copyright © by Holt, Rinehart and Winston. 27 Holt Mathematics Grade 9All rights reserved.

1. Kris has a total of 42 DVDs in two categories. The number of her action DVDs is 12 more than the number of her comedy DVDs. Which system of equations can be used to find the number of action DVDs, a, and the number of comedy DVDs, c, Kris has?

A a � c � 12 C a � c � 12a � c � 42 a � c � 42

B a � 12 � c D a � c � 12a � c � 42 a � c � 42

2. Mr. Smith picked up sandwiches and drinks for his crew at a sandwich shop. All together, he bought 24 items. He bought twice as many sandwiches as drinks. Which system of equations can be used to find the number of sandwiches, s, and the number of drinks, d, he bought?

F s � d � 24 H s � d � 24d � 2s s � 2d

G s � 24 � d J s � d � 24

s � 2d s � d __ 2

3. The length of a rectangle is 4 times the width. Which system of equations can be used to find the dimensions of the rectangle if the perimeter is 120 inches?

A 2� + 2w = 120� = 4w

B 2(� + 2w ) = 120w = 4�

C � + w = 120� = 4w

D 2w = 120 � 2�

� = 4 __ w

4. The diagram below shows two complementary angles. The measure of the larger angle, y, is 10° more than twice the measure of the smaller angle, x. Which system of equations can be used to find the measure of each angle?

y°x°

F x � y � 90 H x � y � 90y � 2x � 10 y � 10 � 2x

G x � y � 90 J x � 90 � yy � 10 � 2x x � 2y � 10

5. The table shows the number of hotdogs and drinks a hotdog stand sold on two consecutive days, along with the total sales for the day.

Day 1 Day 2

Hotdogs 24 20

Drinks 10 12

Total Sales $43.50 $39.00

If the price of a hotdog is represented by h and the price of a drink is represented by d, which system of equations can be used to determine h and d ?

A h � d � 3424h � 10d � 43.50

B h � d � 3220h � 12d � 39.00

C h � d � 34h � d � 82.50

D 24h � 10d � 43.5020h � 12d � 39.00

Ready for TAKS?Benchmark Pre-Test (A.8)(A)4

OBJECTIVE

AGA07_RTAKS09_024-027.indd 27AGA07_RTAKS09_024-027.indd 27 4/13/06 11:19:47 PM4/13/06 11:19:47 PM

3 R D P R I N T

1. How do the graphs of the functions f (x ) � x2 � 7 and g (x ) � x2 � 5 relate to each other?

A The graph of f (x ) is 2 units above the graph of g (x ).

B The graph of f (x ) is 12 units above the graph of g (x ).

C The graph of f (x ) is 2 units to the right of the graph of g (x ).

D The graph of f (x ) is 12 units to the right of the graph of g (x ).

2. If the graph of f (x ) � x2 � 9 is shifted up 8 units, which function represents the new graph?

F f (x ) � (x � 8)2 � 9

G f (x ) � (x � 8)2 � 9

H f (x ) � x2 � 1

J f (x ) � x2 � 8

3. The graph shows the function f (x ) � x 2 � 3.

10

8

6

4

2

�2

�2�4�6 2 4 6

y

x

Which statement describes the shift in the vertex of the parabola if, in the function, 3 is changed to �1?

A 4 units down C 4 units up

B 2 units down D 2 units up

4. If the vertex of the parabola whose equation is f (x ) � x 2 � 6 is (0, 6), what is the vertex of that parabola when it has been shifted down 6 units?

F (0, 0)

G (0, �6)

H (�6, 0)

J (�6, 6)

5. When graphed, which function would appear to be shifted 4 units up from the graph of f (x ) � x 2 � 2?

y

x

A f (x ) � x2 � 1

B f (x ) � x2 � 2

C f (x ) � x2 � 4

D f (x ) � x2 � 6

Copyright © by Holt, Rinehart and Winston. 28 Holt Mathematics Grade 9All rights reserved.

Name Date Class

Ready for TAKS?Benchmark Pre-Test (A.9)(C)5

OBJECTIVE

AGA07_RTAKS09_028-035.indd 28AGA07_RTAKS09_028-035.indd 28 4/13/06 11:07:57 PM4/13/06 11:07:57 PM

3 R D P R I N T

Name Date Class

Copyright © by Holt, Rinehart and Winston. 29 Holt Mathematics Grade 9All rights reserved.

1. Which expression represents the area of the square shown?

3x y2 4

A 3x4y8

B 6x4y8

C 9x4y8

D 9x4y16

2. Which expression is equivalent

to 48x�4y5

_______ 6x2y3

?

F 8y�2

____ x6

G 42y2

____ x6

H 8y2

___ x6

J 8y2

___ x2

3. Which expression is equivalent to

(7x5)(4x4)

________ 2x2

?

A 14x18

B 14x10

C 14x7

D 7x10

4. The area of the rectangle shown is 72m4n6 square units. If the length of the rectangle is 8m3n4 units, how many units wide is the rectangle? (m � 0 and n � 0)

8m n3 4

F 9mn2

G 64mn2

H 80m7n10

J 576m7n10

5. The table shows several values of r and s.

r s

2x 4x2

3x2 9x4

4x3 16x6

Which of these best describes the relationship between r and s?

A s � 2r

B s � r2

C s � �� r

D s � 2r2

Ready for TAKS?Benchmark Pre-Test (A.11)(A)5

OBJECTIVE

AGA07_RTAKS09_028-035.indd 29AGA07_RTAKS09_028-035.indd 29 4/13/06 11:07:58 PM4/13/06 11:07:58 PM

3 R D P R I N T

1. �ABC is similar to �DEF.

D FA C

BE

6 104

5

Which scale factor was used to transform �ABC to �DEF?

A 1 C 2

B 1.5 D 6

2. The rectangle in the graph is to be

dilated by a scale factor of 1 __ 4 and has

the origin as the center of dilation. What

will be the coordinates of the new top,

right corner of the rectangle?

8

4

�4

�8

�12

�4�8�12 4A B

CD

12

y

x

F (2, 3) H (4, 8)

G (2, 12) J (0, 3)

3. �PQR has vertices P(2, 6), Q(6, 12) and

R(10, 6). �PQR is dilated by a factor

of 1 __ 3 and has the origin as the center of

dilation. What are the coordinates of Q �?

A � 2 __ 3 , 2 � C (2, 4)

B � 10 ___ 3 , 2 � D (18, 36)

4. An advertising company can enlarge or reduce advertisements proportionately. Which would not be an enlargement or reduction of the rectangular sign?

2.5 cm

6 cm

F 0.5 cm

1.2 cm

H

3.75 cm

9 cm

G 1.25 cm

5 cm

J

8.75 cm

21 cm

5. Figure 2 is a dilation of Figure 1 and has the origin as the center of dilation. What scale factor was used to enlarge Figure 1 to arrive at Figure 2?

12

8

4

�4

�8

�12

�4�8�12 4 8 12

Figure 1

Figure 2

y

x

A 1 __ 3

C 2

B 1 __ 2

D 3

Copyright © by Holt, Rinehart and Winston. 30 Holt Mathematics Grade 9All rights reserved.

Name Date Class

Ready for TAKS?Benchmark Pre-Test (8.6)(A)6

OBJECTIVE

AGA07_RTAKS09_028-035.indd 30AGA07_RTAKS09_028-035.indd 30 4/13/06 11:07:58 PM4/13/06 11:07:58 PM

3 R D P R I N T

Name Date Class

Copyright © by Holt, Rinehart and Winston. 31 Holt Mathematics Grade 9All rights reserved.

1. Triangle EFG is shown. If this triangle is reflected across the x-axis, what will be the coordinates of the vertices for the image E �F �G �?

12

8

4

�4

�8

�12

�4�8�12 4E

F

G

12

y

x

A {E �(6, 0), F �(9, 3), G �(�3, 6)}

B {E �(�6, 0), F �(�9, �3), G �(3, �6)}

C {E �(0, �6), F �(3, �9), G �(6, 3)}

D {E �(�6, 0), F �(9, �3), G �(�3, �6)}

2. If a point (x, y ) is reflected through the origin, what will be the coordinates of the point’s image?

F (0, 0) H (�x, �y )

G (�x, y ) J (y, x )

3. Trapezoid WXYZ is translated so that W is mapped to W �.

6

4

2

�2

�4

�6

�2�4�6 2

X

Z

W

W�

Y64

y

x

Which coordinate pair best represents Z �?

A (0, 0) C (0, �2)

B (�3, 0) D (�3, �2)

4. Triangles ABC and A �B �C � are shown on the coordinate plane.

6

2

�2

�4

�6

�2�4�6 2

C

A

A�

C�

B�

B

64

y

x

Which is the best description of the transformation used to arrive at A �B �C � from ABC?

F translation down 3 units and to the right 3 units

G translation down 3 units and to the left 3 units

H reflection across the x-axis

J dilation with a scale factor of 1 __ 2

5. At what coordinates should vertex S be placed to create a quadrilateral QRST that is similar to quadrilateral MNOP?

20

18

16

14

12

10

8

6

4

2 M

N

O

P

Q

R

T

4 6 8 20181614121020

y

x

A (9, 12) C (27, 12)

B (27, 4) D (27, 27)

Ready for TAKS?Benchmark Pre-Test (8.6)(B)6

OBJECTIVE

AGA07_RTAKS09_028-035.indd 31AGA07_RTAKS09_028-035.indd 31 4/13/06 11:07:59 PM4/13/06 11:07:59 PM

3 R D P R I N T

1. A portion of rhombus GHJK is shown on the grid below.

10

6

2

�6

�10

�6�10 2 6 10

y

x

GH

J

At what coordinates should vertex K be placed to make

_ GK parallel to

_ HJ in

order to complete rhombus GHJK?

A (�6, �1)

B (�6, 0)

C (�6, 1)

D (4, �1)

2. Which point on the grid below satisfies the conditions x � 2.5 and y � �1.5?

5

3

1

�1

�3

�5

�3�5 1 3 5

y

x

A

B

C

D

F Point A

G Point B

H Point C

J Point D

3. If a circle has center (�2, 6) and radius 5 units, in which quadrant(s) does the circle lie?

A I only

B II only

C I and II

D II and III

4. Triangle PQR has coordinates P(�7, 4), Q(�3, 2), and R(2, 5). What will be the new coordinates of point R if the triangle is translated 5 units to the right and 2 units down?

y

x

F (�3, 3)

G (�2, 2)

H (7, 3)

J (0, 10)

5. The vertices of a triangle are (�2, 1), (3, 1), and (0, 5). If the triangle is reflected across the x-axis, what will be the coordinates of the lowest vertex?

A (3, �5)

B (0, �5)

C (�2, �5)

D (�5, �5)

Copyright © by Holt, Rinehart and Winston. 32 Holt Mathematics Grade 9All rights reserved.

Name Date Class

Ready for TAKS?Benchmark Pre-Test (8.7)(D)6

OBJECTIVE

AGA07_RTAKS09_028-035.indd 32AGA07_RTAKS09_028-035.indd 32 4/13/06 11:07:59 PM4/13/06 11:07:59 PM

3 R D P R I N T

Name Date Class

Copyright © by Holt, Rinehart and Winston. 33 Holt Mathematics Grade 9All rights reserved.

1. The drawing shows a rectangular prism whose dimensions are 3 � 3 � 7.

Which best represents the shape of the solid when viewed from the top?

A rhombus C parallelogram

B square D rectangle

2. Which of the following shapes could be the bottom view of a pyramid?

F square H triangle

G rectangle J Any of these

3. Which of the following is not a possible view of the three-dimensional solid shown?

Front Right

A C

B D

4. Below is a three-dimensional view of a structure built with cubes.

Front Right

Which of the following is the correct top view of the structure along with the number of cubes in each column of the structure?

F 3 3 2

4 3 1

H 3 2

4 3 1

G 4 3 1

3 3 2

J 3 1

4 3 2

5. The drawing shows a cone.

Which best represents the shape of the solid when viewed from the top?

A C

B D

Ready for TAKS?Benchmark Pre-Test (8.7)(A)7

OBJECTIVE

AGA07_RTAKS09_028-035.indd 33AGA07_RTAKS09_028-035.indd 33 4/13/06 11:07:59 PM4/13/06 11:07:59 PM

3 R D P R I N T

1. An 18- by 42-foot rectangular roof will be covered by square panels that measure 3 feet on each side. If the panels are not cut, how many of them will be needed to cover the roof?

A 756 C 120

B 84 D 40

2. Ms. Garcia wants to buy enough plastic to cover the garden shown. Which geometric formula should she use to determine how much plastic she needs?

30 ft

20 ft

14 ft

F A � (20)(14)

G A � 14 ___ 2 (20 � 30)

H A � �(14)2

J P � 2(20 � 30)

3. Mr. Brantley decided to fill in his circular in-ground pool after all his children grew up and moved away. Once the hole is filled in, he will need to re-seed the lawn. If the diameter of the pool is 16 feet and it takes 1 pound of seed for every 80 square feet of lawn, approximately how many pounds of seed does Mr. Brantley need?

A 0.6 lb C 10 lb

B 2.5 lb D 201 lb

4. A carpenter is replacing the floor in his laundry room. The plans for his house

use a scale factor in which 1 __ 4

inch equals

1 foot. If the plans indicate that his laundry room is 2 inches by 2.5 inches, what are the actual dimensions of the room?

F 6 ft by 8 ft

G 7 ft by 8 ft

H 8 ft by 10 ft

J 10 ft by 12 ft

5. The Carmichels want to build a swing set in one corner of their yard. The yard is in the shape of a triangle as shown.

60 ft 65 ft

140 ft

House

If they decide to build the swing set in the corner with the smallest angle, where should the swing set be built?

A In the corner of the lot opposite the side that is 60 feet.

B In the corner of the lot opposite the side that is 65 feet.

C In the corner of the lot opposite the side that is 140 feet.

D In the center of the triangular lot.

Copyright © by Holt, Rinehart and Winston. 34 Holt Mathematics Grade 9All rights reserved.

Name Date Class

Ready for TAKS?Benchmark Pre-Test (8.7)(B)7

OBJECTIVE

AGA07_RTAKS09_028-035.indd 34AGA07_RTAKS09_028-035.indd 34 4/13/06 11:08:00 PM4/13/06 11:08:00 PM

3 R D P R I N T

Name Date Class

Copyright © by Holt, Rinehart and Winston. 35 Holt Mathematics Grade 9All rights reserved.

1. Based on the visual representation of the triangle below, which of the following are most likely the triangle’s dimensions?

A 5, 12, 17

B 6.2, 9, 11.4

C 4, 5, 8

D 1.5, 2, 2.5

2. Use the Pythagorean Theorem to determine which figure is a right triangle.

F

12

15

18

G 25 18

30

H

60

45

75

J 19

2414

3. The coordinate grid below shows three squares.

y

x

A

O B

If the distance from A to B is 5 units and the distance from O to B is 4 units, what is the area of the smallest square?

A 3 unit2

B 9 unit2

C 12 unit2

D 16 unit2

4. The drawing below represents directions on a standard map.

N

S

EW

NW NE

SESW

Which of the following pairs of directions would not meet at a right angle?

F due N and due S

G due W and due N

H due E and due N

J 45° NE and 45° SE

Ready for TAKS?Benchmark Pre-Test (8.7)(C)7

OBJECTIVE

AGA07_RTAKS09_028-035.indd 35AGA07_RTAKS09_028-035.indd 35 4/13/06 11:08:00 PM4/13/06 11:08:00 PM

3 R D P R I N T

1. A shoebox has dimensions 8 in. � 6 in. � 14 in. What is the surface area of the box?

A 244 in2 C 672 in2

B 488 in2 D 784 in2

2. The bottom of a swimming pool has dimensions 20 ft by 8 ft. The depth of the pool is 5 ft everywhere. A net of the pool is shown below.

8 ft20 ft

5 ft

What is the surface area of the pool?

F 800 ft2 H 440 ft2

G 600 ft2 J 66 ft2

3. The net of a triangular prism is shown along with its approximate dimensions.

3.5 cm

10 cm

4 cm

What is the approximate total surface area of the prism?

A 47 cm2 C 134 cm2

B 127 cm2 D 140 cm2

The net of a cylinder is shown below. Use the net to answer questions 4 and 5.

3.125 in.

1.25 in.

1 in.

1 in.

4. Which formula could NOT be used to find the surface area of the cylinder?

F SA � 2�r 2 � 2�rh

G SA � 2�(r 2 � rh)

H SA � 2�r (h � r )

J SA � �r 2(2 � 2h)

5. Use a ruler to measure the dimensions of the cylinder to the nearest eighth of an inch. Which of the following BEST represents the total surface area of the cylinder?

A 11.4 in2

B 5.5 in2

C 4.7 in2

D 2.0 in2

Copyright © by Holt, Rinehart and Winston. 36 Holt Mathematics Grade 9All rights reserved.

Name Date Class

Ready for TAKS?Benchmark Pre-Test (8.8)(A)8

OBJECTIVE

AGA07_RTAKS09_036-042.indd 36AGA07_RTAKS09_036-042.indd 36 4/13/06 11:08:23 PM4/13/06 11:08:23 PM

3 R D P R I N T

Name Date Class

Copyright © by Holt, Rinehart and Winston. 37 Holt Mathematics Grade 9All rights reserved.

1. The net of a cube is shown below. Use a ruler to measure the dimensions of the cube to the nearest eighth of an inch.

Which best represents the formula to find the volume of this cube in square inches?

A V � � 3 __ 8 � 2

B V � 6 � 3 __ 8 � 2

C V � � 3 __ 8 � 3

D V � 6 � 3 __ 8 � 3

2. A cube with sides of length s is topped by a square pyramid with height h. Which formula can be used to find the volume of the composite solid?

F V � s2h � s3

G V � 1 __ 3 s2h

H V � 1 __ 3 s2h � s3

J V � 1 __ 3 (s2h � s3 )

3. A sea aquarium has a shark tank that is in the shape of a cylinder. The base of the tank has a diameter of 200 feet and the tank is 16 feet tall. Which formula could be used to find the amount of water needed to fill the tank when there are no sharks in it?

A V � �(16)2(200)

B V � �(100)2(16)

C V � �(200)2(16)

D V � 2�(100)(16) � 2�(100)2

4. A right triangular prism is shown below.

5 in.

12 in.

4 in.

3 in.

What is the volume of the prism?

F 72 in3

G 144 in3

H 156 in3

J 720 in3

5. A landscaping company stores its fertilizer in a conical pile. If the base of the pile has a diameter of 20 yards and the pile is 6 yards tall, what is the approximate volume of the fertilizer?

A 628 yd3

B 754 yd3

C 1,884 yd3

D 2,513 yd3

Ready for TAKS?Benchmark Pre-Test (8.8)(B)8

OBJECTIVE

AGA07_RTAKS09_036-042.indd 37AGA07_RTAKS09_036-042.indd 37 4/13/06 11:08:24 PM4/13/06 11:08:24 PM

3 R D P R I N T

1. A rectangular storage shed is shown below.

6 ft

4 ft8 ft

If the sides and the floor of the shed must be painted, how much paint is needed?

A 144 ft2

B 176 ft2

C 192 ft2

D 208 ft2

2. The volume of the cone shown below is 44 cubic units.

7

Which of the following is a reasonable estimate for the radius of the cone?

F 0.8 unit H 2.5 units

G 1.4 units J 6.0 units

3. If the volume of a cylindrical can is 48 in3 and its height is 5 in., what is the approximate radius of the can?

A 3.5 in.

B 3.1 in.

C 1.75 in.

D 0.6 in.

4. The volume of the cylinder shown is approximately 150 cubic centimeters. What is the approximate volume of the cone?

d d

h h

F 50 cm3

G 75 cm3

H 150 cm3

J cannot be determined

5. Which of the following is a reasonable estimate for the surface area of the cube shown?

4.012 cm

A 48 cm2

B 64 cm2

C 96 cm2

D 384 cm2

Copyright © by Holt, Rinehart and Winston. 38 Holt Mathematics Grade 9All rights reserved.

Name Date Class

Ready for TAKS?Benchmark Pre-Test (8.8)(C)8

OBJECTIVE

AGA07_RTAKS09_036-042.indd 38AGA07_RTAKS09_036-042.indd 38 4/13/06 11:08:24 PM4/13/06 11:08:24 PM

3 R D P R I N T

Name Date Class

Copyright © by Holt, Rinehart and Winston. 39 Holt Mathematics Grade 9All rights reserved.

1. A pigeon leaves its nest and flies 8 km due north. The pigeon then flies 4 km due east. Approximately how far is the pigeon from its nest?

Nest

Pigeon

A 4 km

B 9 cm

C 12 km

D 80 km

2. A telephone pole broke in a storm leaving a 6-foot piece below the break. The top of the pole came to rest 22 feet away from the break. About how tall was the pole originally?

6 ft

22 ft

F 7 ft H 23 ft

G 16 ft J 29 ft

3. A fire truck parks 12 feet away from a building that is on fire. The fire truck extends its 25-foot ladder completely. How far up the building from the truck’s roof does the ladder reach?

A 13 ft

B 22 ft

C 28 ft

D 37 ft

4. The Whitby’s yard is in the shape of a right triangle as shown below.

40 ft 82 ft

House

The Whitbys want to put a fence around their entire yard. The posts for the fence need to be 5 feet apart. Approximately how many posts do they need?

F 18

G 24

H 43

J 91

5. The park committee wants to install a brick walkway diagonally across a square playground. The walkway will be 30 feet long. To the nearest tenth, how long is a side of the playground?

30 ft

??

??

A 3.9 ft

B 15.0 ft

C 21.2 ft

D 42.4 ft

Ready for TAKS?Benchmark Pre-Test (8.9)(A)8

OBJECTIVE

AGA07_TAKs_WBK09_036-042.indd 39AGA07_TAKs_WBK09_036-042.indd 39 9/6/06 8:17:41 PM9/6/06 8:17:41 PM

3 R D P R I N T

1. Two similar triangles are shown below.

15 cm 14 cm12 cm s

Use the dimensions given to find the approximate length of the side labeled s.

A 11 cm

B 11.2 cm

C 12.9 cm

D 17.5 cm

2. In the figure below, �ABC is similar to �DEF.

B

A C

D F

E

3 5

8

6

What is the length of _

DF ?

F 4 H 11

G 10 J 16

3. In a scale model of a new high rise, 1 inch represents 6 feet. The actual high rise will be 80-feet tall. Which proportion can be used to determine h, the height of the scale model?

A 1 __ 6 � h ___

80 C 6 __

1 � h ___

80

B 1 __ 6 � 80 ___

h D 1 ___

80 � 6 __

h

4. The cylinders below are similar. What is the radius of cylinder A?

1827

33

BA

F 7.35 units

G 11 units

H 22 units

J 24.75 units

5. Parallelogram ABCD has the dimensions shown.

42 in.

25 in.

Which set of dimensions would produce a similar figure?

A 12.5 in. by 84 in.

B 25 in. by 168 in.

C 75 in. by 126 in.

D 100 in. by 210 in.

Copyright © by Holt, Rinehart and Winston. 40 Holt Mathematics Grade 9All rights reserved.

Name Date Class

Ready for TAKS?Benchmark Pre-Test (8.9)(B)8

OBJECTIVE

AGA07_RTAKS09_036-042.indd 40AGA07_RTAKS09_036-042.indd 40 4/13/06 11:08:25 PM4/13/06 11:08:25 PM

3 R D P R I N T

Name Date Class

Copyright © by Holt, Rinehart and Winston. 41 Holt Mathematics Grade 9All rights reserved.

1. The two quadrilaterals shown are similar. The scale of the two quadrilaterals is 1:3. The perimeter of the larger quadrilateral is 108 centimeters.

What is the perimeter of the smaller quadrilateral?

A 12 cm

B 36 cm

C 54 cm

D 324 cm

2. Describe the change in the area of a circle when the radius of the circle is tripled.

F The area is reduced by 1 __ 3

.

G The area remains constant.

H The area is tripled.

J The area is increased nine times.

3. The length of the sides of a square are 3 times the length of the sides of a smaller square. If the area of the smaller square is 150 in2, what is the area of the larger square?

A 1,350 in2

B 450 in2

C 50 in2

D 16.7 in2

4. Rectangle MNOP has a perimeter of 26 cm. The dimensions of the rectangle are tripled to form rectangle TUVW.

M N

P O

T U

W V

12 cm

What is the length of rectangle TUVW?

F 27 cm

G 54 cm

H 78 cm

J 105 cm

5. The radius of circle O is 1 __ 4

the radius of circle P.

O

P

What is the ratio of the circumference of circle O to the circumference of circle P ?

A 1 to 64

B 1 to 16

C 1 to 4

D 4 to 1

Ready for TAKS?Benchmark Pre-Test (8.10)(A)8

OBJECTIVE

AGA07_RTAKS09_036-042.indd 41AGA07_RTAKS09_036-042.indd 41 4/13/06 11:08:25 PM4/13/06 11:08:25 PM

3 R D P R I N T

1. The edges of cube 2 are 5 times longer than the edges of cube 1. How many times greater is the volume of cube 2?

Cube 1

Cube 2

A 5

B 15

C 25

D 125

2. A box in the shape of a rectangular

prism has a volume of 324 cubic

inches. If the box is dilated by a scale

factor of 1 __ 3 , what will be the volume of

the resulting box?

F 12 in3

G 36 in3

H 108 in3

J 216 in3

3. The volume of a triangular prism is

1,250 cm3. If each dimension of the

triangular prism is reduced to 1 __ 5 of

its original measure, what will be the

volume of the resulting triangular

prism?

A 10 cm3

B 50 cm3

C 83.3 cm3

D 250 cm3

4. The diameter and height of cylinder C are each 4 times the diameter and height of cylinder D.

Cylinder C

Cylinder D

What is the ratio of the volume of cylinder C to cylinder D.

F 4 to 1

G 16 to 1

H 64 to 1

J 256 to 1

5. Cone A and cone B are similar. The ratio of the volume of cone A to cone B is 8 to 1.

A B

What is the ratio of the area of cone A to the area of cone B ?

A 2 to 1

B ��

8 to 1

C 4 to 1

D 64 to 1

Copyright © by Holt, Rinehart and Winston. 42 Holt Mathematics Grade 9All rights reserved.

Name Date Class

Ready for TAKS?Benchmark Pre-Test (8.10)(B)8

OBJECTIVE

AGA07_TAKs_WBK09_036-042.indd 42AGA07_TAKs_WBK09_036-042.indd 42 9/6/06 8:17:42 PM9/6/06 8:17:42 PM

3 R D P R I N T

Copyright © by Holt, Rinehart and Winston. 43 Holt Mathematics Grade 9All rights reserved.

Name Date Class

1. Mary’s car can go 182 miles on 7 gallons of gas. Mary is taking a trip of 455 miles. Which proportion can be used to determine approximately how many gallons of gas, g, Mary will need for her trip?

A 7 ____ 455

� 182 ____ g

B 182 ____ 455

� g __

7

C 182 ____ 7 � 455 ____ g

D 7 ____ 182

� 455 ____ g

2. A park ranger in Oklahoma captures and tags 40 armadillos. He then releases them at various places in the park. The following month, he captures another 50 armadillos. Of the 50, only 3 have his tags. Which proportion can be used to estimate the number of armadillos, a, in the park?

F 3 ___ 50

� 40 ___ a

G 50 ___ 40

� 3 __ a

H 40 ___ 50

� 3 __ a

J 40 ___ 50

� a __ 3

3. David is on a 30-day bike trip. For the first several days he bikes 26.5 miles per day. If he bikes at the same rate over the entire 30-day period, which proportion can be used to determine how many miles, m, he will bike in all?

A 1 ____ 26.5

� m ___ 30

C 30 ____ 26.5

� 1 __ m

B 26.5 ____ 30

� 1 __ m D 26.5 ____ 1

� m ___ 30

4. The chart shows the number of defective eyeglasses that were found in several production batches.

Number of Glasses in Batch

Number of Defective Glasses

110 17

220 34

330 51

If this rate remains the same, which proportion can be used to estimate how many defective glasses, d, would be found in a batch of 2,000 glasses?

F 110 ____ 17

� d _____ 2000

H 17 ____ 110

� d _____ 2000

G 17 _____ 2000

� d ____ 110

J 2000 _____ 110

� 17 ___ d

5. The diagram shows the length of a shadow of a 5-foot tall person at a certain time during the day. The diagram also shows a tree that is 18-foot tall and its shadow at the same time.

11 ft s

Which proportion can be used to determine the length of the tree’s shadow, s?

A 5 ___ 11

� 18 ___ s C 5 ___ 18

� 11 ___ s

B 11 ___ 5

� 18 ___ s D 18 ___ 11

� s __ 5

Ready for TAKS?Benchmark Pre-Test (8.1)(B)9

OBJECTIVE

AGA07_RTAKS09_043-049.indd 43AGA07_RTAKS09_043-049.indd 43 4/13/06 11:08:42 PM4/13/06 11:08:42 PM

3 R D P R I N T

1. A football team has 48 players. Twenty-eight of them have already been fitted for shoulder pads. What percent of the team has not yet been fitted?

A 20%

B 42%

C 58%

D 80%

2. The table shows the distribution of players on a basketball team.

Number of Players

Grade

8 12th

4 11th

2 10th

To the nearest tenth, what percent of the basketball players are in the 11th grade?

F 4.0%

G 14.3%

H 28.6%

J 57.1%

3. Maria answered 85% of the questions on her math test correctly. If she answered 17 questions correctly, how many questions were there on the test?

A 3

B 14

C 15

D 20

4. The circle-graph shows the distribution of the ages of the 240 people at a concert.

25%Over 30

75%Under 30

Of the people under the age of 30, 5% are younger than 16. How many people at the concert are younger than 16?

F 4

G 9

H 12

J 180

5. A certain kind of bird can fly 24 miles per hour. If this kind of bird flew in a straight path at this rate, what distance would it fly in 10 minutes?

A 2.4 mi

B 4 mi

C 144 mi

D 240 mi

Copyright © by Holt, Rinehart and Winston. 44 Holt Mathematics Grade 9All rights reserved.

Name Date Class

Ready for TAKS?Benchmark Pre-Test (8.3)(B)9

OBJECTIVE

AGA07_RTAKS09_043-049.indd 44AGA07_RTAKS09_043-049.indd 44 4/13/06 11:08:43 PM4/13/06 11:08:43 PM

3 R D P R I N T

Name Date Class

Copyright © by Holt, Rinehart and Winston. 45 Holt Mathematics Grade 9All rights reserved.

1. A multiple-choice test has five choices for each answer. There are 20 questions. If a student guesses on the first four questions, what is the probability that the student will miss the first two and get the next two correct?

A 1 ____ 625

B 16 ____ 625

C 256 ____ 625

D 16 ___ 25

2. One ball is drawn at random from a box containing five red balls, three white balls, and four blue balls. What is the probability that the ball will be red or blue?

F 3 __ 4

G 5 ___ 12

H 1 __ 3

J 5 ___ 36

3. A box of fruit contains 5 red apples and 4 green apples. What is the probability of randomly choosing a red apple and then a green apple from the box WITHOUT replacing them?

A 1 ___ 81

B 20 ___ 81

C 5 ___ 18

D 19 ___ 18

4. A spinner is made by dividing a circle into six sections as shown. Each of the larger sections represents 25% of the circle and each of the smaller sections represents 12.5% of the circle.

1 2

3645

If a person spins the spinner twice, what is the probability that the person will get an odd number on the first spin and the number 5 on the second spin?

F 0.625

G 0.5

H 0.25

J 0.0625

5. One student is chosen at random from the pre-calculus class and one from the calculus class to compete in a math contest.

Pre-Calculus

Grade 9th 10th 11th 12th

% of Class 5% 13% 34% 48%

Calculus

Grade 9th 10th 11th 12th

% of Class 1% 5% 24% 70%

What is the probability that both students chosen are in the 12th grade?

A 0.336

B 0.48

C 0.70

D 1.18

Ready for TAKS?Benchmark Pre-Test (8.11)(A)9

OBJECTIVE

AGA07_RTAKS09_043-049.indd 45AGA07_RTAKS09_043-049.indd 45 4/13/06 11:08:43 PM4/13/06 11:08:43 PM

3 R D P R I N T

Use the bar graph to answer questions 1 and 2.

Jon conducted an experiment by rolling a standard number cube 400 times. The results of Jon’s experiment are shown in the bar graph.

0

10

20

30

40

50

60

70

80

90

1 2 3 4 5 6

5562

80

70 68 65

Nu

mb

er o

f T

imes

To

ssed

Digit

400 Tosses of a Number Cube

1. According to the data, what is the experimental probability of rolling a 3 on the next roll of the number cube?

A 1 __ 6

B 1 __ 5

C 7 ___ 40

D 4 __ 5

2. What is the approximate difference between the experimental probability and the theoretical probability of rolling a 3 on the next roll?

F 0.033

G 0.167

H 0.20

J 0.367

Use the circle graph to answer questions 3 and 4.

Elise conducted an experiment by tossing a fair coin 150 times. The results of Elise’s experiment are shown in the circle graph.

Tails58%

Heads42%

150 Coin Tosses

3. According to the data, what is the experimental probability of tossing a heads on the next toss of the coin?

A 0.28

B 0.42

C 0.50

D 0.58

4. What is the approximate difference between the experimental probability and the theoretical probability of tossing a heads on the next roll?

F 0.92

G 0.50

H 0.42

J 0.08

5. Mike has been keeping a tally of his bowling scores. So far, he has bowled 30 games with a score less than 150 and 70 games with a score above 150. If he bowls 1,000 games, and he does not get any better or any worse, how many games can he expect to bowl a score of over 150?

A 970 C 670

B 700 D 300

Copyright © by Holt, Rinehart and Winston. 46 Holt Mathematics Grade 9All rights reserved.

Name Date Class

Ready for TAKS?Benchmark Pre-Test (8.11)(B)9

OBJECTIVE

AGA07_RTAKS09_043-049.indd 46AGA07_RTAKS09_043-049.indd 46 4/13/06 11:08:43 PM4/13/06 11:08:43 PM

3 R D P R I N T

Name Date Class

Copyright © by Holt, Rinehart and Winston. 47 Holt Mathematics Grade 9All rights reserved.

1. During Peter’s first week of selling televisions, he sold a total of 29 TVs. His sales per day, Monday through Friday, were 5, 4, 7, 9, and 4. Which measure of central tendency would be the most impressive to report to his store manager?

A range

B mean

C median

D mode

2. Hannah earned the following grades on her English papers: 86, 92, 84, and 89. If Hannah scores a 92 on her last paper, which measure of central tendency will give her the highest overall score?

F range

G mean

H median

J mode

3. Consider the given set of data:

{25, 20, 15, 25, 20, 15, 25, 25, 50}.

Which statement is an accurate interpretation of the data?

A Only the mode of the set of data is 25.

B The mean of the set of data is 25.

C The range of the data set is less than the mode.

D The median and the mode are both greater than the mean.

4. Maggie’s scores on her first five history quizzes are shown in the table.

Maggie’s Scores

Quiz 1 80

Quiz 2 82

Quiz 3 88

Quiz 4 100

Quiz 5 90

Which measure of central tendency would not change if Maggie had scored a 90 on Quiz 3?

F range

G mean

H median

J mode

5. The stem-and-leaf plot shows the scores on the last test in Mr. Jandi’s science class.

Stem Leaf9 8 4 18 9 7 6 4 3 2 0 07 8 8 5 6 7 45 2

Which statement about the scores is true?

A The highest score was a 92.

B The median score was an 80.

C The range of the scores was 50.

D More than 50% of the class scored above an 80.

Ready for TAKS?Benchmark Pre-Test (8.12)(A)9

OBJECTIVE

AGA07_RTAKS09_043-049.indd 47AGA07_RTAKS09_043-049.indd 47 4/13/06 11:08:44 PM4/13/06 11:08:44 PM

3 R D P R I N T

1. A travel agency surveyed visitors to Washington D.C. to find out how many historical sites they visited. The survey results are shown in the bar graph.

0

10

20

30

40

50

60

70

0 1 2 3 4 ormoreNumber of Sites Visited

Washington D.C. Survey Results

Fre

qu

ency

Approximately how many people were surveyed?

A 20 C 230

B 70 D 350

2. Of the 800 people at a shopping mall, 200 people are shopping alone, 318 people are shopping with a friend, 160 are shopping with a spouse, and the rest are shopping with another member of their family. If a circle graph is constructed, which of the following are the approximate percentages needed to represent each category, in the order presented above?

F 15%, 45%, 28%, 12%

G 25%, 40%, 20%, 15%

H 30%, 40%, 18%, 17%

J 200%, 318%, 160%, 122%

3. The juniors and seniors at a local high school recorded the number of votes that each candidate received in the race for prom queen. A total of 240 students voted and Charlene received 37.5% of the votes. If a bar graph is constructed, and the vertical axis represents the number of votes received, what should be the height of the bar for Charlene?

A 37.5 C 90

B 62.5 D 150

4. Marti gathered information about the household income of families in her community. She used the information to create the bar graph and the circle graph shown. The circle graph accurately reflects the information gathered, but two columns in the bar graph were switched.

0

5

10

15

20

25

30

Under20

20–39 40–59 60–79 80–99

Fre

qu

ency

Income (in thousands of dollars)

Household Income Survey Results

$20–$3925%

$40–$5930%$60–$79

18%

$80–$9915%

Under $2012%

Household Income(in thousands of dollars)

According to the information in the circle graph, which two columns in the bar graph were switched?

F 60–79 and 80–89

G under 20 and 80–89

H under 20 and 60–79

J under 20 and 20–39

Copyright © by Holt, Rinehart and Winston. 48 Holt Mathematics Grade 9All rights reserved.

Name Date Class

Ready for TAKS?Benchmark Pre-Test (8.12)(C)9

OBJECTIVE

AGA07_RTAKS09_043-049.indd 48AGA07_RTAKS09_043-049.indd 48 4/13/06 11:08:44 PM4/13/06 11:08:44 PM

3 R D P R I N T

Name Date Class

Copyright © by Holt, Rinehart and Winston. 49 Holt Mathematics Grade 9All rights reserved.

Use the circle graph to answer questions 1 and 2.

The circle graph shows the percent of sales for each color of a particular model of vehicle sold at a car dealership last month.

Red15%

White35%

Silver40%

Black10%

Car Sales by Color

1. Which statement is NOT true?

A The color of car sold the least was black.

B The color of car sold the most was silver.

C More than twice as many red cars were sold as white cars.

D The number of white cars sold was more than the number of red and black cars combined.

2. Which is a reasonable conclusion from the information provided in the graph?

F Silver cars outsold black cars by a ratio of 4 to 1.

G White cars outsold all other colors.

H Sales of red cars are growing every year.

J Car manufacturers will eventually stop making black cars.

Use the bar graph to answer questions 3 and 4.

The bar graph shows the number of students enrolled in different math classes at a local high school.

0 100 200 300 400

Pre-Calc

Algebra 2

Geometry

Algebra 1

Student Enrollment: Mathematics

3. Which statement is NOT true?

A There are more students enrolled in Algebra 1 than in all the other classes together.

B Pre-Calculus has the least number of students enrolled.

C There are more than twice as many students enrolled in Algebra I as in Pre-Calculus.

D There are slightly less than half as many students enrolled in Algebra 2 as there are in Algebra 1.

4. Which is a reasonable conclusion from the information provided in the graph?

F More than one third of the students in the school are enrolled in Algebra 1.

G The geometry teacher is more popular than the Algebra 2 teacher.

H The school will soon need to hire a new Algebra 1 teacher because the enrollment is so high.

J As the math courses increase in difficulty, fewer students enroll in them.

Ready for TAKS?Benchmark Pre-Test (8.13)(B)9

OBJECTIVE

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3 R D P R I N T

1. Samantha found a pair of roller blades on sale for 20% off the original price. If the sale price is x, which equation could Samantha use to find the original price, p, of the roller blades?

A p � x � 1 __ 5 x

B p � 1 __ 5 p � x

C p � x � 1 __ 5 x

D p � x � 1 __ 5

2. Tasha’s age is 3 years more than twice David’s. If Tasha is 19 years old, which equation can be used to determine David’s age?

F 2(x � 3) � 19

G 2x � 19 � 3

H 2x � 3 � 19

J 2x � 3 � 19

3. A construction company reported that the average price of lumber in the U.S. increased by 8% per year from 1998 to 2004. What additional information is needed to calculate the average price of lumber in 2004?

A the average price of lumber in 1998

B the anticipated price of lumber for the next year

C the range of the lumber prices from 1998 to 2004

D the amount of lumber sold between 1998 and 2004

Mr. Hennesey wants to tile several rooms in his house. The diagram shows the dimensions of the rooms he wants to tile. Use the diagram to answer questions 4 and 5.

14� by 16�

8� by 18�14� by 14�

4. The tile Mr. Hennesey has chosen is a square tile with sides of length 12 in. The tile comes in boxes. If Mr. Hennesey calculates the number of square feet that he is going to tile, what additional information does he need to determine how many boxes to order?

F the number of tiles each box contains

G the size of the tile in each box

H the amount of tax on each box of tile

J the weight of each box of tile

5. Each box of tiles costs $31 plus tax. There is also a shipping and handling fee. If the shipping and handling is a flat fee of $49, what additional information does Mr. Hennesey need to determine the total cost of the tiles?

A the number of boxes he needs

B the number of boxes he needs and the weight of the boxes

C the number of boxes he needs and the tax rate

D the weight of the boxes he needs and the tax rate

Copyright © by Holt, Rinehart and Winston. 50 Holt Mathematics Grade 9All rights reserved.

Name Date Class

Ready for TAKS?Benchmark Pre-Test (8.14)(A)10

OBJECTIVE

AGA07_RTAKS09_050-055.indd 50AGA07_RTAKS09_050-055.indd 50 4/13/06 11:09:02 PM4/13/06 11:09:02 PM

3 R D P R I N T

Name Date Class

Copyright © by Holt, Rinehart and Winston. 51 Holt Mathematics Grade 9All rights reserved.

1. An oil tanker is being emptied at a rate of 20 gallons every 5 minutes. The tank holds 2,400 gallons of oil. How many hours would it take to empty the tank at that rate?

A 600 hr

B 24 hr

C 10 hr

D 2 hr

2. Ellen bought a coat that was on sale for 30% off. The original cost of the coat was $150.00. If the tax rate is 6.25% and Ellen gives the salesclerk three $50.00 bills, how much change should she get back?

F $38.44

G $45.00

H $102.19

J $111.56

3. Michael wants to put a fence around the perimeter of his yard.

16 ft19.2 ft

38.4 ft

25.4 ft

Michael’s Yard

If the fence cost $6.50 per linear foot including tax and the installation costs $4.25 per 6-foot panel, how much would it cost to fence the entire yard?

A $177.38

B $643.50

C $713.63

D $1,064.25

4. John wants to know how far it is around a lake. The lake is an irregular shape. To measure the distance around the lake, John makes a roller that has a diameter of 9 inches as shown.

Lake

9 �

Roller

If the roller goes around 52 times, what is the approximate distance around the lake?

F 39 ft

G 123 ft

H 245 ft

J 1,470 ft

5. Pierre’s car uses approximately 580 gallons of gasoline each year. If high octane gas costs $2.19 per gallon and regular gas costs $1.97 per gallon, what percent of Pierre’s yearly gas cost would he save by switching from high octane to regular gas?

A 10%

B 11%

C 12%

D 14%

Ready for TAKS?Benchmark Pre-Test (8.14)(B)10

OBJECTIVE

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3 R D P R I N T

1. Janet, Allie, and Carissa all collect thimbles. Janet has 4 more thimbles than Allie has. Carissa has 3 times as many thimbles as Janet has. Altogether the girls have 121 thimbles. Which equation can be used to find out how many thimbles each person has?

A x � 3x � 4x � 121

B x � (x � 4) � 3x � 121

C x � (x � 4) � 3(x � 4) � 121

D x � 3(4x) � 3x � 121

2. The lobby of a conference center is a square that covers and area of 576 square feet. What is the best way to determine the length of each side of the lobby?

F Divide the area in half.

G Divide the area by 4.

H Square the area.

J Find the square root of the area.

3. Which of the equations below represents the second step of the solution process?

Step 1. 6(3x � 8) � 2 � �10

Step 2.

Step 3. 18x � 46 � �10

Step 4. 18x � 36

Step 5. x � 2

A 18x � 8 � 2 � �10

B 18x � 48 � 2 � �10

C 18x � 48 � 12 � �10

D 6(3x � 6) � �10

4. A rectangle has an area of 36 square centimeters and a perimeter of 30 centimeters. What are the dimensions of the rectangle?

F 1 cm by 36 cm

G 2 cm by 18 cm

H 3 cm by 12 cm

J 4 cm by 9 cm

5. Three vertices of a square lie at the points whose coordinates are (�4, 0), (�2, �3), and (�1, 2). What are the coordinates of the fourth vertex?

8

6

4

2

�2

�4

�6

�8

�2�4�6�8 2 4 86

y

x

A (0, 0)

B (1, 0)

C (1, �1)

D (2, �1)

Copyright © by Holt, Rinehart and Winston. 52 Holt Mathematics Grade 9All rights reserved.

Name Date Class

Ready for TAKS?Benchmark Pre-Test (8.14)(C)10

OBJECTIVE

AGA07_RTAKS09_050-055.indd 52AGA07_RTAKS09_050-055.indd 52 4/13/06 11:09:03 PM4/13/06 11:09:03 PM

3 R D P R I N T

Name Date Class

Copyright © by Holt, Rinehart and Winston. 53 Holt Mathematics Grade 9All rights reserved.

Use the figure shown to answer questions 1 and 2.

1. If the figure is a gift box, the amount of paper needed to cover the outside of the box best represents the box’s —

A perimeter.

B circumference.

C surface area.

D volume.

2. If the figure is a swimming pool, the amount of water needed to fill the pool best represents the pool’s —

F perimeter.

G lateral area.

H surface area.

J volume.

3. Which of the following names cannot be used to describe the figure shown if x � y ?

y

x

A rhombus

B rectangle

C quadrilateral

D parallelogram

4. If the area of a rectangle is given by the equation A � � � w, then the value of w is the result of which of the following ratios comparing a rectangle’s area to its length?

F � __ A

G A __ �

H w __ �

J � __ w

5. Which of the following is an accurate description of the algebraic equation

given by 2(x � 3)

_______ x � 5

� �15?

A Five more than x divided by the product of 2 and 3 less than x is equal to �15.

B Three less than twice x divided by the sum of x and 5 is equal to �15.

C Two times the difference of x and 3 divided by the sum of x and 5 is equal to �15.

D Twice the difference of x and 3 divided by 5 times x is equal to �15.

Ready for TAKS?Benchmark Pre-Test (8.15)(A)10

OBJECTIVE

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3 R D P R I N T

1. A Pythagorean Triple is a set of three integers, a, b, and c for which the following properties are both true:

Property 1: a � c and b � c

Property 2: a2 � b2 � c2

Which set of three integers below could not be a Pythagorean Triple?

A a � 3, b � 4, and c � 5

B a � 4, b � 5, and c � 8

C a � 8, b � 15, and c � 17

D a � 20, b � 48, and c � 52

2. The tables shows several powers of the number 3.

Powers of 3 Resulting Value

31 3

32 9

33 27

34 81

35 243

36 729

37 2,187

38 6,561

Given that the digit in the ones place will continue to repeat in the pattern above, what will be the digit in the ones place in 346?

F 3

G 9

H 7

J 1

3. The first six powers of the number 4 are 4, 16, 64, 256, 1024, and 4096. Which of the following is a reasonable conjecture?

A Each digit in the ones place increases by 2 from the previous digit in the ones place.

B All multiples of 4 end in either a 4 or 6.

C All powers of 4 end in either a 4 or 6.

D There is no pattern regarding the digits in the powers of 4.

4. Each figure in a pattern is a square whose width is one unit more than the width of the square before it. If the first square in the pattern has a perimeter of 16 units, what is the perimeter of the fifth square in the pattern? 4, 5, 6, 7, 8, …

F 28 units

G 32 units

H 36 units

J 40 units

5. Joe made the conjecture that other than 12, no other perfect square ends in the number 1. Which of the following is a counterexample to Joe’s conjecture?

A 92 � 81

B 112 � 121

C 212 � 441

D any of these

Copyright © by Holt, Rinehart and Winston. 54 Holt Mathematics Grade 9All rights reserved.

Name Date Class

Ready for TAKS?Benchmark Pre-Test (8.16)(A)10

OBJECTIVE

AGA07_RTAKS09_050-055.indd 54AGA07_RTAKS09_050-055.indd 54 4/13/06 11:09:03 PM4/13/06 11:09:03 PM

3 R D P R I N T

Name Date Class

Copyright © by Holt, Rinehart and Winston. 55 Holt Mathematics Grade 9All rights reserved.

1. If the variables x and y both represent positive integers greater than 1, which statement is not true?

A If x y, then 1 __ x 1 __ y .

B If x y, then 2x 2y.

C If x y, then �� x �

� y .

D If x y, then x2 y2.

2. If the variables x and y are related so that x2 y2, which statement must be true?

F The variable x is greater than the variable y.

G The variable y is greater than the variable x.

H The variable y is a negative number.

J It is not possible to determine which variable is greater.

3. Figure ABCD is a parallelogram and none of its angles has a measure of 90°. Which statement is NOT a valid conclusion?

B C

A D

A m�A � m�C

B 2(m�A) � 2(m�B ) � 360°

C m�C � m�D � 180°

D m�A � 180° � m�C

4. Which statement about the triangles below is true?

x x

x

7

7

77

7

F Exactly one of the triangles is an equilateral triangle.

G Only one of the triangles is not an equilateral triangle.

H All three of the triangles could be equilateral triangles.

J The perimeter of the right triangle is larger than the perimeter of the other two triangles.

5. Figure ABCD is a parallelogram whose diagonals are different lengths. Which statement is a valid conclusion?

A Figure ABCD must be a rectangle.

B Figure ABCD could be a rectangle.

C Figure ABCD could not be a rectangle.

D Figure ABCD could be a square.

Ready for TAKS?Benchmark Pre-Test (8.16)(B)10

OBJECTIVE

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3 R D P R I N T

Copyright © by Holt, Rinehart and Winston. 56 Holt Mathematics Grade 9All rights reserved.

Name Date Class

Ready for TAKS?Benchmark Post-Test (A.1)(A)1

OBJECTIVE

1. A relation exists between the number of buses needed for a school trip and the number of students going on the trip. In this relation, what is the dependent variable?

A the number of students going on the trip

B the number of parents going on the trip

C the number of buses

D the number of miles the bus must travel

2. The relation between the number of hours a plumber works, h, and the total amount he charges a customer, A, is given by the function A � 55h. In this relation, what is the dependent variable?

F the hourly charge, 55

G the number of hours worked, h

H the total amount the plumber charges, A

J the number of days worked, d

3. The table shows a relation between two variables, h and t. Which statement is the best description of the relationship between h and t?

h t

1 10

4 6

6 2

2 8

7 1

5 3

3 7

A As h increases, t increases.

B As h increases, t decreases.

C It does not appear that h is dependent on t.

D There is a linear relationship between h and t.

4. Which of the following relations is least likely to have an independent variable and a dependent variable?

F length of the paper, number of hours it takes to type a paper

G the measure of the circle’s radius, circumference of a circle

H the number of miles traveled on a trip, the price per gallon of gas purchased

J the number of hours worked, the total amount earned

5. The graph shows a function in which the variable y is the dependent variable. Which statement is the best description of the relation between x and y ?

y

x

20

18

16

14

12

10

8

6

4

2

–2

–2 2 4 6 8 10 12 14 16 18 20

A As x increases, y increases.

B As x increases, y decreases.

C As x increases, y increases at a constant rate.

D As x increases, y decreases at a constant rate.

AGA07_RTAKS09_056-060.indd 56AGA07_RTAKS09_056-060.indd 56 4/13/06 11:09:20 PM4/13/06 11:09:20 PM

3 R D P R I N T

Name Date Class

Copyright © by Holt, Rinehart and Winston. 57 Holt Mathematics Grade 9All rights reserved.

1OBJECTIVE

1. A middle school is purchasing new football helmets for their team. A sports equipment company quoted the following prices for the helmets.

Football Helmet Pricing

Number of helmets, h

Total cost, c ($)

5 100

10 175

20 325

30 475

Which function represents the relationship between the total cost, c, and the number of football helmets, h?

A c � 20h

B c � 10h � 50

C c � 15h

D c � 15h � 25

2. The graph shows the relationship between two variables, x and y. Which function represents this relationship?

y

x

10

8

6

4

2

2 4 6 8 10 12

F y � 9x H y � �2x � 9

G y � 2x � 9 J y � � 1 __ 2

x � 9

3. Which function could be used to describe the data set shown?

{(5, �1), (3, �3), (1, �5), (�1, �7)}

A y � x � 6 C y � � 1 __ 5

x

B y � x � 2 D y � x � 6

4. Which function represents the data set shown?

Domain

�2

�1

1

3

Range

3

0

8

F y � x 2 H y � x � 5

G y � x 2 � 1 J y � x � 1

5. The total amount paid, p, to enter an amusement park and ride the rides is shown in the table.

Number of rides ridden (r )

Total paid, p ($)

2 6.50

5 8.75

10 12.50

20 20.00

Which function represents the relationship between the total amount paid, p, and the number of rides ridden, r ?

A p � 3.25r

B p � r � 2.25

C p � 0.50r � 5.50

D p � 0.75r � 5.00

Ready for TAKS?Benchmark Post-Test (A.1)(B)

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3 R D P R I N T

Copyright © by Holt, Rinehart and Winston. 58 Holt Mathematics Grade 9All rights reserved.

Name Date Class

1OBJECTIVE

1. Sarah opened a checking account with her first summer paycheck, which was in the amount of $120. Each week she deposits $50 of her pay into the account. The table shows the balance in the account, b, after w weeks have passed. Which equation best describes the balance?

Checking Account Balance

Number of weeks, w

Balance, b

1 $170

2 $220

3 $270

4 $320

A b � 120 � 50 � w

B b � (120 � 50)w

C b � 120(50w)

D b � 120 � 50w

2. A company that makes signs charges $100 for a six-foot by three-foot sign. The company also charges $4 per word and $15 per graphic image to be included on the sign. Which equation best expresses the total cost of a sign, c, in terms of the number of words, w, and the number of graphic images, g ?

F c � 100 � 4w � 15g

G c � 100(4w � 15g )

H c � 4w � 15g

J c � 100 � (4w )(15g )

3. A pool and spa company is installing a child safety fence around a pool that is three times as long as it is wide. If the width of the pool is w feet, and the safety fence costs $12 per foot, which equation describes the price, p, of the fence?

A p � 8w

B p � 12(8w)

C p � 12(4w)

D p � 12(3w2)

4. A catering company charges $600 to cater an event for up to 25 people. The company charges $20 extra for each additional person that attends. Which equation best expresses the total charge to cater the event, c, in terms of the number of people who attend, p ?

F c � 600 � 20p

G c � 600 � (p � 25)

H c � 600 � 20(p � 25)

J c � 600 � p � 25

______ 20

5. The photographic club has $240 to spend on displaying its club members’ photos. Some of the photos will be framed and some will be mounted on photo boards. It costs $12 to frame a photo and $5 to mount a photo. Which inequality best expresses the number of photos that can be mounted, m, or framed, f ?

A m � f � 240

B 5m � 12f � 240

C 5m(12f ) � 240

D (5 � m)(12 � f ) � 240

Ready for TAKS?Benchmark Post-Test (A.1)(C)

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3 R D P R I N T

Name Date Class

Copyright © by Holt, Rinehart and Winston. 59 Holt Mathematics Grade 9All rights reserved.

1OBJECTIVE

1. The function f (x) � {(�3, 9), (�1, 3), (1, �3), (3, �9)} can be represented in a variety of different ways. Which of the following is NOT an accurate representation of f (x )?

A y � �3x with domain of {�3, �1, 1, 3}

B x � � y __

3 with range of {�9, �3, 3, 9}

C y

x

6

4

2

–2

–4

–6

–2–4–6–8 2 4 6 8

D Domain

�3

�1

1

3

Range

9

3

�3

�9

2. Which of the following does NOT represent a function?

F {(0, 0), (�2, 4), (2, 4), (�3, 6), (3, 6)}

G x �3 �2 0 2 3

y 6 4 0 4 6

H y � �2x

J y

x

6

4

2

–4

–6

–2–4–6 2 4 6

3. Which of the following equations does NOT represent a function?

A x � 2y � 4

B x 2 � 2y � 4

C 2x � y 2 � 4

D y � x 2 � 4

4. Identify the graph that best represents the relationship between the number of football tickets purchased at $20 per ticket and the total cost of the tickets.

F H

G J

5. A function is defined as follows: x is a natural number such that 0 � x � 3 and y is the square of x. Which of the following is a correct representation of the function?

A y � x 2 with domain of {1, 2, 3}

B f (x) � {(0,0), (1, 1), (2, 4), (3, 9)}

C Domain

123

Range

149

D y

x

6

4

2

–2

–4

–2 2 4 6 8

Ready for TAKS?Benchmark Post-Test (A.1)(D)

AGA07_TAKs_WBK09_056-060.indd 59AGA07_TAKs_WBK09_056-060.indd 59 9/6/06 8:18:01 PM9/6/06 8:18:01 PM

3 R D P R I N T

Copyright © by Holt, Rinehart and Winston. 60 Holt Mathematics Grade 9All rights reserved.

Name Date Class

1OBJECTIVE

1. The table shows the number of drops of a certain medicine used in a salt-water fish tank to cure “Ick.” If each bottle of the medicine has approximately 50 drops, what is the maximum number of gallons that can be treated with one bottle?

Ick Medicine Dosage

Number of Drops

Number of Gallons

5 10

25 50

40 80

A 25 gal

B 50 gal

C 100 gal

D 150 gal

2. The graph shows the total amount charged by a tailor who makes prom dresses. If the material for the dress costs $64, what is the hourly rate charged by the tailor?

c

h

250

200

150

100

1 2 3 4 5 6 7 8 9

F $25 per hr

G $50 per hr

H $64 per hr

J $75 per hr

3. Which is always a correct conclusion about the quantities in the function y � � x 2 , if x is an integer?

A As x increases, y increases.

B As x increases, y decreases.

C The variable y is always greater than the variable x.

D The variable y is always less than or equal to the variable x.

4. Sam’s weekly salary can be calculated using the formula s � 400 � 15(h � 40), where h represents the number of hours worked and h � 40 hours. In this formula, 400 most likely represents

F Sam’s hourly rate.

G Sam’s regular salary when he works no overtime.

H The amount Sam is paid when he works at least 15 hours.

J The amount Sam is paid when he works more than 40 hours.

5. The function f (h ) � 2.00h � 0.75(h � 4) represents the daily charge for parking at the beach where h � 2 hours of parking. The best interpretation of this function is that it costs

A the same $2 per hour rate for any number of hours parked.

B a $0.75 hourly rate for any hours parked over 4 hours.

C a $2.75 hourly rate for all hours parked up to 4 hours.

D a $2 per hour rate for the first 4 hours parked and an additional $0.75 per hour for hours parked over the first 4 hours.

Ready for TAKS?Benchmark Post-Test (A.1)(E)

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3 R D P R I N T

Name Date ClassName Date Class

Copyright © by Holt, Rinehart and Winston. 61 Holt Mathematics Grade 9All rights reserved.

1. Which of the functions is a linear function?

A 1 __ x � 2y � 3

B 1 __ 2 x � 4y � 5

C x 1 __ 2

� y � 6

D y � (x � 3)(x � 2)

2. Which is the best representation of the function y � �3x ?

F

�3

x

y

G

x

y

H

�3 x

y

J

�3

x

y

3. The graph of which function would pass through the points (�2, �8) and (2, �8)?

A y � 4x

B y � �4x

C y � �4 x 2

D y � �2 x 2

4. Which statement best describes the graph of y � �x ?

F a line with a slope of �1

G a vertical line that passes through x � �1

H a parabola that passes through (1, 1)

J an upside-down parabola whose vertex is at (1, �1)

5. The data in which table CANNOT be modeled using a linear function?

A x �5 �3 �1 1

y 3 1 �1 �3

B x 0 1 2 3

y 0 2 4 6

C x �2 0 1 2

y �4 0 1 4

D x 0 5 10 15

y 5 10 15 20

Ready for TAKS?Benchmark Post-Test (A.2)(A)2

OBJECTIVE

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3 R D P R I N T

Name Date Class

1. The booster club is raising money by selling tee-shirts. The function f (x ) � 8x describes the amount of money, in dollars, that the booster club will earn for selling x tee-shirts. What is the domain of the function?

A x � 0

B {0, 1, 2, 3, …}

C all integers

D all real numbers

2. The volume of a cube with sides of length x is given by the function f (x ) � x 3 . What is the most reasonable domain of f (x )?

F all real numbers

G all integers

H x � 0

J { �1, 2, �3}

3. The area of the rectangle is given by the function A � x 2 � 6x � 8.

x � 4

x � 2

What is the most complete and reasonable domain for this function?

A x � 0

B x � 2

C x � 4

D x � 8

4. What is the domain of the function graphed?

y

x

5

5

F {0, 2, 4}

G {�4, �2, 0, 2, 4}

H y � 0

J �4 � x � 4

5. What is the range of the function graphed?

y

x

–5

5

A all real numbers

B {… 1, 2, 3}

C x � 3

D y � 3

Copyright © by Holt, Rinehart and Winston. 62 Holt Mathematics Grade 9All rights reserved.

Name Date Class

Ready for TAKS?Benchmark Post-Test (A.2)(B)2

OBJECTIVE

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3 R D P R I N T

Name Date ClassName Date Class

Copyright © by Holt, Rinehart and Winston. 63 Holt Mathematics Grade 9All rights reserved.

1. The graph shows the monthly cost for cable TV service, including a flat fee and a per movie cost for certain channels. Which statement is true?

Co

st (

$)

50

40

30

1 32 5 64Number of Movies

A The per movie charge is $30.

B The flat fee per month is $30.

C The maximum charged per month is $30.

D A customer must rent at least 30 movies per month.

2. The graph shows how the balance of Jim’s savings account changed over time. Which statement is true?

Bal

ance

($)

300

250

200

150

100

50

2 64Number of Months

A Jim deposited $100 per month.

B Jim deposited $50 per month.

C Jim deposited $25 per month.

D Jim had $250 at the end of four months.

Use the graph to answer questions 3 and 4.

Hei

gh

t (f

t)

25

4

4 8Number of Seconds

3. The graph shows the height, in feet, of a toy rocket that is launched from a platform. Which statement is true?

F The platform is 8 feet tall.

G The maximum height of the toy rocket is 4 feet.

H The rocket hits the ground after 8 seconds.

J The rocket reaches its maximum height at 25 seconds.

4. What is the maximum height of the toy rocket?

A 3 ft

B 4 ft

C 8 ft

D 25 ft

Ready for TAKS?Benchmark Post-Test (A.2)(C)2

OBJECTIVE

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3 R D P R I N T

Name Date Class

1. The graph shows the price per gallon of gasoline during a period of several months. Which is a reasonable statement about the price of gas during this time period?

Pri

ce p

er G

allo

n (

$)

4.00

3.00

2.00

1 32 5 64Number of Months

A The price of gas consistently increased over the six-month period.

B The price of gas remained constant between months 3 and 4.

C The price of gas decreased more than it increased over the six-month period.

D The price of gas was at its highest in month 2.

2. The table shows the cost to cater a small wedding reception based on the number of people attending.

Number of Attendees

Cost ($)

25 500

30 575

35 650

40 725

45 800

Use the data to predict the cost to cater a reception if 60 people will be attending.

F $800 H $1,025

G $875 J $1,150

Use the scatter plot to answer questions 3�5.

Nu

mb

er o

fC

alo

ries

Grams of Fat

300

200

100

5 10 15 20

The scatter plot shows the number of calories and grams of fat per serving in some common foods. The line of best fit for the data is also shown.

3. Predict the approximate number of calories in a food that has 15 grams of fat.

A 150 C 250

B 200 D 300

4. Which statement best describes the relationship between the number of calories and the grams of fat?

F There does not appear to be any relationship between the calories and grams of fat.

G As the grams of fat increase, the number of calories increases.

H As the grams of fat increase, the number of calories decreases.

J The number of calories is approximately 25 times the grams of fat.

5. For each increase of 5 grams of fat, approximately how much will the number of calories increase?

A 50 C 150

B 100 D 300

Copyright © by Holt, Rinehart and Winston. 64 Holt Mathematics Grade 9All rights reserved.

Name Date Class

Ready for TAKS?Benchmark Post-Test (A.2)(D)2

OBJECTIVE

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3 R D P R I N T

Name Date ClassName Date Class

Copyright © by Holt, Rinehart and Winston. 65 Holt Mathematics Grade 9All rights reserved.

1. Which expression represents the change from a $50 bill when two items that each cost c dollars are purchased?

A 50 � c

B 50 � 2c

C 50 � c

D 50c

2. Martin has $180 in his checking account. If he makes 3 deposits of d dollars each, which expression represents the new balance in Martin’s account?

F 180 � 3d

G 180(3d )

H 180 � 3 � d

J 180 � 3d

3. The table represents the number of radios, r, that w workers can assemble in an hour.

Number of workers

Number of radios

1 7

2 14

3 21

4 28

Which equation can be used to model this relationship?

A r � 2(7)

B r � 7w

C r � 7 � w

D r � w 7

4. A painter began a paint job with 2,000 square feet to paint. If he painted 250 square feet per hour, which equation shows the number of square feet, f, remaining after h hours?

F f � 2000 � 250h

G f � 2000 � 250 � h

H f � 2000(250 � h)

J f � 2000 _____ 250h

5. A biology class is monitoring the growth of a bean sprout over several weeks time. The initial height of the bean sprout is 2 inches. The table shows the change in the sprout’s height over several weeks.

Number of Weeks

Height of Bean Sprout (in.)

0 2

1 2.5

2 3

3 3.5

4 4

Which equation represents the height, h, after w weeks have passed?

A h � w � 0.5

B h � 0.5w

C h � 2.5w

D h � 2 � 0.5w

Ready for TAKS?Benchmark Post-Test (A.3)(A)2

OBJECTIVE

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3 R D P R I N T

Name Date Class

1. According to the pattern shown, if n is the number of sides that a polygon has, which expression represents the sum of the measures of the interior angles?

Sum of Interior Angles

180° 360° 540° 720°

A 180n

B 180(2n)

C 180(n � 2)

D 180(n � 2)

2. The pattern shows the perimeter of a figure made from square tiles based on the number of tiles used.

P � 4 P � 6 P � 8

Which statement accurately describes this pattern if P represents the perimeter and t represents the number of tiles?

F P � t � 2

G P � t � 3

H P � 2t � 2

J P � 4t

3. The length of a rectangle is x � 5, and its width is x � 2. Which expression represents the perimeter of the rectangle?

A 2x � 3

B 4x � 6

C x 2 � 10

D x 2 � 3x � 10

4. A rectangle with an area of 6 x 2 � 8x � 2 is modeled below using algebra tiles.

Which expression gives the correct factorization for 6 x 2 � 8x � 2?

F (3x � 2)(2x � 1)

G (3x � 1)(2x � 2)

H (6x � 2)(x � 1)

J (6x � 1)(x � 2)

5. There are 52 white keys on a piano. The frequency of each key depends on the position of the key. The table shows the frequency of several key positions.

Key position Frequency

1 27.5

8 55

15 110

22 220

29 440

Which statement describes a pattern in the table?

A The frequency is 27.5 times the position of the key.

B As the position of the key increases by 7, the frequency increases by 27.5.

C As the position of the key increases by 1, the frequency doubles.

D As the position of the key increases by 7, the frequency doubles.

Copyright © by Holt, Rinehart and Winston. 66 Holt Mathematics Grade 9All rights reserved.

Name Date Class

Ready for TAKS?Benchmark Post-Test (A.3)(B)2

OBJECTIVE

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3 R D P R I N T

Name Date ClassName Date Class

Copyright © by Holt, Rinehart and Winston. 67 Holt Mathematics Grade 9All rights reserved.

1. If f (x ) � x 2 � 5x � 8, what is f (�3)?

A �14

B �2

C 1

D 16

2. What is the missing value in the function table?

x f (x ) � 3 � 6x

�4 27

�3 21

0 3

? �9

F 2

G 1

H �1

J �2

3. What expression represents the perimeter of the regular pentagon?

x � 4

A x � 20

B 5x � 20

C 6x � 24

D (x � 4 ) 5

4. What is the value of x in the equation 3x � 2 � �x � 14?

F 3

G 4

H 6

J 8

5. Which equation is equivalent to

y � � 1 __ 2

x � 3?

A y � x � 6

B x � 2y � �3

C x � 2y � �6

D x � 2y � �6

6. The rectangle has an area of x 2 � 2x � 24.

x � 4

Which expression represents the length of the rectangle?

F x � 20

G x � 6

H x � 6

J x � 20

Ready for TAKS?Benchmark Post-Test (A.4)(A)2

OBJECTIVE

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3 R D P R I N T

Name Date Class

1. Which real number property is illustrated by the equation (7 � 10x) � 2x � 7 � (10x � 2x)?

A Associative Property of Addition

B Commutative Property of Addition

C Distributive Property

D Additive Identity Property of 0

2. Which real number property is illustrated by the equation 2 x 2 (4x � 5) � 8 x 3 � 10 x 2 ?

F Commutative Property of Addition

G Associative Property of Addition

H Distributive Property

J Multiplicative Identity Property of 1

3. Which expression is equivalent to 12 x 2 � 4(8x � 2 x 2 )?

A 20 x 2 � 32x

B 4 x 2 � 32x

C 20 x 2 � 32x

D 20 x 4 � 32x

4. Which expression is equivalent to 12 x 2 � 6x � 1 � 2x � 9 x 2 � 5?

F 3 x 4 � 4 x 2 � 4

G 3 x 2 � 4x � 6

H 3 x 2 � 4x � 4

J 3 x 2 � 4x � 4

5. What is the perimeter of the quadrilateral?

3x � 4

2x � 3

2x

x � 5

A 7x � 2

B 8x � 2

C 4(8x � 2)

D 8 x 4 � 2

6. The table shows the factored form and the simplified form for several products.

Factored form Simplified form

(x � 4 ) 2 x 2 � 16

(x � 4)(x � 4) x 2 � 16

(x � 4)(x � 5) x 2 � x � 20

(4x � 1)(4x � 1) 16 x 2 � 1

Which product is NOT correctly simplified?

F (x � 4 ) 2

G (x � 4)(x � 4)

H (x � 4)(x � 5)

J (4x � 1)(4x � 1)

Copyright © by Holt, Rinehart and Winston. 68 Holt Mathematics Grade 9All rights reserved.

Name Date Class

Ready for TAKS?Benchmark Post-Test (A.4)(B)2

OBJECTIVE

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3 R D P R I N T

Name Date ClassName Date Class

Copyright © by Holt, Rinehart and Winston. 69 Holt Mathematics Grade 9All rights reserved.

1. Which function notation would represent the same relationship as the linear equation y � 5x � 7?

A f (x ) � x � 7 _____ 5

B f (x ) � 5(x � 7)

C 5f (x ) � x � 7

D f (x ) � 5x � 7

2. Which linear equation would represent the same relationship as the function f (x ) � �2(x � 3)?

F y � �2 _____ x � 3

G y � �2(x � 3)

H y � �2x � 3

J y � x � 3 _____ �2

3. The table shows several values generated by the function f (x ) � 5 � x 2 .

x f (x )

�1 4

0 5

1 4

2 1

Which equation represents the same relationship?

A y � 5 � x 2

B y � ��

5 � x

C y � (5 � x) 2

D y 2 � 5 � x

4. The line graphed is given by the equation y � 3x � 4.

y

x

6

4

2

–2

–4

–2 2 4 6 8

Which function would have the same graph?

F f (x ) � x � 4 _____ 3

G f (x ) � 3(x � 4)

H f (x ) � (x � 4) 3

J f (x ) � 3x � 4

5. A horticulture class monitored a growth pattern of a bean sprout for several weeks. The initial height of the sprout was 1.5 inches and the sprout grew 0.5 inches each week. The results can be represented by the function f (w ) � 1.5 � 0.5w, where w is the number of weeks that passed. Which equation represents the height, h, of the bean sprout after w weeks have passed?

A h � 1.5(1 � 0.5w)

B h � 0.5w ____ 1.5

C h � 1.5 � 0.5w

D h � 10.5(1.5 � w)

Ready for TAKS?Benchmark Post-Test (A.4)(C)2

OBJECTIVE

AGA07_RTAKS09_061-069.indd 69AGA07_RTAKS09_061-069.indd 69 4/13/06 11:09:38 PM4/13/06 11:09:38 PM

3 R D P R I N T

Name Date Class

1. Which situation can best be described by a linear function?

A the path of a ball that is shot upward from ground level with an initial velocity of 8 ft/s towards a basket

B the total cost, c, for a monthly gym membership and the number of months, m, that the person is a member

C the heart rate of a person running quickly for 5 minutes, resting for 20 minutes, and finally continuing to run for another 5 minutes

D the cost of each piece of fruit in a fruit basket

2. Which table represents a linear function?

F x 2 2 4 4

y �3 9 13 17

G x 0 2 4 6

y 5 4 0 4

H x 5 10 15 20

y 3 6 9 12

J x �4 �2 0 2

y 10 15 30 60

3. Which of the following situations could be represented by the linear function shown?

y

x

(1, 4)

(2, 8)8

7

6

5

4

3

2

1

1 2 3 4 5 6 7 8

A The amount of mold in a culture increases each day by four times the amount of the previous day’s increase.

B The area of a square can be approximated using the formula A � s 2.

C The number of a certain kind of insect is decreasing at a rate of 4 thousand insects per year.

D Each month a company’s profits are $4,000 greater than those of the previous month.

4. Which linear function includes the points (1, 3) and (�2, 6)?

F y � 3x

G y � x � 2

H y � x 2 � 2

J y � �x � 4

Copyright © by Holt, Rinehart and Winston. 70 Holt Mathematics Grade 9All rights reserved.

Name Date Class

Ready for TAKS?Benchmark Post-Test (A.5)(A)3

OBJECTIVE

AGA07_RTAKS09_070-078.indd 70AGA07_RTAKS09_070-078.indd 70 4/13/06 11:09:53 PM4/13/06 11:09:53 PM

3 R D P R I N T

Name Date ClassName Date Class

Copyright © by Holt, Rinehart and Winston. 71 Holt Mathematics Grade 9All rights reserved.

1. What is the equation of the line shown?

8

6

4

2

�2

�4

�2�4�6 2 4 6 x

y

A y � � 1 __ 2 x � 8

B y � 1 __ 2 x � 8

C y � 2x � 8

D y � �2x � 8

2. The table shows several points that lie on a given line. Which of the following could be the equation of the line?

x �1 0 2

y 3 0 �6

F y � x � 4 H y � 3x

G y � �3x J x � y � 0

3. Which linear equation is equivalent to

the equation y � � 1 __ 3 x � 5?

A x � 3y � 5 � 0

B x � 3y � 15 � 0

C x � 3y � 15 � 0

D x � 3y � 15 � 0

4. Which linear equation represents the statement “the value of y is 2 less than three times the value of x ”?

F 3y � x � 2

G 3y � 2 � x

H y � 3x � 2

J y � 2 � 3x

5. Which is the graph of the equation 2x � y � 3?

A 5

3

1

�1

�3

�5

531�1�3�5 x

y

B 5

3

1

�1

�3

�5

531�1�3�5 x

y

C 5

3

1

�1

�3

�5

5 x

y

31�1�3�5

D 5

3

1

�1

�3

�5

5 731�1�3 x

y

Ready for TAKS?Benchmark Post-Test (A.5)(C)3

OBJECTIVE

AGA07_RTAKS09_070-078.indd 71AGA07_RTAKS09_070-078.indd 71 4/13/06 11:09:53 PM4/13/06 11:09:53 PM

3 R D P R I N T

Name Date Class

1. What is the slope of the line whose equation is 4y � �5x � 12?

A �5

B �3

C � 5 __ 4

D � 4 __ 5

2. What is the slope of the line whose equation is 2y � 3x � x � 6?

F �1

G 2

H 3

J 4

3. What is the slope of the line whose graph is shown?

6

4

2

�2

�4

�6

�2�4�6 2 4 6

y

x

A �3

B 3

C 6

D 9

4. Which graph shows a line with slope 1 __ 3

?

F 5

3

1

�1

�3

�5

531�1�3�5 x

y

G 5

3

1

�1

�3

�5

531�1�3�5 x

y

H 5

3

1

�1

�3

�5

531�1�3�5 x

y

J 5

3

1

�1

�3

�5

531�1�3�5 x

y

5. Line a passes through each of the points in the table. What is the slope of line a ?

x �3 �3 �3

y �5 0 2

A �3 C 3 __ 5

B 0 D undefined

Copyright © by Holt, Rinehart and Winston. 72 Holt Mathematics Grade 9All rights reserved.

Name Date Class

Ready for TAKS?Benchmark Post-Test (A.6)(A)3

OBJECTIVE

AGA07_RTAKS09_070-078.indd 72AGA07_RTAKS09_070-078.indd 72 4/13/06 11:09:54 PM4/13/06 11:09:54 PM

3 R D P R I N T

Name Date ClassName Date Class

Copyright © by Holt, Rinehart and Winston. 73 Holt Mathematics Grade 9All rights reserved.

1. According to the graph, which statement best describes the relationship between x and y ?

x

y

A As x increases, y remains constant.

B As y increases, x remains constant.

C As x increases, y increases.

D As x increases, y decreases.

2. The slopes of two equations are given. Which pair represents the slopes of parallel lines?

F �10; �10 H �10; � 1 ___ 10

G 10; 1 ___ 10

J 10; �10

3. Which graph could represent a company’s profit if its profit over a year’s time remained constant for a few months, then decreased for a few months, then increased?

A C

B D

4. Jane’s summer reading list consisted of 30 short stories. She had 10 weeks in which to complete the assignment. The graph shows how many stories Jane had left to read at the end of each week.

2 4 6 8 10 12

30

Nu

mb

ero

f S

tori

es

Week

Which statement is the best interpretation of the x-intercept?

F Jane finished the assignment early.

G Jane had 12 stories to read at the end of the 10 weeks.

H Jane read 12 stories per week.

J Jane did not finish the assignment in the allotted time; it took her 12 weeks to finish reading all 30 stories.

5. A student brought a plant to class that she had been growing at home. The class monitored the plant’s growth for 6 weeks. The graph shows how the plant’s height changed over time.

3

1

2

Hei

gh

t (i

n.)

Time (wk)

Which statement is the best interpretation of the y-intercept?

A The plant grew 1.5 inches per week.

B The plant’s height was 1.5 inches when the student brought it to class.

C The plant was the tallest at the end of the 6-week period.

D The plant’s maximum height was 1.5 inches.

Ready for TAKS?Benchmark Post-Test (A.6)(B)3

OBJECTIVE

AGA07_RTAKS09_070-078.indd 73AGA07_RTAKS09_070-078.indd 73 4/13/06 11:09:54 PM4/13/06 11:09:54 PM

3 R D P R I N T

Name Date Class

1. The graphs of line n and line m are shown.

x

y6

4

2

–2

–4

–6

–6 –4 –2 2 4 6

Line n

x

y12

8

4

–4

–8

–12

–12 –8 –4 4 8 12

Line m

How does the graph of line n compare to the graph of line m ?

A The slope of n is less, but the y-intercept is greater.

B The slope of n is less and the y-intercept is less.

C The slope of n is greater and the y-intercept is greater.

D The slope of n is greater, but the y-intercept is less.

2. The graph of the function f (x ) � �2x � 3 is shown.

6

4

2

�2

�4

�6

�2�4�6 2 4 6

y

x

If the graph of f (x ) is shifted down 4 units, what would be the equation of the resulting function?

F f �(x ) � �2x � 1 H f �(x ) � �2x � 7

G f �(x ) � �2x � 1 J f �(x ) � �8x � 3

3. Line a is represented by the equation

y � � 1 __ 2

x � 3 and line b is represented

by the equation y � 1 __ 2 x � 3. Which

statement describes how line b is related

to line a ?

A Line b is a reflection of line a across the x-axis.

B Line b is a reflection of line a across the y-axis.

C Line b is a translation of line a 10 units left.

D Line b is a translation of line a 10 units down.

4. Line a is represented by the equation

y � 5x � 1. Line b has the same

y-intercept as line a, but has a slope

of 1 __ 5

. Which of the following statements

describes how line b is related to line a ?

F Line b is a translation of line a 1 unit down.

G Line b is a reflection of line a across the x-axis.

H Line b is a reflection of line a across the y-axis.

J None of the above

5. A line has the equation y � 3x � 7. If the slope of the line is doubled and 5 is added to the y-intercept, which equation represents the new line?

A y � 6x � 12

B y � 6x � 2

C y � 6x � 2

D y � 8x � 14

Copyright © by Holt, Rinehart and Winston. 74 Holt Mathematics Grade 9All rights reserved.

Name Date Class

Ready for TAKS?Benchmark Post-Test (A.6)(C)3

OBJECTIVE

AGA07_RTAKS09_070-078.indd 74AGA07_RTAKS09_070-078.indd 74 4/13/06 11:09:54 PM4/13/06 11:09:54 PM

3 R D P R I N T

Name Date ClassName Date Class

Copyright © by Holt, Rinehart and Winston. 75 Holt Mathematics Grade 9All rights reserved.

1. Which equation describes a line that passes through the point ( �5, �2) and has a slope of �3?

A y � �3x � 17

B y � �3x � 13

C y � �3x � 7

D y � �3x � 11

2. Which equation describes a line with a slope of �2 and a y-intercept of �5?

F x � 2y � �5

G 2x � y � �5

H 2x � y � �5

J 2x � y � 5

3. Which equation describes the line with an x-intercept of 4 and a y-intercept of �4?

A x � y � 4

B y � x � 4

C 4x � 4y � 0

D 4x � 4y � 1

4. Which equation describes the line whose graph is shown?

6

4

2

�2

�4

�6

�2�4�6 2 4 6

y

x

F y � �x � 2

G y � �x � 2

H y � x � 2

J y � x � 2

5. Which could NOT be the equation of the line whose graph is shown?

x

y

A y � � 1 __ 2

x � 2

B y � � 2 __ 3

x � 1

C y � 1 __ 2

x � 1

D x � y � 2

Ready for TAKS?Benchmark Post-Test (A.6)(D)3

OBJECTIVE

AGA07_RTAKS09_070-078.indd 75AGA07_RTAKS09_070-078.indd 75 4/13/06 11:09:55 PM4/13/06 11:09:55 PM

3 R D P R I N T

Name Date Class

1. If the line 5x � 3y � �15 were graphed, what would be the y-intercept?

A �5

B �3

C 0

D 3

2. If the line y � � 3 __ 4 x � 6 were graphed,

what would be the x-intercept?

F 8

G � 9 __ 2

H �6

J �8

3. What is the x-intercept of the line graphed?

6

4

2

�2

�4

�6

�2�4�6 2 4 6

y

x

A �5

B �1

C 0

D 5

4. The table shows several points that lie on a line. What would be the coordinates of the y-intercept of this line?

x y

�2 �3

�1 0

1 6

F (2, 0)

G (0, 2)

H (3, 0)

J (0, 3)

5. A small appliance company is testing a new iron. The temperature of the iron, in degrees Fahrenheit, is recorded every minute, m, from the time the iron is turned on. The table shows that the temperature increases according to a linear relationship.

Time (m)

Temperature (°F)

0 70

1 120

2 170

3 220

Let x represent the time in minutes and y represent the temperature in degrees Fahrenheit. If the linear relationship were graphed, what would be the y-intercept of the line?

A �70

B 0

C 50

D 70

Copyright © by Holt, Rinehart and Winston. 76 Holt Mathematics Grade 9All rights reserved.

Name Date Class

Ready for TAKS?Benchmark Post-Test (A.6)(E)3

OBJECTIVE

AGA07_RTAKS09_070-078.indd 76AGA07_RTAKS09_070-078.indd 76 4/13/06 11:09:55 PM4/13/06 11:09:55 PM

3 R D P R I N T

Name Date ClassName Date Class

Copyright © by Holt, Rinehart and Winston. 77 Holt Mathematics Grade 9All rights reserved.

1. The graph of a line is shown below. If the slope is divided in half and the y-intercept remains the same, which equation represents the new line?

6

4

2

�2

�4

�6

�2�4�6 2 4 6

y

x

A y � 2x � 6 C y � 4x � 3

B y � 2x � 3 D y � 4x � 6

2. The value of two stocks over a short period of time is represented by the graphs below.

100

Time

100

Time

Val

ue

Val

ue

Stock A Stock B

Which statement best describes the difference in the value of the two stocks?

F The value of Stock A decreased faster since the slope of the line is greater.

G The value of Stock B decreased faster since the slope of the line is greater.

H The value of the two stocks decreased at the same rate since the y-intercepts of the lines are the same.

J The value of the two stocks decreased at the same rate since the slopes of the lines are the same.

Use the information and the graph to answer questions 3�5.

An electrician charges a flat fee of $50 plus an hourly rate to make a house call. The graph shows the total cost for a job based on the flat fee and the number of hours to complete the job.

1

50

Co

st (

$)Number of Hours

2 3

(1, 90)

(2, 130)

(3, 170)

3. If the electrician changed his flat fee to $60, but kept his hourly rate the same, what would be the total charge for a job that took 3 hours?

A $190 C $170

B $180 D $100

4. If the electrician left his flat fee at $50, but changed his hourly rate to $45, what would be the total charge for a job that took 3 hours?

F $95

G $170

H $185

J $195

5. If the electrician changed his flat fee to $60 and changed his hourly rate to $45, what would be the total charge for a job that took 3 hours?

A $105 C $180

B $170 D $195

Ready for TAKS?Benchmark Post-Test (A.6)(F)3

OBJECTIVE

AGA07_RTAKS09_070-078.indd 77AGA07_RTAKS09_070-078.indd 77 4/13/06 11:09:55 PM4/13/06 11:09:55 PM

3 R D P R I N T

Name Date Class

1. An antique vases’ value increases according to the age of the vase. The table shows the value of the vase depending on its age.

Age (yr) Value (in $)

20 5,000

25 6,000

35 8,000

If the value of the vase continues to increase at the rate shown in the table, what will be the value of the vase when it is 50 years old?

A $9,000

B $10,000

C $11,000

D $12,000

2. The force that must be applied to push an object using a certain trolley varies directly with the weight of the object. If a force of 3.00 pounds is required to push an object that weighs 200 pounds, how much force is required to push an object that weighs 50 pounds?

F 0.075 lb

G 0.75 lb

H 7.5 lb

J 12.0 lb

3. Based on the given exchange rate for Mexican pesos on a certain day at the airport, Mr. Neely purchased a 1,080-peso box of cigars for 120 US dollars. At this same rate, what would a 1,620-peso box of cigars cost in US dollars?

A $140 C $175

B $160 D $180

4. A bicyclist is practicing for a 10-mile race. During a practice run, he traveled at a constant speed. His times and distances are shown in the table.

Time (min) Distance (m)

10 3

25 7.5

If the bicyclist continues to cycle at the same rate, approximately how long would it take him to complete the 10 miles?

F 25 min

G 30 min

H 33 min

J 40 min

5. The amount of blood in a person’s body varies directly with the person’s weight. The table shows several body weights and the approximate number of quarts of blood in those people’s bodies.

Weight (lb) Blood (qt)

200 6.25

160 5

140 4.375

Based on the data in the table, approximately how much blood would there be in a person’s body if the person weighs 100 pounds?

A 3.125 qt

B 3.25 qt

C 3.5 qt

D 3.725 qt

Copyright © by Holt, Rinehart and Winston. 78 Holt Mathematics Grade 9All rights reserved.

Name Date Class

Ready for TAKS?Benchmark Post-Test (A.6)(G)3

OBJECTIVE

AGA07_RTAKS09_070-078.indd 78AGA07_RTAKS09_070-078.indd 78 4/13/06 11:09:56 PM4/13/06 11:09:56 PM

3 R D P R I N T

Name Date ClassName Date Class

Copyright © by Holt, Rinehart and Winston. 79 Holt Mathematics Grade 9All rights reserved.

1. Mark’s house is on the corner of the block. Sandra’s house is 3 blocks north of Mark’s house. If Tina lives south of Mark and the distance from Tina’s house to Mark’s house is b blocks, which equation represents the total distance, d, from Tina’s house to Sandra’s house?

A d � 1 � 3

B d � b � 3

C d � b

D d � 3b

2. Krista is on the school gymnastics team. She has allotted a maximum of 45 minutes total each day to work on the balance beam and the parallel bars. Each balance beam routine, b, takes approximately 6 minutes. Each parallel bars routine, p, takes approximately 4 minutes. Which of the inequalities best represents the time Krista can spend practicing a combination of balance beam and parallel bars routines?

F b � p � 45

G 6b � 4p � 45

H 4b � 6p � 45

J 10(b � p) � 45

3. A submarine is hovering at 50 feet below sea level. If the submarine descends at a constant rate of 200 feet per minute, which equation could be used to determine t, the time in seconds it will take the submarine to reach 1,500 feet below sea level?

A 1500 � 200 � 50t

B 1500 � (200 � 50)t

C 1500 � 50 � 200t

D 1500 � 200(t � 50)

4. Mr. Yancey puts out ears of corn each day for the squirrels in his yard. The table shows the number of squirrels that Mr. Yancey saw on onr day compared to the number of ears of corn he put out.

Ears of Corn

Number of Squirrels

2 1

3 4

4 7

5 10

Which equation best describes the relationship between e, the number of ears of corn, and s, the number of squirrels?

F s � e � 1 H s � 2e � 3

G s � e � 3 J s � 3e � 5

5. Yolanda’s parents gave her $150 to buy several outfits for summer camp. She needs shorts, tee-shirts, and socks. The table shows the price of each item.

Items Price

Shorts $15 per pair

Tee-shirts $10 each

Socks $2 per pair

Which inequality best describes the total number of shorts, s, tee-shirts, t, and socks, k, that can be purchased for $150 or less?

A s � t � k � 150

B 15s � 10t � 2k �150

C 27(s � f � b) � 150

D stk � 150

Ready for TAKS?Benchmark Post-Test (A.7)(A)4

OBJECTIVE

AGA07_RTAKS09_079-082.indd 79AGA07_RTAKS09_079-082.indd 79 4/13/06 11:10:11 PM4/13/06 11:10:11 PM

3 R D P R I N T

Name Date Class

1. A student is solving the equation 4 � x � 9x � x. Which of the following strategies would be the best way to start this problem?

A Add x to both sides of the equation.

B Subtract x from both sides of the equation.

C Divide both sides of the equation by 9.

D Divide both sides of the equation by 4.

2. What is the value of y if (�2, y ) is a solution to the equation 4x � 3y � 10?

F �6

G � 2 __ 3

H 1

J 21

3. Each of the points on the line is a solution to the equation x � 2y � �2.

y

x(0, 1)

(x, –1)

(2, 2)

What is the missing value of x?

A �5

B �4

C �3

D �2

4. The table shows several solutions to the equation 4x � 3y � 24.

x y

0 8

6 0

3 y

What is the missing value of y?

F 3

G 4

H 8

J 12

5. What is the unknown number in the statement “the product of 6 and a number, increased by 3, is 27?”

A 4

B 5

C 18

D 24

6. Sara’s front fender and hood were both damaged. The car dealership charged Sara $1,280 for parts and $60 per hour to install and paint them. The total charge was $1,640. How long did it take to install and paint the new parts?

F 3 hours

G 4 hours

H 5 hours

J 6 hours

Copyright © by Holt, Rinehart and Winston. 80 Holt Mathematics Grade 9All rights reserved.

Name Date Class

Ready for TAKS?Benchmark Post-Test (A.7)(B)4

OBJECTIVE

AGA07_RTAKS09_079-082.indd 80AGA07_RTAKS09_079-082.indd 80 4/13/06 11:10:12 PM4/13/06 11:10:12 PM

3 R D P R I N T

Name Date ClassName Date Class

Copyright © by Holt, Rinehart and Winston. 81 Holt Mathematics Grade 9All rights reserved.

1. The cost of hiring a certain local band is described by the function f (x ) � 40x � 50, in which f (x ) is the cost, and x is the time in hours the band is scheduled to play. If the entertainment committee for the high school dance has $300 to spend on music, what is the maximum number of full hours for which it can hire the band?

A 4

B 5

C 6

D 7

2. The pep club at a local high school is trying to raise money for a new school banner by holding several bake sales. Every Friday, the members of the club make cookies, brownies, rice-cereal treats, or cupcakes. They decide to charge $0.75 for each item. If the banner costs $120, including tax, how many items must they sell?

F 16

G 100

H 160

J 1,000

3. Maria purchased x hair scrunchies at $2 each and y barrettes at $3.50 each. She spent less than $25, not including tax. The number of items she purchased can be described by the linear inequality 2x � 3.5y � 25. If Maria purchased 6 scrunchies, what is the maximum number of barrettes she could have purchased?

A 4 C 2

B 3 D 1

4. The graph of the linear inequality 5x � 2y � 10 is shown below.

12

8

4

�4

�8

�12

�4�8�12 4 8 12

y

x

Which point is in the solution set to the inequality 5x � 2y � 10?

F (3, 1)

G (2, 3)

H (0, 4)

J (1, 3)

5. The graph of the linear equation

y � 1 __ 2

x � 6 is shown below.

12

8

4

�4

�8

�12

�4�8�12 4 8 12

y

x

Which point is not in the solution set of

y � 1 __ 2

x � 6?

A (1, �7) C (0, �4)

B (4, �3) D (�2, �6)

Ready for TAKS?Benchmark Post-Test (A.7)(C)4

OBJECTIVE

AGA07_RTAKS09_079-082.indd 81AGA07_RTAKS09_079-082.indd 81 4/13/06 11:10:12 PM4/13/06 11:10:12 PM

3 R D P R I N T

Name Date Class

1. Jeremy has a total of 56 books in two categories. The number of his classic novels is 8 more than the number of his mysteries. Which system of equations can be used to find the number of classic novels, n, and the number of mysteries, m, Jeremy has?

A n � m � 8 C n � 8 � mn � m � 56 n � m � 56

B n � m � 8 D n � m � 8n � m � 56 n � m � 56

2. Ms. Windham picked up coffee and dessert for her committee meeting. All together, she bought 32 items. She bought three times as many coffees as desserts. Which system of equations can be used to find the number of coffees, c, and the number of desserts, d, that she bought?

F c � d � 32 H c � d � 32

d � c __ 3 c � 3d

G c � 32 � d J c � d � 32d � 3c c � 3d

3. The length of a rectangle is 10 units more than twice the width. Which system of equations can be used to find the dimensions of the rectangle if the perimeter is 68 inches?

A � � w � 68� � 10 � 2w

B 2w � 68 � 2�w � 2� � 10

C 2(� � w ) � 68� � 10 � 2w

D 2(� � w ) � 68w � 2� � 10

4. The diagram below shows two supplementary angles. The measure of the larger angle, y, is 20° more than three times the measure of the smaller angle, x. Which system of equations can be used to find the measure of each angle?

x°y°

F x � y � 180 H x � y � 180y � 20 � 3x y � 3x � 20

G x � y � 180 J x � 180 � yx � 20 � 3y x � 3y � 20

5. The table shows the number of tacos and drinks a taco stand sold on two consecutive days, along with the total sales for the day.

Day 1 Day 2

Tacos 42 38

Drinks 18 20

Total Sales $55.50 $53.00

If the price of a taco is represented by t, and the price of a drink is represented by d, which system of equations can be used to determine t and d ?

A t � d � 6042t � 18d � 55.5

B t � d � 5838t � 20d � 53

C 42t � 18d � 55.538t � 20d � 53

D t � d � 60t � d � 108.5

Copyright © by Holt, Rinehart and Winston. 82 Holt Mathematics Grade 9All rights reserved.

Name Date Class

Ready for TAKS?Benchmark Post-Test (A.8)(A)4

OBJECTIVE

AGA07_RTAKS09_079-082.indd 82AGA07_RTAKS09_079-082.indd 82 4/13/06 11:10:12 PM4/13/06 11:10:12 PM

3 R D P R I N T

Name Date ClassName Date Class

Copyright © by Holt, Rinehart and Winston. 83 Holt Mathematics Grade 9All rights reserved.

1. How do the graphs of the functions f (x ) � x2 � 3 and g (x ) � x2 � 10 relate to each other?

A The graph of f (x ) is 3 units to the left of the graph of g (x ).

B The graph of f (x ) is 13 units to the left of the graph of g (x ).

C The graph of f (x ) is 3 units below the graph of g (x ).

D The graph of f (x ) is 13 units below the graph of g (x ).

2. If the graph of f (x ) � x2 � 7 is shifted down 8 units, which function represents the new graph?

F f (x ) � x2 � 8

G f (x ) � x2 � 1

H f (x ) � (x � 8)2 � 7

J f (x ) � (x � 8)2 � 7

3. The graph shows the function f (x ) � x2 � 4.

6

4

2

�2

�4

�6

�2�4�6 2 4 6

y

x

Which statement describes the shift in the vertex of the parabola if, in the function, �4 is changed to �1?

A 5 units up C 5 units down

B 3 units up D 3 units down

4. If the vertex of the parabola whose equation is f (x ) � x2 � 2 is (0, �2), what is the vertex of that parabola when it has been shifted up 4 units?

F (4, �2)

G (0, 4)

H (0, 2)

J (4, 2)

5. When graphed, which function would appear to be shifted 3 units down from the graph of f (x ) � x2 � 1?

y

x

A f (x ) � x2 � 2

B f (x ) � x2 � 2

C f (x ) � x2 � 3

D f (x ) � x2 � 4

Ready for TAKS?Benchmark Post-Test (A.9)(C)5

OBJECTIVE

AGA07_RTAKS09_083-090.indd 83AGA07_RTAKS09_083-090.indd 83 4/13/06 11:10:26 PM4/13/06 11:10:26 PM

3 R D P R I N T

Name Date Class

1. Which expression represents the area of the square shown?

5x3y5

A 5x6y10

B 5x9y25

C 25x6y10

D 25x9y25

2. Which expression is equivalent to

5x6y4 ________

35x�2y12 ?

F 3x8 ___

y8

G 1 _____ 7x3y3

H x8 ___

7y3

J x8 ___

7y8

3. Which expression is equivalent to

(8x12)(5x4)

_________ 4x2

?

A 10x 24

B 10x14

C 10x 8

D 5x 8

4. The area of the rectangle shown is 36m6n10 square units. If the length of the rectangle is 9m3n2 units, how many units wide is the rectangle? (m � 0 and n � 0)

9m3n2

F 45m9n12

G 27m3n8

H 4m3n8

J 4m2n5

5. The table shows several values of r and s.

r s

2x2 8x6

3x3 27x9

4x4 64x12

Which of these best describes the relationship between r and s?

A s � r 3

B s � 3r 3

C s � 4r 2

D s � 3 �� r

Copyright © by Holt, Rinehart and Winston. 84 Holt Mathematics Grade 9All rights reserved.

Name Date Class

Ready for TAKS?Benchmark Post-Test (A.11)(A)5

OBJECTIVE

AGA07_RTAKS09_083-090.indd 84AGA07_RTAKS09_083-090.indd 84 4/13/06 11:10:27 PM4/13/06 11:10:27 PM

3 R D P R I N T

Name Date ClassName Date Class

Copyright © by Holt, Rinehart and Winston. 85 Holt Mathematics Grade 9All rights reserved.

1. �TUV is similar to �XYZ.

T V X Z

Y

U

6 104

5

Which scale factor was used to transform �TUV to �XYZ?

A 1 __ 2 C 3 __

2

B 2 __ 3 D 2

2. The rectangle in the graph is to be

dilated by a scale factor of 1 __ 3

and has the

origin as the center of dilation. What will

be the coordinates of the new top, left

corner of the rectangle?

8

4

�4

�8

�12

�4�8�12 4A B

CD

12

y

x

F (0, 4) H (3, 4)

G (3, 0) J (3, 12)

3. �LMN has vertices L(�2, 6), M(4, 8)

and N(�4, 4). �LMN is dilated by

a factor of 1 __ 2 and has the origin as

the center of dilation. What are the

coordinates of L�?

A (�1, 3) C (�2, 2)

B (2, 4) D (�4, 12)

4. A photo reproduction company can enlarge or reduce photos proportionately. Which would be an enlargement or reduction of the photo?

2.5 cm

10 cm

F 1.25 cm

5 cm

H 8.75 cm

21 cm

G 0.5 cm

1.2 cm

J 3.75 cm

9 cm

5. If Figure B is a dilation of Figure A and has the origin as the center of dilation, what reduction factor would used to arrive at Figure B from Figure A?

12

8

4

�8

�12

�8�12 4 8 12

Figure A

Figure B

y

x

A 1 __ 3

C 2

B 1 __ 2

D 3

Ready for TAKS?Benchmark Post-Test (8.6)(A)6

OBJECTIVE

AGA07_RTAKS09_083-090.indd 85AGA07_RTAKS09_083-090.indd 85 4/13/06 11:10:27 PM4/13/06 11:10:27 PM

3 R D P R I N T

Name Date Class

1. Triangle EFG is shown. If this triangle is reflected across the y-axis, what will be the coordinates of the vertices for the image E �F �G �?

12

8

4

�4

�8

�12

�4�8�12 4E

F

G

12

y

x

A {E �(6, 0), F �(9, 3), G �(�3, 6)}

B {E �(�6, 0), F �(9, �3), G �(�3, �6)}

C {E �(�6, 0), F �(�9, �3), G �(3, �6)}

D {E �(0, �6), F �(3, �9), G �(6, 3)}

2. If a point (x, y ) is reflected across the x-axis, what will be the coordinates of the point’s image?

F (y, x ) H (�x, y )

G (�x, �y ) J (x, �y )

3. Trapezoid ABCD is translated so that D is mapped to D �.

6

4

2

�2

�4

�6

�2�4�6 2

C

A

BD�

D 64

y

x

Which coordinate pair best represents A �?

A (�3, 1) C (�5, 6)

B (�2, 2) D (5, �1)

4. Triangles DEF and D �E �F � are shown on the coordinate plane.

6

2

�2

�4

�6

�2�4�6 2

F

D

F�

D�

E�E

64

y

x

Which is the best description of the transformation used to arrive at D �E �F � from DEF?

F reflection across the x-axis

G reflection across the y-axis

H translation to the right 4 units

J translation to the left 4 units

5. At what coordinates should vertex G be placed to create a quadrilateral EFGH that is similar to quadrilateral ABCD?

20

18

16

14

12

10

8

6

4

2A

B

D

C

E H

4 6 8 20181614121020

y

x

F

A (24, 24) C (24, 4)

B (24, 16) D (6, 16)

Copyright © by Holt, Rinehart and Winston. 86 Holt Mathematics Grade 9All rights reserved.

Name Date Class

Ready for TAKS?Benchmark Post-Test (A.6)(B)6

OBJECTIVE

AGA07_RTAKS09_083-090.indd 86AGA07_RTAKS09_083-090.indd 86 4/13/06 11:10:28 PM4/13/06 11:10:28 PM

3 R D P R I N T

Name Date ClassName Date Class

Copyright © by Holt, Rinehart and Winston. 87 Holt Mathematics Grade 9All rights reserved.

1. A portion of parallelogram TUVW is shown on the grid below.

10

6

2

�2

�6

�10

�6�10 2 6 10

y

x

T U

V

At what coordinates should vertex W be placed to make

_ TW parallel to

_ UV in

order to complete parallelogram TUVW?

A (�4, �1)

B (�5, �2)

C (�4, �3)

D (�7, �2)

2. Which point on the grid below satisfies the conditions x � 2.5 and y � �1.5?

5

3

1

�1

�3

�5

�3�5 1 3 5

y

x

A

B

C

D

F Point A

G Point B

H Point C

J Point D

3. If a circle has center (2, 4) and radius 5 units, in which quadrant(s) does the circle lie?

A I only

B I and II

C I, II, and III

D I, II, III, and IV

4. Triangle JKL has coordinates J(7, 4), K(�3, 2), and L(2, 1). What will be the new coordinates of point L� if the triangle is translated 3 units to the left and 4 units up?

y

x

F (6, �2)

G (5, 5)

H (4, 8)

J (�1, 5)

5. The vertices of a triangle are (8, 2), (3, 4), and (6, �3). If the triangle is reflected across the y-axis, what will be the coordinates of the lowest vertex?

A (�6, �3)

B (�3, �4)

C (�8, �2)

D (�3, �6)

Ready for TAKS?Benchmark Post-Test (8.7)(D)6

OBJECTIVE

AGA07_RTAKS09_083-090.indd 87AGA07_RTAKS09_083-090.indd 87 4/13/06 11:10:28 PM4/13/06 11:10:28 PM

3 R D P R I N T

Name Date Class

1. The drawing shows a rectangular prism whose dimensions are 3 � 3 � 7.

Which best represents the shape of the solid when viewed from the right side?

A square C rhombus

B rectangle D parallelogram

2. Which of the following shapes could not be the bottom view of a pyramid?

F square H triangle

G rectangle J circle

3. Which of the following is the top view of the three-dimensional solid shown?

Front Right

A C

B D

4. Below is a three-dimensional view of a structure built with cubes.

Front Right

Which of the following could be the correct top view of the structure along with the number of cubes in each column of the structure?

F 3 3 2

3 3 1

H 1 3 2

3 3 1

G 4 3 2

3 3 1

J 3 1

3 3 2

5. The drawing shows a cone.

Which best represents the shape of the solid when viewed from the side?

A C

B D

Copyright © by Holt, Rinehart and Winston. 88 Holt Mathematics Grade 9All rights reserved.

Name Date Class

Ready for TAKS?Benchmark Post-Test (8.7)(A)7

OBJECTIVE

AGA07_RTAKS09_083-090.indd 88AGA07_RTAKS09_083-090.indd 88 4/13/06 11:10:28 PM4/13/06 11:10:28 PM

3 R D P R I N T

Name Date ClassName Date Class

Copyright © by Holt, Rinehart and Winston. 89 Holt Mathematics Grade 9All rights reserved.

1. A 20- by 30-foot rectangular greenhouse roof will be covered by glass panels that measure 4 feet on each side. If the panels are not cut, how many of them will be needed to cover the roof?

A 25

B 100

C 38

D 600

2. A pool company is filling a display pool with water. If it is a round pool with diameter 12 feet and height 4 feet, which geometric formula should the pool company use to determine how much water they need?

F C � 2�(6)

G A � �(6)2

H V � (6)(6)(4)

J V � �(6)2(4)

3. A landscaper wants to buy enough mulch to cover the plot shown below. If each bag of mulch will cover 30 square feet, how many bags of mulch does the landscaper need?

60 ft

40 ft

50 ft50 ft

A 40 bags

B 80 bags

C 160 bags

D 1200 bags

4. Mrs. Choo is replacing the floor in her kitchen. The plans for her house use a

scale factor in which 1 __ 5

inch equals 1 foot.

If the plans indicate that her kitchen is 2 inches by 2.5 inches, what are the actual dimensions of the room?

F 6.5 ft by 10 ft

G 8 ft by 10 ft

H 10 ft by 12 ft

J 10 ft by 12.5 ft

5. The Hollisters want to put a dog house in one corner of their yard. The yard is in the shape of a triangle as shown.

80 ft 75 ft

160 ft

House

If they decide to put the dog house in the corner with the largest angle, where should the dog house be put?

A In the corner of the lot opposite the side that is 75 feet.

B In the corner of the lot opposite the side that is 80 feet.

C In the corner of the lot opposite the side that is 160 feet.

D In the center of the triangular lot.

Ready for TAKS?Benchmark Post-Test (8.7)(B)7

OBJECTIVE

AGA07_RTAKS09_083-090.indd 89AGA07_RTAKS09_083-090.indd 89 4/13/06 11:10:29 PM4/13/06 11:10:29 PM

3 R D P R I N T

Name Date Class

1. Based on the visual representation of the triangle below, which of the following are most likely the triangle’s dimensions?

A 0.75, 1, 1.25

B 3, 6, 10

C 6, 11, 17

D 7.2, 8, 16

2. Use the Pythagorean Theorem to determine which figure is a right triangle.

F

13

14

21

G 20 15

25

H

62

43

75

J 18

2413

3. The coordinate grid below shows three squares.

y

x

A

O B

If the distance from A to B is 5 units and the distance from O to B is 4 units, what is the perimeter of the smallest square?

A 3 unit2

B 9 unit2

C 12 unit2

D 16 unit2

4. The drawing below represents directions on a standard map.

N

S

EW

NW NE

SESW

Which of the following pairs of directions would meet at a right angle?

F due N and due W

G due W and due E

H due E and 45° SW

J 45° NE and 45° SW

Copyright © by Holt, Rinehart and Winston. 90 Holt Mathematics Grade 9All rights reserved.

Name Date Class

Ready for TAKS?Benchmark Post-Test (8.7)(C)7

OBJECTIVE

AGA07_RTAKS09_083-090.indd 90AGA07_RTAKS09_083-090.indd 90 4/13/06 11:10:29 PM4/13/06 11:10:29 PM

3 R D P R I N T

Name Date ClassName Date Class

Copyright © by Holt, Rinehart and Winston. 91 Holt Mathematics Grade 9All rights reserved.

1. A safe has dimensions 12 in. � 8 in. � 18 in. What is the surface area of the safe?

A 76 in2 C 912 in2

B 456 in2 D 1,728 in2

2. The bottom of a fish tank has dimensions 30 in. by 14 in. The depth of the tank is 24 in. everywhere. A net of the tank is shown below.

14 in30 in.

24 in.

.

What is the surface area of the fish tank?

F 136 in2 H 2,952 in2

G 2,532 in2 J 10,080 in2

3. The net of a triangular prism is shown along with its approximate dimensions.

4.3 cm

12 cm

5 cm

What is the approximate total surface area of the prism?

A 258 cm2 C 190.75 cm2

B 201.5 cm2 D 70.75 cm2

The net of a cylinder is shown below. Use the net to answer questions 4 and 5.

2.75 in.

1.125 in.

in.78

in.78

4. Which formula could be used to find the surface area of the cylinder?

F SA � 2�r 2 � 2�rh

G SA � 2�(r 2 � rh)

H SA � 2�r (h � r 2)

J SA � �r 2(2r � 2h)

5. Use a ruler to measure the dimensions of the cylinder to the nearest eighth of an inch. Which of the following BEST represents the total surface area of the cylinder?

A 1.4 in2

B 3.7 in2

C 4.3 in2

D 8.8 in2

Ready for TAKS?Benchmark Post-Test (8.8)(A)8

OBJECTIVE

AGA07_RTAKS09_091-097.indd 91AGA07_RTAKS09_091-097.indd 91 4/13/06 11:10:42 PM4/13/06 11:10:42 PM

3 R D P R I N T

Name Date Class

1. The net of a cube is shown below. Use a ruler to measure the dimensions of the cube to the nearest eighth of an inch.

What is the approximate volume, in cubic inches, of the cube to the nearest eighth?

A 1 __ 8 in3 C 3 __

4 in3

B 1 __ 4 in3 D 1.5 in3

2. A rectangular prism with sides of length �, w, and h is topped by a pyramid whose height is the same as that of the prism. Which formula can be used to find the volume of the composite solid?

F V � 1 __ 3 �wh

G V � 2 __ 3 �wh

H V � 4 __ 3 �wh

J V � 2�wh

3. A water filtration company has a storage tank that is in the shape of a cylinder. The base of the tank has a diameter of 150 feet and the tank is 20 feet tall. Which formula could be used to find the amount of water needed to fill the tank?

A V � 2�(75)(20) � 2�(75)2

B V � �(150)2(20)

C V � �(75)2(20)

D V � �(20)2(75)

4. A right triangular prism is shown below.

13 in.

20 in.

12 in.5 in.

What is the volume of the prism?

F 15,600 in3

G 1,200 in3

H 660 in3

J 600 in3

5. A lumberyard stores its sawdust in a conical pile. If the base of the pile has a diameter of 24 feet and the pile is 10 feet tall, what is the approximate volume of the sawdust?

A 1,256 ft3

B 1,507 ft3

C 4,522 ft3

D 6,029 ft3

Copyright © by Holt, Rinehart and Winston. 92 Holt Mathematics Grade 9All rights reserved.

Name Date Class

Ready for TAKS?Benchmark Post-Test (8.8)(B)8

OBJECTIVE

AGA07_RTAKS09_091-097.indd 92AGA07_RTAKS09_091-097.indd 92 4/13/06 11:10:43 PM4/13/06 11:10:43 PM

3 R D P R I N T

Name Date ClassName Date Class

Copyright © by Holt, Rinehart and Winston. 93 Holt Mathematics Grade 9All rights reserved.

1. A rectangular aquarium is shown below.

3 ft

2 ft4 ft

If the sides and the floor of the aquarium are all glass, how much glass is needed to build an aquarium with these dimensions?

A 52 ft2

B 44 ft2

C 36 ft2

D 24 ft2

2. The volume of the cone shown below is 56 cubic units.

8

Which of the following is a reasonable estimate for the radius of the cone?

F 6.7 units H 1.5 units

G 2.6 units J 0.9 unit

3. If the volume of a cylindrical can is 100 in3 and its height is 5 in., what is the approximate radius of the can?

A 20 in.

B 6.4 in.

C 4.5 in.

D 2.5 in.

4. The volume of the cone shown is approximately 75 cubic centimeters. What is the approximate volume of the cylinder?

d d

h h

F 675 cm3

G 225 cm3

H 150 cm3

J 75 cm3

5. Which of the following is a reasonable estimate for the surface area of the cube shown?

7.008 cm

A 343 cm2

B 294 cm2

C 84 cm2

D 49 cm2

Ready for TAKS?Benchmark Post-Test (8.8)(C)8

OBJECTIVE

AGA07_RTAKS09_091-097.indd 93AGA07_RTAKS09_091-097.indd 93 4/13/06 11:10:43 PM4/13/06 11:10:43 PM

3 R D P R I N T

Name Date Class

1. A boat rower leaves the dock and rows 4 km due south. The rower then rows 4 km due west. Approximately how far is the rower from the dock?

Rower

Dock

A 6 km

B 8 km

C 16 km

D 32 km

2. A tree broke during a hurricane leaving a 4-foot stump. The top of the tree came to rest 27 feet away from the stump. How tall was the tree originally?

4 ft

27 ft

F 7 ft

G 23 ft

H 27 ft

J 31 ft

3. A fire truck parks 15 feet away from a building that is on fire. The fire truck extends its 30-foot ladder completely. How far up the building from the truck’s roof does the ladder reach?

A 15 ft

B 26 ft

C 34 ft

D 45 ft

4. The Warren’s yard is in the shape of a right triangle as shown below.

52 ft 76 ft

House

The Warrens want to plant shrubs around their entire yard. The shrubs need to be 4 feet apart. Approximately how many shrubs do they need?

F 55

G 64

H 92

J 220

5. An artist wants to paint a square design in a round window that has a diameter of 24 inches. What is the largest square design, that will fit in the window? Round your answer to the nearest whole number dimensions.

A 34 in. × 34 in.

B 17 in. × 17 in.

C 12 in. × 12 in.

D 5 in. × 5 in.

Copyright © by Holt, Rinehart and Winston. 94 Holt Mathematics Grade 9All rights reserved.

Name Date Class

Ready for TAKS?Benchmark Post-Test (8.9)(A)8

OBJECTIVE

AGA07_RTAKS09_091-097.indd 94AGA07_RTAKS09_091-097.indd 94 4/13/06 11:10:43 PM4/13/06 11:10:43 PM

3 R D P R I N T

Name Date ClassName Date Class

Copyright © by Holt, Rinehart and Winston. 95 Holt Mathematics Grade 9All rights reserved.

1. Two similar triangles are shown below.

16 cm 14 cm11 cm s

Use the dimensions given to find the approximate length of the side labeled s.

A 20.4 cm

B 12.6 cm

C 9.6 cm

D 9 cm

2. In the figure below, �ABC is similar to �DEF.

B

A C

D F

E

4 6

9

12

What is the length of _

EF ?

F 27 H 14

G 18 J 2

3. In a scale model of a new bridge, 1 inch represents 10 feet. The actual bridge will be 75-feet tall. Which proportion can be used to determine h, the height of the scale model?

A 1 ___ 75

� 10 ___ h C 10 ___

1 � h ___

75

B 1 ___ 10

� 75 ___ h D 1 ___

10 � h ___

75

4. The cones below are similar. What is the radius of cone A?

18A24

32

B

F 12 units

G 21.3 units

H 24 units

J 27 units

5. Parallelogram RSTU has the dimensions shown.

50 in.

35 in.

Which set of dimensions would produce a similar figure?

A 17.5 in. by 25 in.

B 17.5 in. by 100 in.

C 35 in. by 25 in.

D 70 in. by 150 in.

Ready for TAKS?Benchmark Post-Test (8.9)(B)8

OBJECTIVE

AGA07_RTAKS09_091-097.indd 95AGA07_RTAKS09_091-097.indd 95 4/13/06 11:10:44 PM4/13/06 11:10:44 PM

3 R D P R I N T

Name Date Class

1. The two quadrilaterals shown are similar. The scale of the two quadrilaterals is 1: 4. The perimeter of the smaller quadrilateral is 44 centimeters.

What is the perimeter of the larger quadrilateral?

A 2.75 cm

B 11 cm

C 176 cm

D 704 cm

2. Describe the change in the radius of a circle when the area of the circle is multiplied by 16.

F The radius is reduced by 1 __ 4 .

G The radius remains constant.

H The radius is increased sixteen times.

J The radius is increased four times.

3. The length of the sides of a square are 4 times the length of the sides of a smaller square. If the area of the larger square is 192 in2, what is the area of the smaller square?

A 3 in2

B 12 in2

C 48 in2

D 768 in2

4. Rectangle MNOP has a perimeter of 22 cm. The dimensions of the rectangle are tripled to form rectangle TUVW.

M N

P O

T U

W V

9 cm

What is the length of rectangle TUVW?

F 24 cm

G 48 cm

H 66 cm

J 90 cm

5. The radius of circle P is 5 times the radius of circle O.

O

P

What is the ratio of the circumference of circle P to the circumference of circle O ?

A 1 to 5

B 5 to 1

C 25 to 1

D 125 to 1

Copyright © by Holt, Rinehart and Winston. 96 Holt Mathematics Grade 9All rights reserved.

Name Date Class

Ready for TAKS?Benchmark Post-Test (8.10)(A)8

OBJECTIVE

AGA07_RTAKS09_091-097.indd 96AGA07_RTAKS09_091-097.indd 96 4/13/06 11:10:44 PM4/13/06 11:10:44 PM

3 R D P R I N T

Name Date ClassName Date Class

Copyright © by Holt, Rinehart and Winston. 97 Holt Mathematics Grade 9All rights reserved.

1. The edges of cube 1 are 1 __ 6 as long as

the edges of cube 2. How many times

greater is the volume of cube 2?

Cube 1

Cube 2

A 216 C 6

B 36 D 1 __ 6

2. A box in the shape of a rectangular

prism has a volume of 200 cubic

inches. If the box is dilated by a scale

factor of 1 __ 2 , what will be the volume of

the resulting box?

F 400 in3

G 100 in3

H 50 in3

J 25 in3

3. The volume of a triangular prism is

2,700 cm3. If each dimension of the

triangular prism is reduced to 1 __ 3 of

its original measure, what will be the

volume of the resulting triangular

prism?

A 27 cm3

B 100 cm3

C 300 cm3

D 900 cm3

4. The diameter and height of cylinder C are each 3 times the diameter and height of cylinder D.

Cylinder C

Cylinder D

What is the ratio of the volume of cylinder C to cylinder D.

F 81 to 1

G 27 to 1

H 9 to 1

J 3 to 1

5. Cone A and cone B are similar. The ratio of the volume of cone A to cone B is 64:1.

A B

What is the ratio of the area of cone A to the area of cone B ?

A 4 to 1

B 8 to 1

C 16 to 1

D 256 to 1

Ready for TAKS?Benchmark Post-Test (8.10)(B)8

OBJECTIVE

AGA07_RTAKS09_091-097.indd 97AGA07_RTAKS09_091-097.indd 97 4/13/06 11:10:44 PM4/13/06 11:10:44 PM

3 R D P R I N T

Name Date Class

1. Joe’s truck can go 108 miles on 6 gallons of gas. Joe is taking a trip of 270 miles. Which proportion can be used to determine approximately how many gallons of gas, g, Joe will need for his trip?

A 108 ____ 6 � 270 ____ g

B 108 ____ 270

� g __

6

C g ____

108 � 6 ____

270

D 6 ____ 108

� 270 ____ g

2. A catfish farmer captures and tags 30 catfish from his pond. He then releases them at various places in the pond. The following month, he captures 50 catfish. Of the 50, 6 have his tags. Which proportion can be used to estimate the number of catfish, c, in the pond?

F 50 ___ 30

� 6 __ c

G 6 ___ 50

� 30 ___ c

H 30 ___ 50

� 6 __ c

J 30 ___ 50

� c __ 6

3. Marianne is on a 20-day hiking trip. For the first several days she hikes 12 miles per day. If she hikes at the same rate over the entire 20-day period, which proportion can be used to determine how many miles, m, she will hike in all?

A 1 ___ 12

� 20 ___ m C 20 ___ 12

� 1 __ m

B 12 ___ 20

� 1 __ m D 12 ___ 1 � 20 ___ m

4. The chart shows the number of defective watches that were found in several production batches.

Number of Watches in Batch

Number of Defective Watches

90 7

180 14

270 21

If this rate remains the same, which proportion can be used to estimate how many defective watches, d, would be found in a batch of 1,000 glasses?

F 90 ___ 7

� d _____ 1000

H 1000 _____ 90

� 7 __ d

G 7 _____ 1000

� d ___ 90

J 7 ___ 90

� d _____ 1000

5. The diagram shows the length of a shadow of a 6-foot tall person at a certain time during the day. The diagram also shows a telephone pole that is 25-foot tall and its shadow at the same time.

11 ft s

Which proportion can be used to determine the length of the telephone pole’s shadow, s ?

A 6 ___ 25

� 11 ___ s C 6 ___ 11

� 25 ___ s

B 11 ___ 6

� 25 ___ s D 25 ___ 11

� s __ 6

Copyright © by Holt, Rinehart and Winston. 98 Holt Mathematics Grade 9All rights reserved.

Name Date Class

Ready for TAKS?Benchmark Post-Test (8.1)(B)9

OBJECTIVE

AGA07_RTAKS09_098-104.indd 98AGA07_RTAKS09_098-104.indd 98 4/13/06 11:10:59 PM4/13/06 11:10:59 PM

3 R D P R I N T

Name Date ClassName Date Class

Copyright © by Holt, Rinehart and Winston. 99 Holt Mathematics Grade 9All rights reserved.

1. A cheerleading squad has 18 members. Twelve of them have already been fitted for new uniforms. What percent of the squad has not yet been fitted?

A 88%

B 67%

C 33%

D 6%

2. The table shows the distribution of players on a forensics team.

Number of Players

Grade

10 12th

7 11th

4 10th

To the nearest tenth, what percent of the forensics team is in the 10th grade?

F 4.0%

G 19.0%

H 33.0%

J 47.6%

3. The label on a bag of trail mix indicates that it contains 40% dried fruit. If the weight of the dried fruit is 6 ounces, what is the total weight of the contents of the bag?

A 15 ounces

B 9 ounces

C 6.6 ounces

D 2.4 ounces

4. The circle-graph shows the distribution of the ages of the 400 people at a county fair.

35%Over 30

65%Under 30

Of the people under the age of 30, 60% are younger than 16. How many people at the county fair are younger than 16?

F 260

G 240

H 156

J 140

5. Under certain wind conditions, an airplane can fly approximately 500 miles per hour. If the plane flew in a straight path at this rate under the same wind conditions, what distance would it fly in 15 minutes?

A 7,500 mi

B 2,000 mi

C 125 mi

D 33 mi

Ready for TAKS?Benchmark Post-Test (8.3)(B)9

OBJECTIVE

AGA07_RTAKS09_098-104.indd 99AGA07_RTAKS09_098-104.indd 99 4/13/06 11:11:00 PM4/13/06 11:11:00 PM

3 R D P R I N T

Name Date Class

1. A multiple-choice test has four choices for each answer. There are 25 questions. If a student guesses on the first three questions, what is the probability that the student will miss the first one but get both the next two correct?

A 9 ___ 64

B 3 ___ 25

C 3 ___ 64

D 1 ___ 64

2. One ball is drawn at random from an urn containing four red balls, four white balls, and seven blue balls. What is the probability that the ball will be red or white?

F 4 ___ 15

G 7 ___ 15

H 8 ___ 15

J 16 ____ 225

3. A box of fruit contains 6 pink grapefruits and 4 yellow grapefruits. What is the probability of randomly choosing a yellow grapefruit and then a pink grapefruit from the box WITHOUT replacing them?

A 16 ___ 15

B 4 ___ 15

C 6 ___ 25

D 1 ____ 100

4. A spinner is made by dividing a circle into four sections as shown. Each of the larger sections represents 30% of the circle and each of the smaller sections represents 20% of the circle.

1 2

4 3

If a person spins the spinner twice, what is the probability that the person will get an even number on the first spin and the number 3 on the second spin?

F 0.1

G 0.25

H 0.5

J 0.6

5. One student is chosen at random from the French II class and one from the Spanish II class to compete in a foreign language contest.

French II

Grade 9th 10th 11th 12th

% of Class 12% 20% 42% 26%

Spanish II

Grade 9th 10th 11th 12th

% of Class 18% 36% 32% 14%

What is the probability that both students chosen are in the 9th grade?

A 0.3

B 0.18

C 0.12

D 0.0216

Copyright © by Holt, Rinehart and Winston. 100 Holt Mathematics Grade 9All rights reserved.

Name Date Class

Ready for TAKS?Benchmark Post-Test (8.11)(A)9

OBJECTIVE

AGA07_RTAKS09_098-104.indd 100AGA07_RTAKS09_098-104.indd 100 4/13/06 11:11:00 PM4/13/06 11:11:00 PM

3 R D P R I N T

Name Date ClassName Date Class

Copyright © by Holt, Rinehart and Winston. 101 Holt Mathematics Grade 9All rights reserved.

Use the bar graph to answer questions 1 and 2.

Demetria conducted an experiment by rolling a standard number cube 200 times. The results of Demetria’s experiment are shown in the bar graph.

0

5

10

15

20

25

30

35

40

1 2 3 4 5 6

31 3235

3834

30

Nu

mb

er o

f T

imes

To

ssed

Digit

200 Tosses of a Number Cube

1. According to the data, what is the experimental probability of rolling a 6 on the next roll of the number cube?

A 3 ___ 20

B 1 __ 6

C 3 ___ 10

D 17 ___ 20

2. What is the approximate difference between the experimental probability and the theoretical probability of rolling a 3 on the next roll?

F 0.317

G 0.167

H 0.150

J 0.008

Use the circle graph to answer questions 3 and 4.

Marco conducted an experiment by tossing a fair coin 200 times. The results of Marco’s experiment are shown in the circle graph.

Tails54%

Heads46%

200 Coin Tosses

3. According to the data, what is the experimental probability of tossing a tails on the next toss of the coin?

A 0.27

B 0.46

C 0.50

D 0.54

4. What is the approximate difference between the experimental probability and the theoretical probability of tossing a tails on the next roll?

F 0.04

G 0.27

H 0.50

J 0.54

5. So far this season, Marcus has gotten a base hit 32 times. He has been at bat 128 times. If Marcus continues to bat with the same success rate, how many base hits can he expect to get in the next 120 times he bats?

A 24 C 30

B 25 D 32

Ready for TAKS?Benchmark Post-Test (8.11)(B)9

OBJECTIVE

AGA07_TAKs_WBK09_098-104.indd 101AGA07_TAKs_WBK09_098-104.indd 101 9/6/06 8:18:29 PM9/6/06 8:18:29 PM

3 R D P R I N T

Name Date Class

1. During Janie’s first year of selling cars, she sold a total of 42 cars. Her sales per month were 2, 2, 4, 6, 4, 1, 2, 4, 4, 5, 5, and 3. Which measure of central tendency would be the most impressive to report to her store manager?

A range

B mean

C median

D mode

2. Joshua earned the following grades on his debate presentations: 92, 86, 84, and 91. If Joshua scores an 86 on his last presentation, which measure of central tendency will give him the highest overall score?

F range

G mean

H median

J mode

3. Consider the given set of data:

{18, 32, 28, 18, 36, 20, 18, 24, 28}.

Which statement is an accurate interpretation of the data?

A The mode of the set of data is 28.

B The mean of the set of data is 18.

C The range of the data set is equal to the mode.

D The median and the mode are both greater than the mean.

4. The number of patients treated at a local clinic each day for a week is shown in the table.

Patients Treated

Monday 72

Tuesday 55

Wednesday 70

Thursday 50

Friday 44

Which measure of central tendency would not change if the clinic had treated an additional 6 patients on Friday?

F range

G mean

H median

J mode

5. The stem-and-leaf plot shows the scores on the last test in Mrs. Morris’ algebra class.

Stem Leaf9 5 2 18 9 7 6 4 3 0 07 9 8 4 6 7 45 8 2

Which statement about the scores is true?

A The highest score was a 91.

B The median score was an 80.

C The range of the scores was 40.

D Less than 50% of the class scored an 80 or above.

Copyright © by Holt, Rinehart and Winston. 102 Holt Mathematics Grade 9All rights reserved.

Name Date Class

Ready for TAKS?Benchmark Post-Test (8.12)(A)9

OBJECTIVE

AGA07_RTAKS09_098-104.indd 102AGA07_RTAKS09_098-104.indd 102 4/13/06 11:11:00 PM4/13/06 11:11:00 PM

3 R D P R I N T

Name Date ClassName Date Class

Copyright © by Holt, Rinehart and Winston. 103 Holt Mathematics Grade 9All rights reserved.

1. A family planning agency surveyed families in a certain geographic region to find out how many children lived in the homes. The survey results are shown in the bar graph.

0

10

20

30

40

50

60

70

0 1 2 3 4 ormoreNo. of Children Living at Home

Family Planning Survey Results

Fre

qu

ency

Approximately how many families were surveyed?

A 275 C 155

B 230 D 100

2. Of the 420 people at a movie theater, 80 people are seeing a movie alone, 105 people are with a friend, 135 are with a spouse, and the rest are with another member of their family. If a circle graph is constructed, which of the following are the approximate percentages needed to represent each category, in the order presented above?

F 80%, 105%, 135%, 100%

G 25%, 40%, 20%, 15%

H 22%, 27%, 30%, 21%

J 19%, 25%, 32%, 24%

3. The seniors at a local high school recorded the number of votes that each candidate received in the race for senior class president. A total of 280 students voted and Elizabeth received 42.5% of the votes. If a bar graph is constructed, and the vertical axis represents the number of votes received, what should be the height of the bar for Elizabeth?

A 161 C 57.5

B 119 D 42.5

4. Shane gathered information about the approximate price range of cars parked at a business center. He used the information to create the bar graph and the circle graph shown. The bar graph accurately reflects the information gathered, but two sections of the circle graph were switched.

0

5

10

15

20

25

30

35

Under15

15–25 25–35 35–50 Over 50

Fre

qu

ency

Price (in thousands of dollars)

Price Range of Cars

Price Range of Cars(in thousands of dollars)

Under $1528%

$15–$2528%

$25–$3510%

$35–$5014%

Over $5015%

According to the information in the bar graph, which two sections of the circle graph were switched?

F Under 15 and 15–25

G Under 15 and Over 50

H 25–35 and Over 50

J 25–35 and 35–50

Ready for TAKS?Benchmark Post-Test (8.12)(C)9

OBJECTIVE

AGA07_RTAKS09_098-104.indd 103AGA07_RTAKS09_098-104.indd 103 4/13/06 11:11:01 PM4/13/06 11:11:01 PM

3 R D P R I N T

Name Date Class

Use the circle graph to answer questions 1 and 2.

The circle graph shows how a school’s budget was distributed last year.

Salaries46%

Labs6%

Other9%

Books33%

Janitorial6%

Budget Distribution

1. Which statement is NOT true?

A Books made up nearly one third of the budget.

B Salaries made up more of the budget than all the other categories combined.

C Lab expenses and janitorial expenses made up equal parts of the budget.

D Books and salaries together made up nearly four fifths of the budget.

2. Which is a reasonable conclusion from the information provided in the graph?

F The school needs to increase the amount budgeted for salaries.

G The school needs to cut down on the amount it spends on books.

H The school spent nearly half of its budget on its teachers’ salaries.

J The school spent more than one tenth of its budget on other expenses.

Use the bar graph to answer questions 3 and 4.

The bar graph shows the number of students enrolled in different foreign language classes at a certain college.

0 100 200 300 400

German

Latin

Italian

Spanish

French

Student Enrollment: Foreign Languages

3. Which statement is NOT true?

A Latin has the least number of students enrolled.

B There are approximately half as many students enrolled in German as there are in Spanish.

C There are more than twice as many students enrolled in French as in Latin.

D There are more students enrolled in Spanish than in all the other classes together.

4. Which is a reasonable conclusion from the information provided in the graph?

F More than one third of the students in the college are enrolled in Spanish.

G Students believe that taking Spanish will benefit them more than taking other foreign languages.

H There are 3 times as many students taking Spanish as students taking German.

J The Italian teacher is more popular than the Latin teacher.

Copyright © by Holt, Rinehart and Winston. 104 Holt Mathematics Grade 9All rights reserved.

Name Date Class

Ready for TAKS?Benchmark Post-Test (8.13)(B)9

OBJECTIVE

AGA07_TAKs_WBK09_098-104.indd 104AGA07_TAKs_WBK09_098-104.indd 104 9/6/06 8:18:30 PM9/6/06 8:18:30 PM

3 R D P R I N T

Name Date ClassName Date Class

Copyright © by Holt, Rinehart and Winston. 105 Holt Mathematics Grade 9All rights reserved.

1. Olewole found a pair of jeans on sale for 25% off the original price. If the original price was x, which equation could Olewole use to find the sale price, s, of the jeans?

A s � x � 1 __ 4 x

B s � 1 __ 4 s � x

C s � x � 1 __ 4 s

D s � x � 1 __ 4 x

2. Clare’s age is 5 years less than twice Mark’s. If Clare is 17 years old, which equation can be used to determine Mark’s age?

F 5 � 2x � 17

G 2x �5 � 17

H 2x � 17 �5

J 2(x � 5) � 17

3. An interior decorating company reported that the average price of imported fabric increased by 5% per year from 1990 to 2005. What additional information is needed to calculate the average price of imported fabric in 2005?

A the range of imported fabric prices from 1990 to 2005

B the maximum price of imported fabric between 1990 and 2005

C the average price of imported fabric in 1990

D the anticipated price of imported fabric for the next year

Ms. Morrow wants to carpet several rooms in her house. The diagram shows the layout of the rooms she wants to carpet. Use the diagram to answer questions 4 and 5.

4. The carpet Ms. Morrow has chosen comes in rolls that are 12 ft by 12 ft. Assuming the carpet can be cut and pieced together, what additional information is needed to determine how many rolls of carpet are required?

F the number of square feet in a roll

G the perimeter around each of the rooms

H the total number of rooms to be carpeted

J the dimensions of each room

5. Each roll of carpet costs $864. If Ms. Morrow wants to compare this price to another carpet store that prices its carpet per square foot, which calculation could Ms. Morrow use to determine how much per square foot the carpet she has chosen costs?

A 864 � 12

B 864 � (12 � 12)

C 864 � 12 � 12

D cannot be determined

Ready for TAKS?Benchmark Post-Test (8.14)(A)10

OBJECTIVE

AGA07_RTAKS09_105-110.indd 105AGA07_RTAKS09_105-110.indd 105 4/13/06 11:11:15 PM4/13/06 11:11:15 PM

3 R D P R I N T

Name Date Class

1. A swimming pool is being emptied at a rate of 60 gallons every 10 minutes. The pool holds 1,800 gallons of water. How many hours would it take to empty the pool at that rate?

A 3 hr

B 5 hr

C 6 hr

D 30 hr

2. Scott bought a leather jacket that was on sale for 25% off. The original cost of the coat was $210.00. If the tax rate is 5.5% and Scott gives the salesclerk nine $20.00 bills, how much change should he get back?

F $166.16

G $124.61

H $22.50

J $13.84

3. Rose wants to plant bushes around the perimeter of her yard.

17 ft19.6 ft

37.4 ft

26 ft

Rose’s Yard

The bushes should be spaced approximately 4 feet apart and each bush costs $12. If it costs $4.50 per bush to have them professionally planted, what is the approximate total cost to put bushes around the entire yard?

A $300.00

B $412.50

C $1,031.25

D $1,650.00

4. A landscaper wants to know how far it is around an irregularly shaped plot of land. To measure, he makes a roller that has a diameter of 10 inches as shown.

Plot ofLand 10�

Roller

If the roller goes around 46 times, what is the approximate distance around the lake in feet?

F 301 ft

G 241 ft

H 120 ft

J 38 ft

5. Joan’s car uses approximately 420 gallons of gasoline each year. If high octane gas costs $2.29 per gallon and regular gas costs $2.04 per gallon, what percent of Joan’s yearly gas cost would she save by switching from high octane to regular gas?

A 8%

B 9%

C 11%

D 12%

Copyright © by Holt, Rinehart and Winston. 106 Holt Mathematics Grade 9All rights reserved.

Name Date Class

Ready for TAKS?Benchmark Post-Test (8.14)(B)10

OBJECTIVE

AGA07_RTAKS09_105-110.indd 106AGA07_RTAKS09_105-110.indd 106 4/13/06 11:11:16 PM4/13/06 11:11:16 PM

3 R D P R I N T

Name Date ClassName Date Class

Copyright © by Holt, Rinehart and Winston. 107 Holt Mathematics Grade 9All rights reserved.

1. Beth, Melinda, and Toyneshia all collect figurines. Beth has 5 less figurines than Melinda has. Toyneshia has 4 times as many figurines as Beth has. Altogether the girls have 125 figurines. Which equation can be used to find out how many figurines each person has?

A x � 5x � 4x � 125

B x � 5(4x) � 4x � 125

C x � (x � 5) � 4x � 125

D x � (x � 5) � 4(x � 5) � 125

2. A cylinder has a volume of 1,078 cubic inches. The height of the cylinder is equal to the radius. What is the BEST way to determine the length of the radius?

F Divide the volume by 3�.

G Find the cube root of the volume.

H Divide the volume by � and then find the cube root.

J Multiply the volume by � and then find the cube root.

3. Which of the equations below represents the second step of the solution process?

Step 1. 12 � 3(2x � 5) � �15

Step 2.

Step 3. 27 � 6x � �15

Step 4. �6x � �42

Step 5. x � 7

A 15(2x � 5) � �15

B 12 � 6x � 5 � �15

C 12 � 6x � 5 � �15

D 12 � 6x � 15 � �15

4. A rectangle has an area of 40 square inches and a perimeter of 26 inches. What are the dimensions of the rectangle?

F 5 in. by 8 in.

G 4 in. by 10 in.

H 2 in. by 20 in.

J 1 in. by 40 in.

5. Three vertices of a square lie at the points whose coordinates are (�8, 0), (�2, 4), and (2, �2). What are the coordinates of the fourth vertex?

8

6

4

2

�2

�4

�6

�8

�2�4�6�8 2 4 86

y

x

A (�5, �7)

B (�4, �6)

C (�4, �4)

D (�3, �8)

Ready for TAKS?Benchmark Post-Test (8.14)(C)10

OBJECTIVE

AGA07_RTAKS09_105-110.indd 107AGA07_RTAKS09_105-110.indd 107 4/13/06 11:11:16 PM4/13/06 11:11:16 PM

3 R D P R I N T

Name Date Class

Use the figure shown to answer questions 1 and 2.

1. If the figure is a soup can, the amount of soup inside the can best represents the can’s —

A perimeter.

B circumference.

C surface area.

D volume.

2. If the figure is a soup can, the amount of space that can fit around the can on a label best represents the can’s —

F perimeter.

G lateral area.

H surface area.

J volume.

3. Which of the following names is the BEST description of the figure shown if x � y ?

y

x

A quadrilateral C square

B rectangle D rhombus

4. If the area of a triangle is given by the

equation A � 1 __ 2 bh, then the value of b

is the result of which of the following

ratios comparing a triangle’s area to its

height?

F 2A ___ h

G A ___ 2h

H A __ h

J h __ A

5. Which of the following is an accurate

description of the algebraic equation

given by 3(x � 2)

_______ x � 5

� 12?

A Five less than x divided by the product of 3 and 2 more than x is equal to 12.

B Two more than 3 times x divided by the difference of x and 5 is equal to 12.

C Three times the sum of x and 2 divided by the sum of x and 5 is equal to 12.

D Three times the sum of x and 2 divided by the quantity 5 less than x is equal to 12.

Copyright © by Holt, Rinehart and Winston. 108 Holt Mathematics Grade 9All rights reserved.

Name Date Class

Ready for TAKS?Benchmark Post-Test (8.15)(A)10

OBJECTIVE

AGA07_RTAKS09_105-110.indd 108AGA07_RTAKS09_105-110.indd 108 4/13/06 11:11:16 PM4/13/06 11:11:16 PM

3 R D P R I N T

Name Date ClassName Date Class

Copyright © by Holt, Rinehart and Winston. 109 Holt Mathematics Grade 9All rights reserved.

1. A Pythagorean Triple is a set of three integers, a, b, and c for which the following properties are both true:

Property 1: a � c and b � c

Property 2: a2 � b2 � c 2

Which set of three integers below could be a Pythagorean Triple?

A a � 3, b � 4, and c � 7

B a � 4, b � 5, and c � 8

C a � 9, b � 12, and c � 15

D a � 20, b � 48, and c � 50

2. The table shows several powers of the number 7.

Powers of 7 Resulting Value

71 7

72 49

73 343

74 2,401

75 16,807

76 117,649

77 823,543

78 5,764,801

Given that the digit in the ones place will continue to repeat in the pattern above, what will be the digit in the ones place in 781?

F 7

G 9

H 3

J 1

3. The first four powers of the number 5 are 5, 25, 125, and 625. Which of the following is a reasonable conjecture?

A There is no pattern regarding the digits in the powers of 5.

B The ones digit in all powers of 5 is a 5.

C All multiples of 5 end in a 5.

D Each power of 5 increases by 20.

4. Each figure in a pattern is an equilateral triangle whose side is one unit shorter than the side of the previous triangle. If the first triangle in the pattern has a perimeter of 60 units, what is the perimeter of the fifth square in the pattern?

F 45 units

G 48 units

H 51 units

J 54 units

5. Miriamo made the conjecture that other than 22, no other perfect square ends in the number 4. Which of the following is a counterexample to Miriamo’s conjecture?

A 26 � 64

B 43 � 64

C 82 � 64

D any of these

Ready for TAKS?Benchmark Post-Test (8.16)(A)10

OBJECTIVE

AGA07_RTAKS09_105-110.indd 109AGA07_RTAKS09_105-110.indd 109 4/13/06 11:11:17 PM4/13/06 11:11:17 PM

3 R D P R I N T

Name Date Class

1. If the variables x and y both represent negative integers less than �1, which statement is not true?

A If x � y, then 1 __ x � 1 __ y .

B If x � y, then 2x � 2y.

C If x � y, then y2 � x2.

D If x � y, then y3 � x3.

2. If the variables x and y are both greater than 0 and are related so that ��

x > ��

y , which statement must be true?

F It is not possible to determine which variable is greater.

G The variable x is greater than the variable y.

H The variable y is greater than the variable x.

J The square of x is greater than the square of y.

3. Figure ABCD is a rhombus, but is NOT a square. Which statement is NOT a valid conclusion?

B C

A D

A _

AB � _

BC

B m�A � m�D

C _

AC _

BD

D m�A � 180° � m�D

4. Which statement about the triangles below is true?

x � 10 x

x

5

5

55

5

F Exactly one of the triangles is an equilateral triangle.

G Only one of the triangles is not an equilateral triangle.

H All three of the triangles could be equilateral triangles.

J The perimeter of the right triangle is larger than the perimeter of the other two triangles.

5. Figure ABCD is a parallelogram whose diagonals are of equal length. Which statement is NOT a valid conclusion?

A Figure ABCD is a quadrilateral.

B Figure ABCD must be a square.

C Figure ABCD could be a square.

D Figure ABCD could be a rectangle.

Copyright © by Holt, Rinehart and Winston. 110 Holt Mathematics Grade 9All rights reserved.

Name Date Class

Ready for TAKS?Benchmark Post-Test (8.16)(B)10

OBJECTIVE

AGA07_RTAKS09_105-110.indd 110AGA07_RTAKS09_105-110.indd 110 4/13/06 11:11:17 PM4/13/06 11:11:17 PM

3 R D P R I N T

Copyright © by Holt, Rinehart and Winston. 111 Holt Mathematics Grade 9All rights reserved.

OBJECTIVE 1: (A.1)(A)

1. A Correct

The profit depends on the number of sandwiches sold and is therefore the dependent variable.

TAKS DOCTOR: Students who answered B identified a quantity that is not given in the description of the relation. If it were given, it would be a constant rather than a dependent variable. Students who answered C identified the independent variable, rather than the dependent variable. Students who answered D identified a quantity that is not given in the description of the relation. If it were given, it would be an independent variable.

2. J Correct

The amount of money earned by the student depends on the number of hours worked and is therefore the dependent variable.

TAKS DOCTOR: Students who answered F identified a quantity that is a constant rather than a dependent variable. Students who answered G identified the independent variable, rather than the dependent variable. Students who answered H identified a quantity that is not given in the description of the relation. If it were given, it would be an independent variable.

3. C Correct

As a increases, b sometimes increases and sometimes decreases. There does not appear to be a pattern. Therefore, it does not appear that b depends on a.

TAKS DOCTOR: Students who answered A did not recognize that as x increases from 1 to 2, from 4 to 5, and from 6 to 7, y decreases, not increases. Students who answered B did not recognize that as x increases from 2 to 4, and from 5 to 6, y increases, not decreases. Students who answered D did not understand that a function that is both increasing and decreasing cannot be linear.

4. J Correct

The price of the carpet would most likely be the same regardless of the size of the room. This means that a dependent relationship probably does not exist.

TAKS DOCTOR: Students who answered F did not recognize that the area of a rectangle always depends on the length of its side since A � � • w. Students who answered G did not recognize that a test grade usually depends on how much time a student spends studying. Students who answered H did not recognize that the weight of a book depends on the number of pages in the book.

5. B Correct

According to the graph, as the x-value gets larger (moves from left to right), the y-value gets smaller, and the function is therefore decreasing.

TAKS DOCTOR: Students who answered A did not recognize that the y-values are decreasing from left to right, not increasing. Students who answered C did not recognize that the y-values are decreasing from left to right, not increasing. Students who answered D did not recognize that the slope changes several times and the function is therefore not decreasing at a constant rate.

Answer KeyBenchmark Pre-Test

3 R D P R I N T

Copyright © by Holt, Rinehart and Winston. 112 Holt Mathematics Grade 9All rights reserved.

Answer Key continued

Benchmark Pre-TestOBJECTIVE 1: (A.1)(B)

1. B Correct

The table shows that the cost is always 10 more than 3 times the number of letters. This is represented by the expression 3n � 10.

TAKS DOCTOR: Students who answered A identified the expression that represents how each value of c is related to the previous value of c. Students who answered C identified the expression that represents the first value of c in the table in terms of the corresponding value of n. The expression does not correctly represent any other pair of values. Students who answered D identified the expression whose slope is the same as the correct expression, but is missing the y-intercept.

2. G Correct

The y-intercept of the line graphed is

3 and the slope of the line is 4 __ 2 � 2.

The equation of the line must be

h � 2t � 3.

TAKS DOCTOR: Students who answered F found the correct slope of the line but failed to include the y-intercept. Students who answered H found the correct y-intercept for the line but incorrectly identified the slope as 1. Students who answered J identified an expression that is not a

linear relation, since 2 __ t � 2 t �1 .

3. B Correct

Each value of y is 3 more than the corresponding value of x. This is expressed by the function y � x � 3.

TAKS DOCTOR: Students who answered A identified the expression that represents how each value of y is related to the previous value of y, rather than how it is related to x.

Students who answered C identified an expression for which each value of y is 3 less than the corresponding value of x, rather than 3 more than x. Students who answered D identified an expression for which each value of y is 3 times the corresponding value of x, rather than 3 more than x.

4. H Correct

Each value of y is the square of the corresponding value of x, which is represented by the expression y � x 2 .

TAKS DOCTOR: Students who answered F identified an expression that is true for only the first two values in the domain. Students who answered G identified an expression that is not true for any value in the domain. Students who answered J identified an expression that is the opposite of the correct answer because they did not understand that (�3)2 � �9.

5. C Correct

The table shows that the cost is always 15 more than 0.4 times the number of miles driven. This is represented by the expression 0.4m � 15.

TAKS DOCTOR: Students who answered A identified an expression that is true for only the first value of m. Students who answered B identified the expression that represents how each value of c is related to the previous value of c, rather than how each value of c is related to the corresponding value of m. Students who answered D inverted the slope of the line (change in x ’s over change in y ’s, instead of the reverse.)

3 R D P R I N T

Copyright © by Holt, Rinehart and Winston. 113 Holt Mathematics Grade 9All rights reserved.

Answer Key continued

Benchmark Pre-TestOBJECTIVE 1: (A.1)(C)

1. B Correct

The table shows that the balance is always 50 more than 5 times the number of weeks that have passed. This is represented by the expression 50 � 5w.

TAKS DOCTOR: Students who answered A identified an expression in which 5 is added to the number of weeks that have passed, rather than multiplied by the number of weeks. Students who answered C identified an expression in which the initial deposit of $50 is multiplied by the weekly deposits, rather than added to them. Students who answered D identified an expression that does not represent a single deposit of $50 but rather a weekly deposit of $50 � $5.

2. H Correct

The total cost of the shirt can be calculated by adding the cost of the plain tee-shirt ($8) plus $2.50 per decal (2.50d) plus 15 cents per letter (0.15n). This is represented by the expression 8.00 � 2.5d � 0.15n.

TAKS DOCTOR: Students who answered F identified an expression that does not include the initial cost of the plain tee-shirt ($8). Students who answered G mixed up the per decal cost with the per letter cost. Students who answered J identified an expression in which the initial cost ($8) is multiplied by the additional costs for decals and letters, rather than added to the additional costs.

3. D Correct

The dimensions of the room are w by 2w, so the perimeter of the room is 2(w � 2w) or 6w. The total cost of the chair rail is the product of the per foot price and the number of feet, or 4(6w).

TAKS DOCTOR: Students who answered A did not account for the per foot price of the chair rail. Students who answered B identified an expression that is the product of the per foot price and the area of the room, rather than the perimeter. Students who answered C identified an expression that includes only half of the perimeter of the room.

4. F Correct

The total fee can be calculated by adding the flat fee ($150) to the product of the per pound fee ($2) and the number of pounds in excess of 200 pounds (p � 200). This is represented by the expression 150 � 2(p � 200).

TAKS DOCTOR: Students who answered G identified an expression that divides the excess weight by 2, rather than multiplying it by 2. Students who answered H identified an expression that does not account for the $2 per pound fee for the excess weight. Students who answered J identified an expression that includes an extra $2 per pound fee for all pounds, not only those pounds in excess of 200.

5. C Correct

The product of the per pencil cost and the number of pencils plus the product of the per pad cost and the number of pads must be less than or equal to the amount of money Mary has to spend. This is represented by the expression1.5p � 3.5d � 20.

TAKS DOCTOR: Students who answered A did not account for the price of each item. Students who answered B did not account for the price of each item and used the wrong inequality symbol. Students who answered D used the wrong inequality symbol.

3 R D P R I N T

Copyright © by Holt, Rinehart and Winston. 114 Holt Mathematics Grade 9All rights reserved.

Answer Key continued

Benchmark Pre-TestOBJECTIVE 1: (A.1)(D)

1. D Correct

Written in set notation, the first value in a coordinate pair represents the domain and the second value represents the range. The domain and range have been reversed in this representation and it is therefore not an accurate representation of f (x ).

TAKS DOCTOR: Students who answered A did not recognize that given the domain {�1, 0, 1, 2}, the resulting pairs of values are the same as those in f (x ). Students who answered B did not recognize that given the range {�2, 0, 2, 4}, the resulting pairs of values are the same as those in f (x ). Students who answered C did not recognize that the points on the graph are the same as those given in f (x ).

2. J Correct

The graph shown does not pass the vertical line test and is therefore not a function.

TAKS DOCTOR: Students who answered F, G, or H did not understand that an element in the range may be repeated—only the elements in the domain must be unique.

3. C Correct

Solving the equation for y yields y � � �

� x � 1 . This means that for

each value of x in the domain, there will be 2 different values of y. This does not meet the definition of a function.

TAKS DOCTOR: Students who answered A, B, or D identified an expression that is a function, since there is only one y-value for each value of x.

4. G Correct

As the number of hours worked increases, so does the total pay. The function should be linear since the per hour pay rate is constant. Therefore, the correct answer is an increasing linear function.

TAKS DOCTOR: Students who answered F chose a constant function, rather than an increasing function. Students who answered H chose a decreasing linear function, rather than an increasing function. Students who answered J chose a function that is not linear. This function, although it is increasing, does not represent a constant pay rate.

5. B Correct

The domain elements for the defined function are �4, �3, �2, and �1. The range elements are each 3 more than the corresponding domain elements, or �1, 0, 1, and 2. Answer B is the only function that includes all the correct domain and range elements.

TAKS DOCTOR: Students who answered A chose a function that includes �5 and 0. Students who answered C or D chose a function in which the domain and range are the reverse of those in the defined function.

3 R D P R I N T

Copyright © by Holt, Rinehart and Winston. 115 Holt Mathematics Grade 9All rights reserved.

Answer Key continued

Benchmark Pre-TestOBJECTIVE 1: (A.1)(E)

1. B Correct

Since 3 loads of laundry require 120 gallons of water, which is more than 100 gallons, a person is only able to do 2 loads and use less than 100 gallons of water.

TAKS DOCTOR: Students who answered A did not choose the maximum number of loads. Students who answered C chose a number of loads that will exceed 100 gallons of water since 120 � 100. Students who answered D chose a number of loads that will exceed 100 gallons of water since 140 � 100.

2. F Correct

Since the cost of the materials is $52, the rate for one hour is 102 � 52 � $50. Since the function is linear, the hourly rate is $50 no matter how many hours the electrician works.

TAKS DOCTOR: Students who answered G identified the cost of the materials rather than the hourly rate. Students who answered H did not calculate the hourly rate correctly. Students who answered J did not account for the cost of the materials when calculating the hourly rate.

3. C Correct

Since y is the square of x, the value of y is always a positive number that is greater than or equal to x, given that x is an integer.

TAKS DOCTOR: Students who answered A did not recognize that when x is less than 0, as x increases, y decreases. For example, as x increases from �2 to �1, y decreases from 4 to 1.

Students who answered B did not recognize that when x is greater than 0, as x increases, y also increases. Students who answered D did not understand that the square of an integer is always greater than or equal to the integer itself.

4. H Correct

Since 25 is a constant amount (is not multiplied by the number of hours worked) it most likely represents the cost of the chemicals.

TAKS DOCTOR: Students who answered F did not recognize that the hourly rate is $15 per hour since the number of hours, h, is multiplied by 15 in the formula. Students who answered G did not understand that the number of hours it takes to clean the pool is represented by the letter h. Students who answered J did not understand that the number of miles to the customer’s home is not a part of the formula. If it were, it would be a variable amount, rather than a constant amount.

5. D Correct

In the formula, 5 represents a flat fee for some number of words. Since the second half of the equation involves n � 10, the number of words is 10. After 10 words, the charge is an additional 20 cents per word.

TAKS DOCTOR: Students who answered A did not account for the flat rate of $5 for the first 10 words. Students who answered B did not account for the fact that the flat rate of $5 included the first 10 words. Students who answered C reversed the flat rate for the first 10 words and the per word rate after 10.

3 R D P R I N T

OBJECTIVE 2: (A.2)(A)

1. C Correct

The power of each variable in a linear function is 1. Each of the choices meets this criteria except choice C. The power of x is �1 rather than 1.

TAKS DOCTOR: Students who answered A, B, or D identified a function that is linear since the power of each variable is 1.

2. H Correct

The function y � 2x is a linear function whose graph is a line with slope equal to 2 and y-intercept equal to 0.

TAKS DOCTOR: Students who answered F identified a line whose equation is y � 2. Students who answered G identified a line whose equation is x � 2. Students who answered J identified a graph whose equation is not linear.

3. C Correct

The graph of y � 3 x 2 passes through both points since 12 � 3(�2 ) 2 and 12 � 3(2 ) 2 .

TAKS DOCTOR: Students who answered A did not recognize that y � �6x only passes through the first of the two points since 12 � �6(2). Students who answered B did not recognize that y � 6x only passes through the second of the two points since 12 � 6(�2). Students who answered D did not recognize that y � 6 x 2 does not pass through either of the two points since 12 � 6(�2 ) 2 and 12 � 6(2 ) 2 .

4. J Correct

Since the power of x is 2, the function is a quadratic function whose graph is a parabola. The coefficient of x 2 is negative, so the parabola opens downward. The vertex of the parabola is (0, 0) since 0 � �(0 ) 2 .

TAKS DOCTOR: Students who answered F did not recognize that a function in the form of y � a x 2 is not a line. Students who answered G or H did not recognize that the parabola does not pass through (0, �1) since �1 � 0 2 .

5. A Correct

The data in the table represents a linear function since the slope between each pair of successive points is 3.

TAKS DOCTOR: Students who answered B, C or D did not recognize that the slope between successive points changes from one pair to the next and therefore the data cannot be modeled by a linear function.

Copyright © by Holt, Rinehart and Winston. 116 Holt Mathematics Grade 9All rights reserved.

Answer Key continued

Benchmark Pre-Test

3 R D P R I N T

Copyright © by Holt, Rinehart and Winston. 117 Holt Mathematics Grade 9All rights reserved.

OBJECTIVE 2: (A.2)(B)

1. C Correct

It is possible that the pep club might wash, 0, 1, 2, or more cars. Therefore, the domain is 0, 1, 2, . . . .

TAKS DOCTOR: Students who answered A identified a domain that includes fractions and decimals since “all real numbers” is continuous. The pep club would not wash portions of cars. Students who answered B identified a domain that would include negative numbers. The pep club could not wash a negative number of cars. Students who answered D did not consider that the pep club might not wash any cars.

2. J Correct

If n were less than 2, the sum of the measures of the angles would be negative, which is not possible and if n were equal to 2, the figure would not be a polygon. Therefore, the domain is n � 2.

TAKS DOCTOR: Students who answered F identified a domain that includes fractions and decimals since “all real numbers” is continuous. A polygon would not have a portion of a side. Students who answered G identified a domain that would include negative numbers. A polygon cannot have a negative number of sides. Students who answered H identified a domain that would result in a negative angle sum since 180(1 � 2) � �180 degrees.

3. B Correct

Since each side of the rectangle must be a positive number, x must be greater than 3, or x � 3.

TAKS DOCTOR: Students who answered A did not consider that x could also be 4, 5, or 6. Students who answered C identified a domain that could result in a negative length for one of the sides (x � 3) if x is between 2 and 3. Students who answered D identified a domain that could result in a negative length for both of the sides if x is between 0 and 3.

4. J Correct

The domain of the graph of a set of discrete points is the set of x-values. The x-values of the points graphed are 0, 1, 4, and 10.

TAKS DOCTOR: Students who answered F or G identified a continuous domain, rather than a discrete one. Students who answered H identified the range of the graph, rather than the domain.

5. A Correct

The range of the graph is the set of y-values for all the points that are graphed. Since the graph is continuous and has a maximum value of �2, the range is y � �2.

TAKS DOCTOR: Students who answered B identified a range whose minimum value is �2, rather than a maximum value of �2. Students who answered C did not choose a range, since x-values on a graph are associated with domains rather than ranges. Students who answered D chose a range that is discrete rather than continuous.

Answer Key continued

Benchmark Pre-Test

3 R D P R I N T

OBJECTIVE 2: (A.2)(C)

1. C Correct

The y-intercept is the point (0, 1.50). This means at 0 miles, the fare is $1.50, so the minimum cost is $1.50.

TAKS DOCTOR: Students who answered A did not recognize that if the price were $1.50 per mile, the line would pass through (1, 1.50) rather than (0, 1.50). Students who answered B did not recognize that the graph does not represent per person prices. Students who answered D did not understand that rate of increase is slope rather than an intercept.

2. J Correct

Since the line representing Plumber A is below the line for Plumber B at time equal 3 hours, Plumber A charges less for a job that takes 3 hours, not more.

TAKS DOCTOR: Students who answered F did not recognize that for all times less than 6 hours, the total cost for Plumber A, is less than for Plumber B. Students who answered G did not understand that the point of intersection on the graph can be interpreted to mean that the total cost is the same for each of the plumbers at time equal to 6 hours. Students who answered H did not recognize that for all times greater than 6 hours, the total cost for Plumber B, is less than for Plumber A.

3. C Correct

Since the slope of the line is

100 � 50 ________ 4 � 2

� 50 ___ 2 � 25, John adds

(acquires) 25 cards to his collection each month.

TAKS DOCTOR: Students who answered A did not recognize that John had no cards when he started the collection. Students who answered B did not recognize that John had 100 cards at the end of 4 months, not 50. Students who answered D calculated the slope of the line incorrectly.

4. F Correct

The x-intercept is the point (4, 0). Since the x-value represents the number of seconds, and the height is 0 at 4 seconds, the ball hits the ground at 4 seconds.

TAKS DOCTOR: Students who answered G did not recognize that the minimum height of the ball is 0 feet (when it hits the ground). Students who answered H did not recognize that the maximum height of the ball is 18 feet (at the vertex at the parabola). Students who answered J did not recognize that the ball’s height only increases for 2 seconds, and then decreases for 2 seconds.

Copyright © by Holt, Rinehart and Winston. 118 Holt Mathematics Grade 9All rights reserved.

Answer Key continued

Benchmark Pre-Test

3 R D P R I N T

Copyright © by Holt, Rinehart and Winston. 119 Holt Mathematics Grade 9All rights reserved.

OBJECTIVE 2: (A.2)(D)

1. C Correct

A decreasing slope indicates that the stock lost value. The only portion of the graph with a decreasing (negative) slope is between months 4 and 6.

TAKS DOCTOR: Students who answered A did not recognize that an increasing slope means the value of the stock went up rather than down. Students who answered B did not recognize that the slope of the curve is steeper between months 1 and 2 than between months 0 and 1. Students who answered D did not recognize that the value of the stock only increased from 10 to 25 by month 3, which is not triple.

2. J Correct

According to the data, for each $50 increase in the wholesale price, the retail price increases by $100. The change in wholesale price between $350 and $500 is $150, or 3($50). Therefore, the retail price should be 600 � 3(100) or $900.

TAKS DOCTOR: Students who answered F identified the retail price of a recliner with a wholesale price of $350, not $500. Students who answered G identified the retail price of a recliner with a wholesale price of $400 (the next value in the table), rather than $500. Students who answered H doubled the price of a recliner with a wholesale price of $250.

3. A Correct

According to the line of best fit, the y-value at x � 7 is approximately 5, which represents a price of $5,000.

TAKS DOCTOR: Students who answered B did not recognize that at 5 years (rather than 7) the approximate value is $10,000. Students who answered C did not recognize that at 3 years (rather than 7) the approximate value is $15,000. Students who answered D did not recognize that at 0 years (rather than 7) the approximate value is $25,000.

4. G Correct

Since the line of best fit has a negative slope, as one value increases (the age of the vehicle), the other value decreases (the asking price).

TAKS DOCTOR: Students who answered F did not recognize the negative correlation between the age and the asking price as indicated by the negative slope of the line of best fit. Students who answered H did not recognize that there is a clear correlation between the age and the asking price. Students who answered J did not recognize that the change in price is approximately $5,000 per year rather than $10,000 per year.

5. C Correct

A new car would be represented by time equals 0 years, or the y-intercept of the graph. The value of the y-intercept is 25, which represents $25,000.

TAKS DOCTOR: Students who answered A, B, or D did not understand that a new car would be represented by time equals 0 years, or the y-intercept of the graph, rather than some other point on the graph.

Answer Key continued

Benchmark Pre-Test

AGA07_RTAKS09_116-124.indd 119AGA07_RTAKS09_116-124.indd 119 2/27/07 9:59:23 AM2/27/07 9:59:23 AM

3 R D P R I N T

OBJECTIVE 2: (A.3)(A)

1. A Correct

When you receive change, you subtract the amount of the purchase from the amount of money you have, so the change from a $20 dollar bill will be 20 minus the cost of the item or 20 � d.

TAKS DOCTOR: Students who answered B identified an expression that involves addition rather than subtraction. If you purchased a $5 item, your change would be $15, which does not equal 20 � 5. Students who answered C identified an expression that involves multiplication rather than subtraction. If you purchased a $5 item, your change would be $15, which does not equal 20(5). Students who answered D identified an expression that involves exponents rather than subtraction. If you purchased a $5 item, your change would be $15, which does not equal 205.

2. G Correct

Since Mary purchased 4 items that each cost d dollars, the total cost is 4d, so the new balance is 220 � 4d.

TAKS DOCTOR: Students who answered F only identified the total cost of the items, not the new amount in the purse. Students who answered H added the cost to the amount in the purse rather than subtracting. Students who answered J multiplied the cost by the amount in the purse, rather than subtracting.

3. C Correct

According to the table, each DVD costs $15 so the total cost for n DVDs is 15 times the number of DVDs purchased, or 15n.

TAKS DOCTOR: Students who answered A did not include a variable in the expression to represent the number of DVDs purchased. Students who answered B added the price per DVD rather than multiplying. Students who answered D confused multiplication with raising a variable to a power.

4. H Correct

Since the typist can type 18 pages per hour, she types 18h pages in h hours. The number of pages remaining after h hours will be the difference (subtraction) between the starting amount and 18h, or 420 � 18h.

TAKS DOCTOR: Students who answered F expressed the number of pages typed in h hours incorrectly (18 � h rather than 18h). Students who answered G added the number of completed pages rather than subtracting them. Students who answered J divided by the number of completed pages, rather than subtracting them.

5. D Correct

Since the initial temperature is 72°, each change in the temperature should be added to 72. According to the table, the temperature rises 2 degrees each minute, or 2m. The correct equation is 72 � 2m.

TAKS DOCTOR: Students who answered A did not account for the initial temperature of 72° and incorrectly expressed the change in temperature per minute (m � 2 rather than 2m). Students who answered B did not account for the initial temperature of 72°. Students who answered C incorrectly expressed the change in temperature per minute (m � 2 rather than 2m).

Copyright © by Holt, Rinehart and Winston. 120 Holt Mathematics Grade 9All rights reserved.

Answer Key continued

Benchmark Pre-Test

3 R D P R I N T

Copyright © by Holt, Rinehart and Winston. 121 Holt Mathematics Grade 9All rights reserved.

OBJECTIVE 2: (A.3)(B)

1. D Correct

Each of the figures has 2 sides more than the number of triangular regions (3 and 1; 4 and 2; 5 and 3; and 6 and 4). Therefore, the number of triangular regions is 2 less than the number of sides or n � 2.

TAKS DOCTOR: Students who answered A, B, or C did not recognize that each figure has exactly 2 more sides than triangular regions.

2. J Correct

The increase in the total number of blocks from step 1 to step 2 is 2 blocks; the increase from step 2 to step 3 is 3 blocks; the increase from step 3 to step 4 is 4 blocks.

TAKS DOCTOR: Students who answered F did not recognize that only the first step has a number of blocks (1) that is the square of the number of the step (1). Students who answered G did not recognize that none of the steps have a number of blocks that is 2 more than the number of the step (e.g. 1 � 2 � 1, 3 � 2 � 3, etc.) Students who answered H did not recognize that in step 4, the number of blocks is not 3(4).

3. B Correct

The area of a rectangle is found by multiplying the length times the width, even when the dimensions are expressed with variables. The area of the given rectangle is (x � 5)(x � 2) � x 2 � 2x � 5x � 10 � x 2 � 3x � 10.

TAKS DOCTOR: Students who answered A found the perimeter of the rectangle rather than the area. Students who answered C multiplied the two expressions incorrectly (the middle term is 3x rather than �3x). Students who answered D only multiplied the first and last terms in the expressions rather than distributing correctly (FOIL).

4. F Correct

Each large square has dimensions x by x and each rectangle has dimensions 1 by x. Therefore the top row represents 4x �2 and the first column represents x � 3. The correct factorization is (4x � 2)(x � 3).

TAKS DOCTOR: Students who answered G did not recognize that the middle term of this product would be 11x, not 14x. Students who answered H did not recognize that the middle term of this product would be 10x, not 14x. Students who answered J did not recognize that the middle term of this product would be 10x, not 14x.

5. C Correct

According to the table, as each x-value increases by 3, the y-value is 3 times the previous y-value. Therefore, for every increase of 3 in the x-values, the y-value triples 5(3) � 15; 15(3) � 45; 45(3) � 135.

TAKS DOCTOR: Students who answered A did not recognize that 0(5) � 5, 6(5) � 45, and 9(5) � 135. Students who answered B did not recognize that 15 � 15 � 45 and 15 � 15 � 45. Students who answered D did not recognize that 3 0 � 5; 3 3 � 15, and so on.

Answer Key continued

Benchmark Pre-Test

3 R D P R I N T

OBJECTIVE 2: (A.4)(A)

1. A Correct

Substitute x � �3 into f (x ) to evaluate: (�3 ) 2 � 4(�3) � 5 � 9 � 12 � 5 � 16.

TAKS DOCTOR: Students who answered B multiplied �3 by 2 instead of raising it to the 2 nd power. Students who answered C squared �3 and got �9, instead of 9. Students who answered D multiplied �4 times �3 and got �12 instead of 12.

2. J Correct

To find the missing value, solve 2 � 4x � �14. Subtract 2 from both sides of the equation, then divide by �4. 2 � 4x � �14 → �4x � �14 � 2 → �4x � �16

so x � �16 ____ �4

� 4.

TAKS DOCTOR: Students who answered F divided by 4 in the last step, instead of �4. Students who answered G simply chose the next consecutive value of x in the table, which would not result in �14. Students who answered H added 2 to both sides of the equation in the first step, instead of subtracting 2.

3. D Correct

Since the triangle is an equilateral triangle, all three sides have length 3x � 2. To find the perimeter, multiply 3(3x � 2) � 9x � 6.

TAKS DOCTOR: Students who answered A raised 3x � 2 to the third power, instead of multiplying by 3. Students who answered B did not distribute the 3 to the constant term. Students who answered C only multiplied the constant term by 3, rather than both the variable term and the constant term.

4. G Correct

Solve the equation for x: 7x � 3 � 3 � �2x � 42 � 37x � 2x � �2x � 2x � 459x � 45

x � 45 ___ 9 � 5

TAKS DOCTOR: Students who answered F subtracted 3 from both sides of the equation, instead of adding 3. Students who answered H subtracted 2x from both sides of the equation, instead of adding 2x. Students who answered J subtracted 9 in the last step, instead of dividing by 9.

5. B Correct

Rewrite the equation in the form y � mx � b by subtracting 4x from both sides, then dividing each term by �2.

4x � 4x � 2y � �4x � 6

�2y

____ �2

� �4x ____ �2

� 6 ___ �2

y � 2x � 3

TAKS DOCTOR: Students who answered A forgot to divide 6 by �2. Students who answered C divided 6 by 2, rather than by �2. Students who answered D divided the entire equation by 2, rather than �2.

6. F Correct

Since area � length times width, the correct answer is the other factor of x 2 � 6x � 16, which is x � 2.

TAKS DOCTOR: Students who answered G, H, or J factored incorrectly. x 2 � 6x � 16 � (x � 8)(x � 2)

Copyright © by Holt, Rinehart and Winston. 122 Holt Mathematics Grade 9All rights reserved.

Answer Key continued

Benchmark Pre-Test

3 R D P R I N T

Copyright © by Holt, Rinehart and Winston. 123 Holt Mathematics Grade 9All rights reserved.

OBJECTIVE 2: (A.4)(B)

1. C Correct

The Distributive Property states that a(b � c) � ab � ac, which is precisely what is being illustrated by the equation.

TAKS DOCTOR: Students who answered A did not understand that the Commutative Property involves the order of the terms: a � b � b � a. Students who answered B did not understand that the Associative Property involves the arrangement of the terms: a � (b � c) � (a � b) � c. Students who answered D did not understand that the Identity Property involves multiplication by 1: a(1) � a.

2. G Correct

The Associative Property states that a � (b � c) � (a � b) � c, which is precisely what is being illustrated by the equation.

TAKS DOCTOR: Students who answered F did not understand that the Commutative Property involves the order of the terms: a � b � b � a. Students who answered H did not understand that the Distributive Property involves multiplication of terms: a(b � c) � ab � ac. Students who answered J did not understand that the Additive Identity Property involves addition of 0: a � 0 � a.

3. B Correct

Simplify the expression by distributing the �6 to each of the terms inside the parentheses and then combining terms where possible: 15 m 2 � 6( m 2 � 2m) � 15 m 2 � 6 m 2 � 12m � 9 m 2 � 12m.

TAKS DOCTOR: Students who answered A did not distribute the �6 to both terms. Students who answered C multiplied �6 by 2 incorrectly. Students who answered D subtracted 15 m 2 � 6 m 2 incorrectly.

4. G Correct

Combine like terms using the Commutative Property and rules for adding with exponents: 6 x 2 � 4x � 3 � 8x � 11 x 2 � 8 � 6 x 2 � 11 x 2 � 4x � 8x � 3 � 8 � �5 x 2 � 12x � 11.

TAKS DOCTOR: Students who answered F or H added �3 and �8 incorrectly. Students who answered J added the exponents of the variables, rather than the coefficients.

5. A Correct

Add the lengths of the sides to find the perimeter:

(2x � 5) � (3x � 1) � x � (2x � 1) � (3x � 7) � (2x � 3x � x � 2x � 3x) � (5 � 1 � 1 � 7) � 11x � 12

TAKS DOCTOR: Students who answered B added the variable terms incorrectly. Students who answered C added the exponents of the variables. Students who answered D multiplied the perimeter by 5 since the figure is a pentagon, rather than just adding the length of the sides.

6. H Correct

The quantity (x � 2 ) 2 means (x � 2)(x � 2) whose product is x 2 � 2x � 2x � 4 � x 2 � 4.

TAKS DOCTOR: Students who answered F, G, or J did not realize that each of the products is multiplied correctly.

Answer Key continued

Benchmark Pre-Test

3 R D P R I N T

OBJECTIVE 2: (A.4)(C)

1. B Correct

An equation is used to describe a relationship between two variables, one that is independent (usually x ) and one that is dependent (usually y ). Function notation can also be used to describe such a relationship, using input values and output values. A function is equivalent to a given equation if y is replaced by f (x ) and the other side of the equal sign stays the same. In the equation y � 3x � 2, replacing y with f (x ) will result in the function f (x ) � 3x � 2.

TAKS DOCTOR: Students who answered A, C, or D did not simply replace y with f (x ). Substituting a given value of x (such as x � 1) will not result in the same value for any of these functions, as it will in the original equation.

2. J Correct

An equation is equivalent to a given function if f (x ) is replaced by y and the other side of the equal sign stays the same. In the function f (x ) � �(x � 5), replacing f (x ) with y will result in the equation y � �(x � 5).

TAKS DOCTOR: Students who answered F, G, or H did not simply replace f (x ) with y. Substituting a given value of x (such as x � 1) will not result in the same value for any of these equations as it will in the original function.

3. C Correct

An equation is equivalent to a given function if f (x ) is replaced by y and the other side of the equal sign stays the same. In the function f (x ) � x 2 � 3, replacing f (x ) with y will result in the equation y � x 2 � 3.

TAKS DOCTOR: Students who answered A, B, or D did not simply replace f (x ) with y. Substituting a given value of x (such as x � 1) will not result in the same value for any of these equations as it will in the original function.

4. F Correct

A function is equivalent to a given equation, and will therefore have the same graph, if y is replaced by f (x ) and the other side of the equal sign stays the same. In the equation

y � 1 __ 2 x � 1, replacing y with f (x ) will

result in the function f (x ) � 1 __ 2 x � 1.

TAKS DOCTOR: Students who answered G, H, or J did not simply replace y with f (x ). Substituting a given value of x (such as x � 1) will not result in the same value for any of these functions, as it will in the original equation.

5. D Correct

An equation is equivalent to the given function if f (m ) is replaced by t and the other side of the equal sign stays the same. In the function f (m ) � 72 � 2m, replacing f (m ) with t will result in the equation t � 72 � 2m.

TAKS DOCTOR: Students who answered A, B, or C did not simply replace f (m ) with t. Substituting a given value of m (such as m � 1) will not result in the same value for any of these equations as it will in the original function.

Copyright © by Holt, Rinehart and Winston. 124 Holt Mathematics Grade 9All rights reserved.

Answer Key continued

Benchmark Pre-Test

3 R D P R I N T

Copyright © by Holt, Rinehart and Winston. 125 Holt Mathematics Grade 9All rights reserved.

Answer Key continued

Benchmark Pre-TestOBJECTIVE 3: (A.5)(A)

1. A Correct

TAKS DOCTOR: Students who answered B chose a situation that when graphed would be in the shape of a parabola and not a straight line. Students who answered C chose a situation that when graphed would result in a straight line with a positive slope, followed by a horizontal line (to represent the time resting), followed by a straight line with a positive slope. Students who answered D chose a situation that when graphed initially looks like a linear function with a positive slope, but changes to a line with a slope of zero.

2. G Correct

The table represents a horizontal line with the equation y � 4.

TAKS DOCTOR: Students who answered F, H, or J did not calculate the constant difference correctly between the x- and y-values to determine if the change between the values was constant. The table of data in these choices, when graphed, does not result in a straight line.

3. B Correct

The graph is linear, and according to the labeled points the slope of the line is 3. This means the value of y increases by 3 for each increase in x by 1. Choice B describes a situation of this nature.

TAKS DOCTOR: Students who answered A chose a situation in which the function is not linear. Students who answered C chose a situation in which the function has a negative slope (decreasing), rather than a positive slope. Students who answered D chose a situation in which the function would be represented by 3x, rather than 3x.

4. H Correct

For a function to include both of the given points, the coordinates of both points must satisfy the function’s equation. Both (1, 2) and (�2, 5) satisfy the equation y � �x � 3.

TAKS DOCTOR: Students who answered F chose a function that is not linear, although it does include both of the points. Students who answered G chose a function that only includes the first point. Students who answered J chose a function that only includes the first point.

3 R D P R I N T

Copyright © by Holt, Rinehart and Winston. 126 Holt Mathematics Grade 9All rights reserved.

Answer Key continued

Benchmark Pre-TestOBJECTIVE 3: (A.5)(C)

1. B Correct

The graph shows a line whose y-intercept is (0, 6) and whose slope (from the two labeled points) is

6 � 0 _____ 0 � 2

� �3. Written in slope-intercept

form, the equation of the line is y � �3x � 6.

TAKS DOCTOR: Students who answered A inverted the slope in their calculation. Students who answered C calculated the slope incorrectly (inverted and left of the negative sign). Students who answered D calculated the slope incorrectly (left off the negative sign).

2. J Correct

If a point lies on a line, then the coordinates of that point satisfy the equation of the line. Each of the points in the table satisfies the equation y � �2x.

TAKS DOCTOR: Students who answered F chose a line that only contains the second of the three points (0 � 2(0)). Students who answered G chose a line that only contains the second of the three points (0 � 0 � 0). Students who answered H chose a line that only contains the first of the three points (4 � (�2) � 6).

3. D Correct

To rewrite the equation, first multiply each of the terms by 2 to clear the fractions. The equation is now 2y � �x � 12. Next, add x to both sides of the equation to get x � 2y � 12. Finally, subtract 12 from both sides to get x � 2y � 12 � 0.

TAKS DOCTOR: Students who answered A did not multiply the constant (6) by 2 in the first step. Students who answered B multiplied one side of the equation by �2 and the other by �2. Students who answered C multiplied 6 by �2 rather than by 2.

4. F Correct

The given statement means that the value of y is double the value of x (“twice”) minus 3 (“3 less than”). This can be expressed by the equation y � 2x � 3.

TAKS DOCTOR: Students who answered G subtracted 2x from 3, rather than the reverse. Students who answered H doubled the y, rather than the x, and subtracted in the wrong order. Students who answered J doubled the y, rather than the x.

5. A Correct

Rewrite the equation in slope-intercept form by subtracting 2x from both sides: y � �2x � 4. The graph of this line has a y-intercept of 4 and a slope of �2. The graph in choice A meets these requirements.

TAKS DOCTOR: Students who answered B chose the graph of a line whose slope is �2, rather than �2. Students who answered C chose the graph of a line whose y-intercept is �4, rather than 4. Students who answered D chose the graph of a line

whose slope is � 1 __ 2 , rather than �2.

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Answer Key continued

Benchmark Pre-TestOBJECTIVE 3: (A.6)(A)

1. B Correct

Divide both sides of the equation by 2 to rewrite the equation in

slope-intercept form

(y � mx � b): 2y

___ 2 � �3x ____

2 � 8 __

2 .

Simplify to get y � � 3 __ 2 x � 4. The

slope of this line, m, is � 3 __ 2 .

TAKS DOCTOR: Students who answered A did not divide the equation by 2. Students who answered C inverted the slope. Students who answered D identified the y-intercept of the line rather than the slope.

2. F Correct

Subtract x from both sides of the equation: 3y � 4x � x � 6 → 3y � 3x � 6. Then divide by 3 to rewrite in slope-intercept form:

3y

___ 3 � 3x ___

3 � 6 __

3 → y � x � 2.

The slope of the line is 1.

TAKS DOCTOR: Students who answered G added x to the right side of the equation, rather than subtracting x. Students who answered H identified the y-intercept of the line rather than the slope. Students who answered J did not divide both sides of the equation by 3.

3. C Correct

Use the two labeled points to calculate the slope:

m � y2 � y1 ______ x2 � x1

� 2 � 0 ________ 0 � (�4)

� 1 __ 2

.

TAKS DOCTOR: Students who answered A used an incorrect form

of the slope formula: x2 � x1 ______ y2 � y1

.

Students who answered B subtracted incorrectly to arrive at a negative slope. Students who answered D inverted the slope.

4. J Correct

A slope of �2 means to “fall” 2 and “run” 1 on a graph. The only graph that meets this criteria is choice J.

TAKS DOCTOR: Students who answered F chose the graph of an equation whose slope is 0 (a horizontal line) rather than �2. Students who answered G chose an

equation whose slope is � 1 __ 2 rather

than �2. Students who answered H chose the graph of an equation whose slope is �2 rather than �2.

5. C Correct

Graph the given points to find that the line is a horizontal line. The slope of every horizontal line is 0.

TAKS DOCTOR: Students who answered A chose the common y-value, rather than the slope of the line. Students who answered B

calculated y __ x using the first point,

rather than finding the slope of the line. Students who answered D identified the slope of a vertical line rather than the slope of a horizontal line.

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Answer Key continued

Benchmark Pre-TestOBJECTIVE 3: (A.6)(B)

1. D Correct

The line graphed has a negative slope since the line is falling from left to right. Therefore, as x increases (moves from left to right), y decreases (falls).

TAKS DOCTOR: Students who answered A chose a description of a horizontal line rather than a line with a negative slope. Students who answered B chose a description of a vertical line. Students who answered C chose a description of a line that has a positive slope.

2. H Correct

Parallel lines have the same slope.

TAKS DOCTOR: Students who answered F thought that the slopes of parallel lines are opposites. Students who answered G or J may be confusing the definition of slopes of parallel lines with the definition of slopes of perpendicular lines—which are opposite reciprocals.

3. D Correct

You are looking for a graph that has a positive slope, then a slope of 0 (horizontal line), then a positive slope again. The only choice that meets these criteria is choice D.

TAKS DOCTOR: Students who answered A chose a graph that is increasing, then constant, then decreasing. Students who answered B chose a graph that is always increasing, although at slightly different rates. Students who answered C chose a graph that is decreasing, then constant, then increasing.

4. F Correct

The x-intercept is the place where the graph of the line crosses the x-axis (the horizontal axis). The x-intercept of this graph is 3. The point (3, 0) can be interpreted to mean that at the end of 3 weeks, there were 0 lawns left to be cut, or Bob finished cutting all the lawns by the third week.

TAKS DOCTOR: Students who answered G did not understand that the horizontal axis represents the number of weeks, not the number of lawns. Students who answered H did not pay attention to the axis label (weeks not months). Students who answered J confused the meaning of an x-intercept with the meaning of slope.

5. C Correct

The y-intercept is the place where the graph of the line crosses the y-axis (the vertical axis). The y-intercept of this graph is (15,0) which can be interpreted to mean that when time � 0 (at the beginning of the year), Mary had 15 figurines.

TAKS DOCTOR: Students who answered A did not understand that the vertical axis represents the number of figurines, not the number of months. Students who answered B confused the meaning of a y-intercept with the meaning of slope. Students who answered D did not recognize that the number of figurines is increasing over time since the graph has a positive slope.

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Copyright © by Holt, Rinehart and Winston. 129 Holt Mathematics Grade 9All rights reserved.

Answer Key continued

Benchmark Pre-TestOBJECTIVE 3: (A.6)(C)

1. A Correct

The slope of line n is �3 and the slope

of line m is 1 __ 3 , so the slope of line n is

less. The y-intercept of line n is 5 and the y-intercept of line m is 4, so the y-intercept of line n is greater.

TAKS DOCTOR: Students who answered B did not recognize that the y-intercept of line n is greater than the y-intercept of line m. Students who answered C did not recognize that the slope of line n is less than the slope of line m. Students who answered D did not recognize that the slope of line n is less than the slope of line m or that the y-intercept is greater.

2. F Correct

The y-intercept of the original line is �5. If the line is shifted up 5 units, the new y-intercept will be �5 � 5 � 0. A vertical shift does not change the slope of the line, so the equation of the new line is f (x ) � 2x.

TAKS DOCTOR: Students who answered G subtracted 5 from the y-intercept rather than adding 5. Students who answered H added 5 to the slope rather than to the y-intercept. Students who answered J multiplied the slope by 5, rather than adding 5 to the y-intercept.

3. D Correct

The y-intercept of line a is 5 and the y-intercept of line b is �5. The slopes of the two lines are the same. This means that line b is parallel to line a and 5 � (�5) �10 units below line a.

TAKS DOCTOR: Students who answered A or B did not understand that changing the y-intercept simply shifts the line up or down. Students who answered C did not understand that changing the y-intercept shifts the line up or down, not left or right.

4. G Correct

The y-intercept of line a is 3 and the y-intercept of line b is 1. The slopes of the two lines are the same. This means that line b has been shifted down 3 � 1 � 2 units but has not changed otherwise.

TAKS DOCTOR: Students who answered F did not understand that since the y-intercept is lower, the line has been shifted down, not up. Students who answered H or J did not understand that changing the y-intercept simply shifts the line up or down.

5. C Correct

When an equation is written in the form y � mx � b, the slope is represented by m (�2) and the y-intercept by b (3). If the slope is tripled, the new slope is 3(�2) � �6. If 2 is subtracted from the y-intercept, the new y-intercept is 3 � 2 � 1. The resulting equation is y � �6x � 1.

TAKS DOCTOR: Students who answered A simply replaced the slope and the y-intercept with the new values rather than adjusting the existing ones by the correct amounts. Students who answered B subtracted 2 from the slope (rather than from the y-intercept) and tripled the y-intercept (rather than the slope). Students who answered D multiplied the coefficient of y by 3, rather than multiplying the coefficient of x by 3.

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Answer Key continued

Benchmark Pre-TestOBJECTIVE 3: (A.6)(D)

1. B Correct

Use the formula y � y1 � m (x � x1) with m � �2; y1 � 3; and x1 � �1.

TAKS DOCTOR: Students who answered A inverted the slope when finding their answer. Students who answered C did not distribute the �2 correctly in the first step of the solution. Students who answered D subtracted 3 from both sides of the equation in the last step, rather than adding 3.

2. H Correct

Use slope-intercept form to write the equation with m � 4 and b � �3: y � 4x � 3. Since this is not one of the choices, rewrite the equation by adding 3 to both sides and subtracting y. This will result in the equation 4x � y � 3.

TAKS DOCTOR: Students who answered F identified a line that has a slope of �4, rather than �4. Students who answered G identified a line that has a y-intercept of �3, rather than �3. Students who answered J identified a line that has a slope of �4 (rather than �4) and a y-intercept of �3 (rather than �3).

3. B Correct

First find the slope using the slope

formula: m � 0 � (�5)

________ 5 � 0

� 5 __ 5 � 1.

Next, use point-slope form and either point to find the equation of the line: y � 0 � 1(x � 5) → y � x � 5. Rewrite the equation by adding 5 to both sides and subtracting y to yield x � y � 5.

TAKS DOCTOR: Students who answered A identified a line that has a y-intercept of �5 (rather than �5) and an x-intercept of �5 (rather than �5). Students who answered C identified a line whose x- and y-intercepts are both 0. Students who answered D identified a line whose x-intercept is

� 1 __ 5 and whose y -intercept is 1 __

5 .

4. J Correct

First find the slope using the slope formula and the two labeled points:

m � 5 � 1 ________ 1 � (�1)

� 4 __ 2 � 2. Next, use

point-slope form to find the equation of the line. You may use either of the labeled points to find the equation:

y � 5 � 2(x � 1)y � 5 � 2x � 2

y � 2x � 2 � 5y � 2x � 3.

TAKS DOCTOR: Students who answered F inverted the slope of the line. Students who answered G calculated the slope incorrectly. Students who answered H calculated the slope incorrectly.

5. C Correct

The graphed line has a positive slope and a negative y-intercept. If you write each of the given lines in slope-intercept form, the only equation that does not meet these criteria is choice C, which has a slope of �1 and a y-intercept of 3.

TAKS DOCTOR: Students who answered A, B, or D chose lines that do have positive slopes and negative y-intercepts. Choice D can be rewritten in the form y � x � 3 to confirm this.

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Copyright © by Holt, Rinehart and Winston. 131 Holt Mathematics Grade 9All rights reserved.

Answer Key continued

Benchmark Pre-TestOBJECTIVE 3: (A.6)(E)

1. D Correct

To find the y-intercept, substitute x � 0 into the equation and solve for y:

4(0) � 3y � �12 → �3y

____ �3

� �12 ____ �3

y � 4. So the y-intercept is (0, 4).

TAKS DOCTOR: Students who answered A divided �12 by 3 instead of �3. Students who answered B identified the x-intercept rather than the y-intercept. Students who answered C may not have recalled how to find a y-intercept.

2. F Correct

To find the x-intercept, substitute y � 0 into the equation and solve for x:

0 � 2 __ 3 x � 8 → �8 � 2 __

3 x. Multiply both

sides of the equation by the reciprocal

of 2 __ 3 : 3 __

2 (�8) � 3 __

2 � 2 __ 3 x � → �12 � x.

The x-intercept is therefore (�12, 0).

TAKS DOCTOR: Students who answered G may not have recalled how to find an x-intercept. Students who answered H identified the y-intercept rather than the x-intercept. Students who answered J multiplied

by 3 __ 2 rather than � 3 __

2 .

3. B Correct

Graphically, the x-intercept of a line is the point where the line crosses the horizontal axis. For this line, the x-intercept is �4.

TAKS DOCTOR: Students who answered A left off the negative sign. Students who answered C identified the y-intercept rather than the x-intercept. Students who answered D identified the slope of the line, rather than the x-intercept.

4. G Correct

Since every y-intercept is of the form (0, y), continue the linear pattern to find the point where x � 0. The next point in the table would be (�1, 2) and the next would be (0, 1).

TAKS DOCTOR: Students who answered F reversed the x and y coordinates. Students who answered H identified a point that is not on the line. Students who answered J identified a point that is not on the line.

5. C Correct

Since every x-intercept is of the form (x, 0), continue the linear pattern to find the point where y � 0. The next point in the table would be (4, 24), the next (5, 12), and the next (6, 0). The x-intercept is therefore 6.

TAKS DOCTOR: Students who answered A identified the time at which the temperature would be 24°F, rather than 0°F. Students who answered B identified the time at which the temperature would be 12°F, rather than 0°F. Students who answered D identified the time at which the temperature would be �12°F, rather than 0°F.

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Copyright © by Holt, Rinehart and Winston. 132 Holt Mathematics Grade 9All rights reserved.

Answer Key continued

Benchmark Pre-TestOBJECTIVE 3: (A.6)(F)

1. B Correct

Calculate the slope of the line either by using 2 points and the slope

formula � m = y1 � y2 ______ x1 � x2

� or by visual

evaluation of the rise and run. For every 1-unit increase in y there is a 2-unit increase in x, so the slope of

the line is 1 __ 2 . The line crosses the

y-axis at (0, 6), so the y-intercept is 6. The equation of the original line is

y � 1 __ 2 x � 6. If the slope is doubled,

the new slope is 2 � 1 __ 2 � � 1. The

resulting equation is y � x � 6.

TAKS DOCTOR: Students who answered A doubled the y-intercept instead of the slope. Students who

answered C multiplied 1 __ 2 by 2

incorrectly. Students who answered D multiplied the coefficient of y by 2, rather than multiplying the coefficient of x by 2.

2. J Correct

In this problem, slope can be interpreted as rate of growth. Since the slope of Company B’s line is steeper (greater) than the slope of Company A’s line, Company B’s profits grew at a faster rate.

TAKS DOCTOR: Students who answered F did not recognize that the slopes of the two lines are not the same. Students who answered G confused the meaning of the y-intercept with the meaning of slope. Students who answered H did not recognize that the slope of line A is less than the slope of line B.

3. C Correct

Changing the flat fee is equivalent to changing the y-intercept of the line. This will shift the line up 10 units ($50 � $40). Therefore, the total cost for a job that takes 2 hours will be $90 � $10 � $100.

TAKS DOCTOR: Students who answered A found the total charge with the new flat fee for a job that takes 1 hour, not 2 hours. Students who answered B did not change anything in the problem. Students who answered D changed the hourly rate rather than the flat fee to $50.

4. H Correct

Changing the hourly fee is equivalent to changing the slope of the line. Instead of adding $25 to the flat fee twice (2 hours), add $30 twice, or $40 � $30 � $30 � $100.

TAKS DOCTOR: Students who answered F found the total charge with the new hourly rate for a job that takes 1 hour, not 2 hours. Students who answered G did not change anything in the problem. Students who answered J calculated the total charge for a job that took 3 hours.

5. C Correct

Change the flat fee to $50 and then add the new hourly rate of $30 twice (2 hours): $50 � $30 � $30 � $110.

TAKS DOCTOR: Students who answered A found the total charge with the new flat fee and the new hourly rate for a job that takes 1 hour, not 2 hours. Students who answered B did not change anything in the problem. Students who answered D changed the flat fee to $30 and the hourly rate to $50, rather than the reverse.

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Answer Key continued

Benchmark Pre-TestOBJECTIVE 3: (A.6)(G)

1. B Correct

For each increase in age of 1 year, the value of the car is decreasing by $3,000. At 5 years, the value of the car will be $9,000 � $3,000 � $3,000 � $3,000.

TAKS DOCTOR: Students who answered A found the value of the car at 5.5 years, rather than at 5 years. Students who answered C found the value of the car at 4.5 years, rather than at 5 years. Students who answered D found the value of the car at 4 years, rather than at 5 years.

2. G Correct

Since the force varies directly, set up a proportion to solve the problem:

0.75 ____ 30

� x ____ 100

. Multiply both sides of

the equation by 100 to solve the

proportion: x � 100 � 0.75 ____ 30

� � 2.5.

TAKS DOCTOR: Students who answered F or H put the decimal point in the wrong place when dividing. Students who answered J set up the proportion incorrectly.

3. C Correct

Set up a proportion to solve the

problem: 600 ____ 50

� 900 ____ x .

Cross multiply to solve:

600x � 900(50) → x � 900(50)

_______ 600

� 75.

TAKS DOCTOR: Students who answered A or B set up the proportion incorrectly. Students who answered D put the decimal point in the wrong place when dividing.

4. H Correct

The distance varies directly with the time since the rate stays the same:

rate � distance ________ time

. Therefore, set up a

proportion to solve the problem:

3.5 ___ 60

� 30 ___ x . Cross multiply to solve:

3.5x � 30(60) → x � 30(60)

______ 3.5

� 514 meters.

TAKS DOCTOR: Students who answered F, G, or J did not set up the correct proportion. It takes the team 23.

_ 3 seconds to sled 400 meters; it

takes the team 26.25 seconds to sled 450 meters; and it takes the team 35 seconds to sled 600 meters.

5. B Correct

Since the length of time to hear the thunder varies directly with the distance from the lightning, set up a proportion to solve the problem:

10 ___ 2 � 7 __ x . Cross multiply to solve:

10x � 2(7) → x � 2(7)

____ 10

� 1.4 miles.

TAKS DOCTOR: Students who answered A, C, or D did not set up the correct proportion. It takes 6 seconds to hear thunder when the lightning is 1.2 miles away, 70 seconds when it is 14 miles away, and 175 seconds when it is 35 miles away.

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Answer Key continued

Benchmark Pre-TestOBJECTIVE 4: (A.7)(A)

1. B Correct

The number of hours Mary Beth runs is “2 more than the number of hours she does aerobics,” so rewrite r as 2 more than (plus) a or r � 2 � a. Since addition is commutative, this is the same as r � a � 2.

TAKS DOCTOR: Students who answered A did not understand that “2 more than” means plus, not minus. Students who answered C confused which variable is 2 more than the other. Students who answered D multiplied a by 2 instead of adding 2.

2. J Correct

Since Jared allotted a maximum amount of time, an inequality (�) is needed. Since each math question takes 3 minutes, time spent on math can be represented by 3m. Since each verbal question takes 2 minutes, time spent on verbal problems can be represented by 2v. The total time spent will be sum of the time for math and for verbal so 3m � 2v � 60.

TAKS DOCTOR: Students who answered F did not account for the different amounts of time spent on each type of question. Students who answered G chose an equation that would indicate that both types of problems took 5 minutes each. Students who answered H mixed up the times required for math and verbal.

3. A Correct

The height of the rocket is given by the initial height (20) plus the per second increase in height (15t). Since the height we are looking for is 100, set the equation equal to 100: 100 � 20 � 15t.

TAKS DOCTOR: Students who answered B chose an equation in which the initial height would be

15(20) or 300 feet. Students who answered C confused the initial height with the per second increase in height. Students who answered D chose an equation that would have an increase in height of 20 � 15, or 35, feet per second.

4. H Correct

The equation that describes the relationship between h and d must result in a true statement for all the values in the table. The only choice for which this is true is Choice H since 2(1) � 1 � 1; 2(2) �1 � 3; 2(3) � 1 � 5; and 2(4) �1 � 7.

TAKS DOCTOR: Students who answered F chose an equation that is only true for the first pair of values in the table. Students who answered G chose an equation that is only true for the second pair of values in the table. Students who answered J chose an equation that is not true for any of the pairs of values in the table.

5. C Correct

The total cost must be � $250 and must account for the different prices of each item. Streamers will make up 2s dollars of the cost, since they cost $2 per roll; flowers will make up 18f dollars of the cost since they cost $18 per vase; and balloons will make up 3b dollars of the cost since they cost $3 per bag. Therefore, the correct inequality is 2s � 18f � 3b � 250.

TAKS DOCTOR: Students who answered A did not account for the different prices of each item. Students who answered B multiplied the costs, instead of adding, and did not account for the different prices. Students who answered D chose an inequality that would indicate that each item costs $23.

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Answer Key continued

Benchmark Pre-TestOBJECTIVE 4: (A.7)(B)

1. C Correct

Since x is on both sides of the equation, a good way to start the solution would be to move the x on the left side of the equation to the right side by subtracting x from both sides.

TAKS DOCTOR: Students who answered A did not understand that you only divide the equation by a number when that number is a coefficient of the variable. Students who answered B did not recognize that dividing both sides of the equation by 4 as the first step will result in multiple fractions and is therefore not the best strategy. Students who answered D did not recognize that if you add 7 to both sides of the equation, the resulting equation will have constants on both sides.

2. J Correct

Substitute the given value of x into the equation and solve for y:

4(5) � 3y � �1020 � 3y � �10

�3y � �10 � 20�3y � �30

y � �30 ____ �3

� 10

TAKS DOCTOR: Students who answered F added 3 to both sides of the equation in the last step instead of dividing by �3. Students who answered G forgot about the negative sign in the last step. Students who answered H added 20 to the right side of the equation in the third step instead of subtracting 20.

3. C Correct

Substitute the given value of x into the

equation and solve for y :

(2) � 2y � �2�2y � �2 � 2�2y � �4

y � �4 ___ �2

� 2

TAKS DOCTOR: Students who answered A, B, or D chose points that do not lie on the line since 2 � 2(1) � 2 � 2 � 0 � �2; 2 � 2(1.5) � 2 � 3 � � 1 � �2; 2 � 2(2.5) � 2 � 5 � �3 � �2.

4. H Correct

Substitute the value of y associated with the missing value of x into the equation and solve:3x � 5(�3) � 15 3x � 15 � 15

3x � 15 � 153x � 30

x � 30 ___ 3 � 10

TAKS DOCTOR: Students who answered F, G, or J chose values that would not satisfy the given equation since 3(0) � 15 � � 15 � 15; 3(1) � 15 � �12 � 15; 3(27) � 15 � 66 � 15.

5. B Correct

Rewrite the statement algebraically and then solve. The “product of 5 and a number” can be represented by 5x; “decreased by 10” means to subtract; and “is” means equals:

5x � 10 � 405x � 40 � 105x � 50

x � 50 ___ 5 � 10

TAKS DOCTOR: Students who answered A, C, or D chose numbers that do not satisfy the given statement since 5(6) � 10 � 30 � 10 � 20 � 40; 5(18) � 10 � 90 � 10 � 80 � 40; 5(45) � 10 � 225 � 10 � 215 � 40.

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Answer Key continued

Benchmark Pre-TestOBJECTIVE 4: (A.7)(C)

1. B Correct

At 4 days, the total cost is 15(4) � 20 � $80; at 5 days, the total cost is 15(5) � 20 � $95; and at 6 days, the total cost is 15(6) � 20 � $110. This mean 5 is the maximum number of days Mr. Hawthorne can rent the carpet cleaner for less than $100.

TAKS DOCTOR: Students who answered A did not recognize that 5 days will also result in a total cost less than $100. Students who answered C or D chose values that will result in total costs greater than $100.

2. H Correct

Write an inequality that represents the situation and solve. Since the charge for each car is $15, the students will make 15c dollars for washing c cars. Raising at least $2,500 would be represented by the inequality 15c � 2500. Dividing both sides by 15 results in c � 166.

_ 6 . Since you cannot have

fractional cars, the students must wash 167 cars.

TAKS DOCTOR: Students who answered F chose a number that does not result in enough money earned. Students who answer G divided incorrectly. Students who answered J chose a number that exceeds the minimum amount needed.

3. C Correct

Substitute the given number of baseball cards into the inequality:

3(4) � 1.5y � 2012 � 1.5y � 20

1.5y � 20 � 121.5y � 8

y � 8 ___ 1.5

� 5. _ 3

Since 5 is the closest whole number value that does not exceed 5.

_ 3 , 5 is

the correct answer.

TAKS DOCTOR: Students who answered A or B chose a number of packs of gum that could be purchased for less than $20, but not the maximum (largest) number. Students who answered D chose a number of packs of gum that would result in a total cost greater than $20.

4. J Correct

If a point is in the solution set of an inequality, substituting the coordinates of the point into the inequality will result in a true statement. The point (1, 2) is in the solution set of the given inequality since 4(1) � 3(2) � 4 � 6 � 10 � 12.

TAKS DOCTOR: Students who answered F, G, or H chose a point that does not result in a true statement: F: 4(3) � 3(1) � 12 � 3 � 15 12G: 4(2) � 3(3) � 8 � 9 � 17 12H: 4(0) � 3(5) � 0 � 15 � 15 12

5. A Correct

The point that is not in the solution set will result in a false statement when its coordinates are substituted into the inequality. The point (1, 5) is not in the

solution set since 5 � 2 __ 3 (1) � 5 →

5 4 1 __ 3 (not less than or equal to).

TAKS DOCTOR: Students who answered B, C, or D chose a point that is in the solution set since:

B: 2 � � 2 __ 3 (3) � 5 → 2 � 3

C: 2 � � 2 __ 3 (4) � 5 → 2 � 7 __

3

D: �2 � � 2 __ 3 (9) � 5 → �2 � �1

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Answer Key continued

Benchmark Pre-TestOBJECTIVE 4: (A.8)(A)

1. D Correct

Since the total number of DVDs is 42, one of the equations is a � c � 42. Since the number of action movies is 12 more than (plus) the number of comedies, the other equation is a � c � 12. Choice D includes both of these equations.

TAKS DOCTOR: Students who answered A chose an equation that would indicate that Kris has 12 less (not 12 more) action movies than comedies. Students who answered B did not represent the first equation correctly. Students who answered C did not represent the total number of DVDs correctly.

2. G Correct

Since the total number of items Mr. Smith purchased was 24, one of the equations is s � d � 24. Since he bought twice as many sandwiches as drinks, the number of sandwiches is 2 times the number of drinks: s � 2d. None of the choices include both these equations as written. However, rewrite the first equation as s � 24 � d to select choice G.

TAKS DOCTOR: Students who answered F or J did not represent the second equation correctly. Both of these choices would indicate that there were twice as many drinks as sandwiches, rather than the reverse. Students who answered H did not represent the total number of items correctly.

3. A Correct

The perimeter of a rectangle can be calculated using the equation 2� � 2w � P, so 2� � 2w � 120 is one of the equations. Since the length of the rectangle is 4 times the width, the other equation is � � 4w. Choice A includes both these equations.

TAKS DOCTOR: Students who answered B or D did not represent the relationship between width and length correctly. Students who answered C did not represent the perimeter correctly (forgot to multiply by 2).

4. H Correct

Since the sum of the measures of two complementary angles is 90°, one of the equations is x � y � 90. Since the larger angle is 10 more than twice the smaller, the other equation is y � 10 � 2x. Choice H includes both these equations.

TAKS DOCTOR: Students who answered F, G, or J did not represent the second equation correctly.

5. D Correct

Since the number of items for each day are known, the system of equations should involve the price of each item and the total sales. From Day 1, 24h � 10d � 43.50 and from Day 2, 20h � 12d � 39.00 Choice D includes both these equations.

TAKS DOCTOR: Students who answered A, B, or C used the variables incorrectly in the top equation. The variables represent the price of the items, not the number of items. In addition, the bottom equation in Choice C does not account for the numbers of each item.

3 R D P R I N T

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Answer Key continued

Benchmark Pre-TestOBJECTIVE 5: (A.9)(C)

1. B Correct

When a quadratic function is in the form f (x ) � x 2 � c, changing c results in a vertical shift of the graph. The difference in the values of c between f (x ) and g (x ) is 7 � (�5) � 12 units. Since the value of c is greater for f (x ), the graph of f (x ) is 12 units above the graph of g (x ).

TAKS DOCTOR: Students who answered A subtracted �5 from 7 incorrectly. Students who answered C subtracted incorrectly and did not understand that changing c results in a vertical shift, not a horizontal shift. Students who answered D did not understand that changing c results in a vertical shift, not a horizontal shift.

2. H Correct

Since the graph is shifted up 8 units, add 8 to the value of c (�9) in the function. The new function is f (x ) � x 2 � 9 � 8 � x 2 � 1.

TAKS DOCTOR: Students who answered F did not understand that a vertical shift is accomplished by changing the value of c. This function represents a horizontal shift to the left 8 units. Students who answered G did not understand that a vertical shift is accomplished by changing the value of c. This function represents a horizontal shift to the right 8 units. Students who answered J replaced the value of c with 8 rather than adding 8 to the existing value of c.

3. A Correct

When a quadratic function is in the form f (x ) � x 2 � c, the vertex is (0, c). In the given function, changing the value of c from 3 to �1 represents a vertical shift of the vertex 4 units down.

TAKS DOCTOR: Students who answered B subtracted �1 from 3 incorrectly. Students who answered C did not understand that the shift was down, not up. Students who answered D subtracted �1 from 3 incorrectly and did not understand that the shift was down, not up.

4. F Correct

When a quadratic function is in the form f (x ) � x 2 � c, the vertex is (0, c). Shifting the parabola down 6 units will change the y�coordinate of the vertex. Since the shift is down, subtract 6: (0, 6 � 6) � (0, 0).

TAKS DOCTOR: Students who answered G replaced the y-coordinate with �6 instead of subtracting 6 from the existing y-coordinate. Students who answered H subtracted 6 from both the x- and y-coordinates of the vertex rather than from just the y-coordinate. Students who answered J subtracted 6 from the x-coordinate of the vertex rather than from the y-coordinate.

5. B Correct

To shift the graph of f (x ) � x 2 � c up 4 units, add 4 to the value of c (�2) to arrive at the new function f (x ) � x 2 � 2 � 4 or f (x ) � x 2 � 2.

TAKS DOCTOR: Students who answered A identified a function that would be shifted up 3 units, not 4, from the original function. Students who answered C replaced the value of c with 4, rather than adding 4 to the existing value. This function would be shifted up 6 units, not 4, from the original function. Students who answered D subtracted 4 from the value of c instead of adding it. This function would be shifted down 4 units, not up.

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Answer Key continued

Benchmark Pre-TestOBJECTIVE 5: (A.11)(A)

1. C Correct

To find the area, square the length of the side: � (3x2y4)2 � (3x2y4) • (3x2y4) � (3 • 3)(x2�2y4�4) � 9x4y8.

TAKS DOCTOR: Students who answered A forgot to square the coefficient (3). Students who answered B multiplied the coefficient by 2, rather than squaring it. Students who answered D squared the exponents, rather than multiplying them by 2.

2. H Correct

Simplify the coefficients by dividing; then simplify the variable expressions

using the property x a __ x b

� x a�b:

48x�4y 5

_______ 6x 2y 3

� (48 � 6)y 5�3

___________ x 2�(�4)

� 8y 2

___ x 6

.

TAKS DOCTOR: Students who answered F combined the exponents of the variable y incorrectly. Students who answered G subtracted the coefficients instead of dividing them. Students who answered J subtracted the exponents of the variable x incorrectly.

3. C Correct

Simplify the coefficients by multiplying and dividing; then simplify the variable expressions by adding and subtracting the exponents:

(7x 5)(4x 4)

_________ 2x 2

� � 7 • 4 ____ 2 � (x 5�4�2) �

28 ___ 2 x 7 � 14x 7.

TAKS DOCTOR: Students who answered A or B simplified the exponents incorrectly. Students who answered D simplified the exponents and the coefficients incorrectly.

4. F Correct

The area of a rectangle is given by the equation A � � • w. Substitute the given values and simplify: 72m4n6 �

8m3n4 � w so w � 72m4n6 _______

8m3n4 �

(72 � 8)m4�3n6�4 � 9mn2.

TAKS DOCTOR: Students who answered G subtracted the coefficients rather than dividing them. Students who answered H subtracted the coefficients rather than dividing them, and added the exponents rather than subtracting them. Students who answered J multiplied the coefficients instead of dividing them and added the exponents instead of subtracting them.

5. B Correct

Since (2x)2 � (2x)(2x) � 4x 2,

(3x 2)2 � (3x 2)(3x 2) � 9x4, and

(4x 3)2 � (4x 3)(4x 3) � 16x 6, s � r 2.

TAKS DOCTOR: Students who answered A identified an expression that does not represent the relationship between r and s since 4x 2 � 2(2x) � 4x. Students who answered C identified an expression that does not represent the relationship between r and s since 4x2 � �

� 2x . Students who answered

D identified an expression that does not represent the relationship between r and s since 4x 2 � 2(2x), not 2(4x 2) � 8x 2.

3 R D P R I N T

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Answer Key continued

Benchmark Pre-TestOBJECTIVE 6: (8.6)(A)

1. B Correct

Since DEF is an enlargement of ABC, the scale factor must be greater than 1. Compare sides DE to AB (since these are the two corresponding sides whose lengths are known) using the

ratio 6 __ 4 � 3 __

2 . This is equivalent to 1.5.

TAKS DOCTOR: Students who answered A identified a scale factor that would produce a second triangle that is the same size as the first. Students who answered C identified a ratio that would result in side DE of length 4(2) � 8, not 6. Students who answered D identified a ratio that would result in side DE of length 4(6) � 24, not 6.

2. F Correct

The top, right corner of the original rectangle is (8, 12). Since the new rectangle will be dilated using a scale

factor of 1 __ 4 , divide the coordinates of

the point (8, 12) by 4 to arrive at (2, 3).

TAKS DOCTOR: Students who answered G only divided the x-coordinate by 4. Students who answered H subtracted 4 from the coordinates instead of dividing by 4. Students who answered J found the image of the top, left corner (rather than the top, right corner).

3. C Correct

Q � is the image of Q. Since the scale

factor is 1 __ 3

, divide the coordinates of

Q(6, 12) by 3 to arrive at Q �(2, 4).

TAKS DOCTOR: Students who answered A found the image of P, not Q. Students who answered B found the image of R, not Q. Students who answered D multiplied the coordinates by 3 instead of dividing by 3.

4. G Correct

A proportionate enlargement or reduction will have the same ratio (length to width) as the original

advertisement � 6 ___ 2.5

� 2.4 � The

ratio of the length to width of the advertisement in choice G is not 2.4,

but rather 5 ____ 1.25

� 4.

TAKS DOCTOR: Students who answered F, H, or J chose an advertisement that has the same ratio as the original and is therefore a proportionate enlargement or reduction.

5. D Correct

Since Figure 2 is an enlargement of Figure 1, the scale factor will be a whole number greater than 1. Since all the coordinates of the vertices have been multiplied by 3, the scale factor is 3.

TAKS DOCTOR: Students who answered A or B chose a scale factor that would produce a smaller image, not a larger image. Students who answered C chose a scale factor in which the coordinates of all the vertices would be multiplied by 2, not by 3.

3 R D P R I N T

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Answer Key continued

Benchmark Pre-TestOBJECTIVE 6: (8.6)(B)

1. B Correct

The x-axis is the horizontal axis. When a point is reflected across the horizontal axis, the x-coordinate of the point does not change but the new y-coordinate has the opposite sign of the original y-coordinate. Choice B includes the 3 image points that meet this criteria.

TAKS DOCTOR: Students who answered A identified the image points of the triangle if it had been reflected across the y-axis. Students who answered C identified the image points of the triangle if it had been reflected across the line y � x. Students who answered D identified the image points of the triangle if it had been reflected through the origin.

2. H Correct

When a point is reflected through the origin, both the new coordinates will have the opposite sign of the original coordinate. for example, the image of the point (2, 3) will be (�2, �3). The image of a general (x, y ) point will therefore have coordinates (�x, �y ).

TAKS DOCTOR: Students who answered F identified the coordinates of the image of the point (0, 0), not a general point. Students who answered G identified the coordinates of the image of a point that has been reflected across the y-axis. Students who answered J identified the coordinates of the image of a point that has been reflected across the line y � x.

3. D Correct

The point W (�1, 5) has been translated left 3 units and down 2 units to become W �. To find Z �, apply the same translation to Z : (0 � 3, 0 � 2) � (�3, �2).

TAKS DOCTOR: Students who answered A did not apply any translation to the point Z. Students who answered B only applied the horizontal shift to Z. Students who answered C only applied the vertical shift to Z.

4. F Correct

To arrive at each of the image points from the original points, the coordinates have undergone the following changes: add 3 to the x-coordinate and subtract 3 from the y-coordinate. This is the result of a translation to the right 3 units and down 3 units.

TAKS DOCTOR: Students who answered G confused a shift to the left with a shift to the right. Students who answered H did not recognize that the triangle has undergone a horizontal and vertical shift, not a reflection. Students who answered J did not recognize that the triangle has undergone a horizontal and vertical shift, not a dilation (reduction) that would have resulted in a smaller triangle.

5. C Correct

In order for the new quadrilateral to be similar to the original quadrilateral, all of the vertices must undergo the same transformation. Each of the coordinates of the 3 given points has been dilated using a scale factor of 3 (multiplied by 3 to enlarge the figure). Apply the same dilation to point O (9, 4) to arrive at the new point S (27, 12).

TAKS DOCTOR: Students who answered A only multiplied the y-coordinate by 3. Students who answered B only multiplied the x-coordinate by 3. Students who answered D dilated the point (9, 9) that is not one of the original vertices.

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Answer Key continued

Benchmark Pre-TestOBJECTIVE 6: (8.7)(D)

1. A Correct

The horizontal distance from H to G is � 2 � (�3) � � 5. Since the shape is a rhombus, the horizontal distance from J to K must also equal 5 so the x-coordinate of K must be �1 � 5 � �6. Also, since the opposite sides of a parallelogram must be parallel, the y-coordinate of K must be the same as the y-coordinate of J or �1. The point K must have the coordinates (�6, �1).

TAKS DOCTOR: Students who answered B chose a point that would not form a rhombus when connected to the other three points. Students who answered C chose a point that would not form a rhombus when connected to the other three points. Students who answered D chose a point that does form a rhombus, but does not meet the requirement that

_ GK is parallel to

_ HJ .

2. J Correct

Since 0.5 2.5 and �1 �1.5, Point D satisfies both the given conditions.

TAKS DOCTOR: Students who answered F chose a point that does not meet either of the given conditions since 4 is not less than 2.5 and �3 is not greater than �1.5. Students who answered G chose a point that does not meet the first condition since 3 is not less than 2.5. Students who answered H chose a point that does not meet the second condition since �3.5 is not greater than �1.5.

3. C Correct

Since the circle has radius 5, its furthest points will be as follows: top (�2, 11); bottom (�2, 1); left (�7, 6); and right (3, 6). The first three points are in Quadrant II (along with the center) and the last is in Quadrant I.

TAKS DOCTOR: Students who answered A did not recognize that the majority of the circle, including the center, is in Quadrant II. Students who answered B did not recognize that a small part of the circle will extend into Quadrant I. Students who answered D did not recognize that the circle does not extend into the third quadrant since its lowest point will be (�2, 1) which is still in Quadrant II.

4. H Correct

A horizontal shift to the right is achieved by adding to the x-coordinate of the point and a vertical shift downwards by subtracting from the y-coordinate. Since the question asks for the image of R, apply the transformation to (2, 5): (2 � 5, 5 � 2) � (7, 3).

TAKS DOCTOR: Students who answered F applied a shift to the left, rather than to the right. Students who answered G found the image of P rather than R. Students who answered J applied the horizontal change to the y-coordinate (instead of the x-coordinate), and the vertical change to the x-coordinate (instead of the y-coordinate).

5. B Correct

When a point is reflected across the x-axis, the new y-coordinate has the opposite sign of the original y-coordinate. Therefore, the vertex with largest original y-coordinate will result in the lowest vertex when reflected: (0, 5) is reflected to (0, �5).

TAKS DOCTOR: Students who answered A, C, or D chose points that are not reflected images of the original vertices since they are not of the form (x, �y ) as compared to the original coordinates.

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Answer Key continued

Benchmark Pre-TestOBJECTIVE 7: (8.7)(A)

1. B Correct

Since the solid is a rectangular prism, the top view will either be a square or a rectangle. Since the dimensions are given as 3 � 3 � 7, the lengths of the sides of the top are 3 � 3 and the top is therefore a square.

TAKS DOCTOR: Students who answered A or C did not understand that when viewed from the top, a prism will be in the shape of its base. In this case, the base is a square, since the dimensions are 3 � 3. Students who answered D did not recognize that the dimensions given indicate that the top and bottom (bases) of the prism are squares rather than rectangles. A side view would be a rectangle.

2. J Correct

The base of a pyramid can be virtually any two-dimensional shape (other than a circle), as long as the edges of the pyramid all meet in a single vertex above the base. Therefore, any of the shapes is a valid choice for a base.

TAKS DOCTOR: Students who answered F, G, or H did not understand that the base of a pyramid can be many different shapes.

3. D Correct

The shape shown in Choice D would be the result of multiple views, not a single view, of the given solid.

TAKS DOCTOR: Students who answered A did not recognize that that the given shape is the view from the right side of the solid. Students who answered B did not recognize that that the given shape is the view from the top of the solid. Students who answered C did not recognize that that the given shape is the view from the front of the solid.

4. F Correct

Label each of the columns of the structure with the number of cubes to arrive at the top view:

33

33 3 2

2 4

4

3 1

1

=

TAKS DOCTOR: Students who answered G inverted the columns with 1 and 2 cubes, and 3 and 4 cubes. Students who answered H did not include the back corner column. Students who answered J did not include the back corner column and inverted the columns with 1 and 2 cubes.

5. C Correct

The drawing is of a circular cone. The top view of any pyramid or cone will be the 2-dimensional shape of its base. Therefore, the top view of the cone will be a circle.

TAKS DOCTOR: Students who answered A, B, or D did not understand that top view of any pyramid or cone will be the two-dimensional shape of its base.

3 R D P R I N T

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Answer Key continued

Benchmark Pre-TestOBJECTIVE 7: (8.7)(B)

1. B Correct

Since the roof will be covered by the shingle panels, the required measure is the area of the roof. The area of a rectangle is given by the equation A � �w � (18)(42). The area of the roof is 756 square feet. Since each panel covers 3 � 3 square feet, divide by 9 to arrive at 84 panels.

TAKS DOCTOR: Students who answered A forgot to divide by 9. Students who answered C found the perimeter of the roof (instead of the area) and forgot to divide by 9. Students who answered D divided the perimeter (instead of the area) of the roof by 9.

2. G Correct

Since the garden will be covered by the plastic, the required measure is the area of the garden. The area of a trapezoid is given by the equation

A � 1 __ 2 (h)(b1 � b2). Substitute the

given dimensions of the garden to arrive at choice G.

TAKS DOCTOR: Students who answered F identified the formula for the area of a rectangle, not a trapezoid. Students who answered H identified the formula for the area of a circle, not a trapezoid. Students who answered J identified the formula for the perimeter of a rectangle, not the area of a trapezoid.

3. B Correct

Since the seeds will need to cover the area where the pool was, the required measure is area. The area of a circle is given by the equation A � �r 2 � �(8)2. (The radius is 8 since the diameter is 16). The area is approximately 201 square feet. Since each pound of seeds covers 80 square feet, divide by 80: 201 � 80 � 2.5.

TAKS DOCTOR: Students who answered A divided the circumference (not the area) of the circle by 80. Students who answered C calculated the area of the circle using the diameter rather than the radius. Students who answered D calculated the area of the circle correctly, but forgot to divide by 80.

4. H Correct

Use the scale factor to set up a

proportion: 0.25 ____ 1 � 2 __ x and 0.25 ____

1 � 2.5 ___ x .

To solve each proportion, cross-multiply and then divide by 0.25: 2 � 0.25 � 8 and 2.5 � 0.25 � 10. The actual dimensions of the room are 8 ft by 10 ft.

TAKS DOCTOR: Students who answered F, G, or J did not set up the correct proportion and solve. A 6-foot by 8-foot room would have measurements of 1.5 inches by 2 inches on the plans; a 7 by 8 room would have measurements of 1.75 by 2; and a 10 by 12 room would have measurements of 2.5 by 3.

5. A Correct

In a triangle, the longest side is always across from the largest angle and the shortest side is always across from the smallest angle. Since the shortest side of the lot is 60 feet, the angle across from the side that is 60 feet is the smallest and the swing set should be built there.

TAKS DOCTOR: Students who answered B did not identify the smallest angle, but rather the 2nd smallest angle. Students who answered C identified the largest angle, not the smallest angle. Students who answered D did not identify one of the three angles.

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Answer Key continued

Benchmark Pre-TestOBJECTIVE 7: (8.7)(C)

1. D Correct

The drawing appears to be a right triangle which indicates that the lengths of the sides should meet the requirement of the Pythagorean Theorem that a 2 � b 2 � c 2. The triangle in choice D meets this requirement since 2.25 � 4 � 6.25.

TAKS DOCTOR: Students who answered A chose a triangle that is not a right triangle since 25 � 144 � 289. Students who answered B chose a triangle that is not a right triangle since 38.44 � 81 � 129.96. Students who answered C chose a triangle that is not a right triangle since 16 � 25 � 64.

2. H Correct

The triangle in choice H meets the requirement of the Pythagorean Theorem since 2025 � 3600 � 5625.

TAKS DOCTOR: Students who answered F chose a triangle that does not meet the requirement of the Pythagorean Theorem since 144 � 225 � 324. Students who answered G chose a triangle that does not meet the requirement of the Pythagorean Theorem since 324 � 625 � 900. Students who answered J chose a triangle that does not meet the requirement of the Pythagorean Theorem since 196 � 361 � 576.

3. B Correct

The drawing of the three squares form a right triangle. Use the Pythagorean Theorem to find the distance from O to A: A2 � 42 � 52, so A � 3. The area of the smallest square is therefore 3 � 3 � 9 unit2.

TAKS DOCTOR: Students who answered A found the length of the side of the smallest square, not the area. Students who answered C found the perimeter of the smallest square, not the area. Students who answered D found the area of the 2nd smallest square, not the smallest square.

4. F Correct

Look at the diagram to visually determine which pairs of directions meet at a right angle (90°). The only pair that does not is due N and due S, which would form a straight angle or 180°.

TAKS DOCTOR: Students who answered G, H, or J identified pairs of directions that would meet in a 90° (right) angle. Using a protractor would confirm this.

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Answer Key continued

Benchmark Pre-TestOBJECTIVE 8: (8.8)(A)

1. B Correct

Since the solid is a rectangular prism with a top and bottom, use the equation SA � 2(�w � �h � wh) to find the surface area:

SA � 2[(8 � 6) � (8 � 14) � (6 � 14)]� 2(48 � 112 � 84)� 488 in2

TAKS DOCTOR: Students who answered A did not multiply by 2. Students who answered C found the volume of the solid, not the surface area. Students who answered D added the dimensions of the solid and then squared the result.

2. H Correct

The pool is a rectangular prism with no top. Use the net to find the area of each of the 5 regions and then find the sum: (20 � 8) � 2(8 � 5) � 2(5 � 20) � 440 ft2.

TAKS DOCTOR: Students who answered F found the volume of the pool, not the surface area. Students who answered G found the surface area of the pool with a top included. Students who answered J added the dimensions of the pool and then multiplied by 2.

3. C Correct

The net shows that there are 3 rectangles of equal size and two triangles of equal size. Use the appropriate area formulas for each figure and then find the sum to calculate the total surface area:

3(�w) � 2 � 1 __ 2 bh � � 3(4 � 10) �

2 � 1 __ 2 � 4 � 3.5 � � 3(40) � 2(7) �

134 cm2

TAKS DOCTOR: Students who answered A found the area of only one rectangle and one triangle. Students who answered B found the area of all 3 rectangles, but only one triangle. Students who answered D multiplied the dimensions together.

4. J Correct

The surface area of a cylinder is given by the equation SA � 2�r 2 � 2�rh. The only choice that cannot be simplified to arrive at this equation is choice J since �r 2(2 � 2h) � 2�r 2 � 2�r 2h.

TAKS DOCTOR: Students who answered F chose a formula that does represent the surface area of a cylinder. Students who answered G chose a formula that will simplify to the correct formula since 2�(r 2 � rh) � 2�r 2 � 2�r h. Students who answered H chose a formula that will simplify to the correct formula since 2�r (h � r ) � 2�rh � 2�r 2.

5. B Correct

Once measured, the dimensions of the net are approximately as follows: r � 0.5 in. and h � 1.25 in. Using the formula for SA, the total surface area is SA � 2�(0.5)2 � 2�(0.5)(1.25) � 5.5 in2.

TAKS DOCTOR: Students who answered A used the wrong value for h (3.125 instead of 1.25). Students who answered C only included the area of one circle. Students who answered D multiplied the dimensions of the net, rather than using the correct formula for surface area.

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Answer Key continued

Benchmark Pre-TestOBJECTIVE 8: (8.8)(B)

1. C Correct

The formula for finding the volume of a cube is given by V � s 3. The student’s measurement should be

approximately 3 __ 8 of an inch, so the

volume can be found using the

equation V � � 3 __ 8 � 3.

TAKS DOCTOR: Students who answered A identified a formula that represents the area of one of the squares, not the volume of the cube. Students who answered B identified a formula that represents the surface area of the cube, not the volume. Students who answered D identified a formula that combined surface area and volume.

2. H Correct

The volume of the composite solid is the sum of the volume of the cube and the volume of the pyramid. The formula for finding the volume of a cube is given by V � s 3, and the formula for finding the volume of a

pyramid is V � 1 __ 3 Bh. Since the base of

the pyramid has sides of length s, the

volume of the pyramid is V � 1 __ 3 s2h.

This means the volume of the solid is V � 1 __

3 s2h � s3.

TAKS DOCTOR: Students who

answered F forgot to include the 1 __ 3

in the volume formula for a pyramid. Students who answered G only found the volume of the pyramid, not the pyramid and the cube. Students who answered J incorrectly distributed the

1 __ 3 to the volume of both the pyramid

and the cube.

3. B Correct

The volume of a cylinder is given by the formula V � �r 2h. The radius of the tank is 100 (half the diameter) and the height is 16. The correct formula for the volume is therefore V � �(100)2(16).

TAKS DOCTOR: Students who answered A switched the dimensions for the diameter and the height. Students who answered C used the diameter of the base, instead of the radius. Students who answered D chose a formula that represents surface area, not volume.

4. F Correct

The volume of any prism is given by the formula V � Bh. For a triangular prism, the area of the base (B) is found using the formula for the area of

a triangle � A � 1 __ 2 bh � . The volume of

the prism is V � 1 __ 2 (3)(4)(12) � 72 in3.

TAKS DOCTOR: Students who answered G forgot to multiply by 1 __

2 .

Students who answered H found the surface area of the prism. Students who answered J multiplied all the dimensions together.

5. A Correct

The volume of a cone is given by the

formula V � 1 __ 3 �r 2h. The radius of the

base is 10 (half the diameter) and the height of the cone is 6. The volume is

V � 1 __ 3 �(10)2(6) � 628 ft3.

TAKS DOCTOR: Students who answered B switched the dimensions for d and h. Students who answered C

forgot to multiply by 1 __ 3 . Students who

answered D used the diameter instead of the radius.

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Answer Key continued

Benchmark Pre-TestOBJECTIVE 8: (8.8)(C)

1. B Correct

To cover the area with paint, find the surface area. Since the top of the shed does not have to be painted, the surface area is equal to (4 � 8) � 2(4 � 6) � 2(6 � 8) or 176 square feet.

TAKS DOCTOR: Students who answered A did not include the bottom of the shed. Students who answered C found the volume of the shed, not the surface area. Students who answered D included the top in their calculations.

2. H Correct

Substitute the given values into the formula for finding the volume of

a cone: 44 � 1 __ 3 �r 2(7). Solve the

equation for r 2.

3 � 44 _____ �(7)

� r 2

6.005 � r 2

��

6.005 � r � 2.5

TAKS DOCTOR: Students who answered F multiplied by 1 __

3 instead

of dividing by 1 __ 3 when solving for r.

Students who answered G forgot to

include 1 __ 3 in the formula they solved.

Students who answered J found r 2, not r.

3. C Correct

To approximate the radius, substitute the given values into the formula for the volume of a cylinder: 48 � �r 2(5). Solve for r 2 by dividing both sides of

the equation by 5�: 48 ___ 5�

� 3.06 � r 2.

Square root the result to find the radius: �

� 3.06 � 1.75.

TAKS DOCTOR: Students who answered A found the diameter of the can, not the radius. Students who answered B found r 2, not r. Students who answered D substituted 5 for the radius (instead of the height) and then solved the equation.

4. F Correct

The formula for the volume of a cylinder is given by V � �r 2h and the formula for the volume of a cone is

given by V � 1 __ 3 �r 2h. Since the given

dimensions of both solids are the same, the volume of the cone will be one-third the volume of the cylinder,

or 150 ____ 3 � 50.

TAKS DOCTOR: Students who answered G divided the volume of the cylinder by 2 instead of by 3. Students who answered H did not understand that a cone has a volume equal to one-third of a cylinder with the same dimensions. Students who answered J did not understand that a cone has a volume equal to one-third of a cylinder with the same dimensions.

5. C Correct

To estimate the surface area, round the length of the side to 4. Then use the formula SA � 6s 2: SA � 6(4)2 � 96 cm2.

TAKS DOCTOR: Students who answered A found the distance around the edges of the cube, not the surface area. Students who answered B found the volume of the cube. Students who answered D combined the formulas for volume and surface area.

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Answer Key continued

Benchmark Pre-TestOBJECTIVE 8: (8.9)(A)

1. B Correct

Use the Pythagorean Theorem with legs of lengths 4 and 8 to find the distance (hypotenuse):

42 � 82 � c 2 → 16 � 64 � c 2

80 � c 2 → c � ��

80 � 9.

TAKS DOCTOR: Students who answered A subtracted the lengths rather than using the Pythagorean Theorem. Students who answered C added the lengths rather than using the Pythagorean Theorem. Students who answered D forgot to square root the answer.

2. J Correct

Use the Pythagorean Theorem with legs of lengths 6 ft and 22 ft to find the height of the broken telephone pole (hypotenuse). Add the broken pole’s height and 6 ft:

62 � 222 � c 2 → 36 � 484 � c 2

520 � c 2 → c � ��

520 � 23.

6 � 23 � 29

TAKS DOCTOR: Students who answered F calculated the sum of the square roots, rather than the square root of the sum of a 2 � b 2. Students who answered G subtracted the lengths rather than using the Pythagorean Theorem. Students who answered H did not add the broken length and the standing length.

3. B Correct

Use the Pythagorean Theorem with one leg of length 12 and the hypotenuse of length 25 to find the distance:

122 � b 2 � 252

144 � b 2 � 625

b 2 � 625 � 144 � 481

b � ��

481 � 22 ft.

TAKS DOCTOR: Students who answered A subtracted the lengths rather than using the Pythagorean Theorem. Students who answered C used 25 as the length of a leg rather than the length of the hypotenuse. Students who answered D added the lengths rather than using the Pythagorean Theorem.

4. H Correct

First use the Pythagorean Theorem with legs of lengths 40 and 82 to find the length of the back of the yard (hypotenuse):

402 � 822 � c 2

8,324 � c 2

c � ��

8,324 � 91

Next find the perimeter of the entire yard: 40 � 82 � 91 � 213. Since the posts are 5 feet apart, divide 213 by 5 � 43 posts.

TAKS DOCTOR: Students who answered F found the number of posts for the back of the yard only. Students who answered G found the number of posts for the two “legs” of the yard only. Students who answered J found the length of the back of the yard, but did not answer the question about the posts.

5. C Correct

Since the playground is square, use

the equation x 2 � x 2 � 302 to find the length: x 2 � x 2 � 302 → 2x 2 � 900

x 2 � 900 ____ 2 = 450 so x � �

� 450 �

21.2 ft.

TAKS DOCTOR: Students who answered A divided 30 by 2 and then took the square root. Students who answered B divided 30 in half. Students who answered D used 30 as the leg of the triangle instead of the hypotenuse.

3 R D P R I N T

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Answer Key continued

Benchmark Pre-TestOBJECTIVE 8: (8.9)(B)

1. B Correct

Set up a proportion to find the length

of s: 15 ___ 12

� 14 ___ s . Cross-multiply and then

divide by 15 to solve:

15s � 12(14)

s � 12(14)

______ 15

� 11.2

TAKS DOCTOR: Students who answered A subtracted 1 from 12 since 14 � 15 � 1. Students who answered C set up an incorrect

proportion: 14 ___ 15

� 12 ___ s . Students who

answered D set up an incorrect

proportion: 14 ___ 12

� s ___ 15

.

2. J Correct

Set up a proportion to solve. The order of the letters is very important:

AB ___ DE

� AC ___ DF

. So 3 __ 6 � 8 ___

DF → 3DF � 6(8)

→ DF � 48 ___ 3 � 16.

TAKS DOCTOR: Students who answered F divided AC by 2 instead of multiplying by 2. Students who answered G found the length of EF, not DF. Students who answered H added 3 to AC since DE � AB � 3.

3. A Correct

Set up a proportion to solve:

scale _____ actual

� scale _____ actual

. So the correct

proportion is 1 __ 6 � h ___

80 .

TAKS DOCTOR: Students who answered B, C, or D set up an incorrect proportion.

4. G Correct

Since the cylinders are similar, set up a proportion using the given

dimensions: diameter ________ height

� diameter ________ height

.

So d ___ 18

� 33 ___ 27

→ 27d � 18(33) →

d � 18(33)

______ 27

� 22. The value found

using the proportion is the diameter of cylinder A, so divide by 2 to arrive at a radius of 11 units.

TAKS DOCTOR: Students who answered F set up an incorrect

proportion: 18 ___ d � 33 ___

27 . Students who

answered H found the diameter, not the radius. Students who answered J set up an incorrect proportion:

18 ___ 27

� 33 ___ d .

5. C Correct

To produce a similar figure, the ratio of the longer side to the shorter side must be the same. The ratio for the

given figure is 42 ___ 25

� 1.68. The only

figure that has the same ratio is the

figure in choice C since 126 ____ 75

� 1.68.

TAKS DOCTOR: Students who answered A identified a figure that is not similar to the given figure since

84 ____ 12.5

� 6.72 � 1.68. Students who

answered B identified a figure that is not similar to the given figure since

168 ____ 25

� 6.72 � 1.68. Students who

answered D identified a figure that is not similar to the given figure since

210 ____ 100

� 2.1 � 1.68.

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Answer Key continued

Benchmark Pre-TestOBJECTIVE 8: (8.10)(A)

1. B Correct

If the ratio of two similar figures is a:b, then the ratio of their perimeters is also a:b. Since the given ratio is 1:3 and the perimeter of the larger quadrilateral is 108, divide by 3 to arrive at the perimeter of the smaller quadrilateral � 36 cm.

TAKS DOCTOR: Students who answered A divided by b2 or 9 rather than by b 3. Students who answered C divided by 2 instead of dividing by 3. Students who answered D multiplied by 3 instead of dividing by 3.

2. J Correct

If the ratio of two similar figures is a:b, then the ratio of their areas is a 2: b 2. When the radius of a circle is tripled, the ratio of the first circle to the second circle is 1:3. This means the areas are in the ratio 1:9. So the area is increased nine times.

TAKS DOCTOR: Students who answered F did not understand that the area should be multiplied by 9, not divided by 3. Students who answered G did not understand that the area will be multiplied by 9, not remain constant. Students who answered H did not understand that the circumference should be multiplied by 3, and the area multiplied by 9.

3. A Correct

If the ratio of two similar figures is a:b, then the ratio of their areas is a 2:b 2. Since all squares are similar, use the ratio to find the area of the larger square. The ratio of the two squares is 1:3, so the ratio of their areas is 12:32 or 1:9. To find the area of the larger square, multiply 150 by 9 to arrive at 1,350 square inches.

TAKS DOCTOR: Students who answered B multiplied by 3 instead of by 9. The new perimeter would by multiplied by 3, but not the area. Students who answered C divided by 3 instead of multiplying by 9. Students who answered D divided by 9 instead of multiplying by 9.

4. F Correct

If the ratio of two similar figures is a:b, then the ratio of their perimeters is also a:b. Since the dimensions of the first rectangle are tripled, the perimeter of the new rectangle will also be tripled, or 78 cm. Since the width of the larger rectangle is 12 cm, subtract 2(12) from the perimeter and divide by 2 to get the new length:

78 � 24 _______ 2 � 54 ___

2 � 27 cm.

TAKS DOCTOR: Students who answered G forgot to divide by 2. Students who answered H found the new perimeter, not the new length. Students who answered J multiplied the perimeter by 9, instead of by 3, and then found the length.

5. C Correct

Since the radius of the smaller circle

is 1 __ 4 the radius of the larger circle,

the ratio of the radii is 1:4. The ratio of the circumferences will be the same: 1:4.

TAKS DOCTOR: Students who answered A found the ratio of the volumes of two spheres whose radii are in the ratio 1:4. Students who answered B found the ratio of the areas of the two circles. Students who answered D found the ratio of the circumference of circle P to circle O instead of the ratio of O to P.

3 R D P R I N T

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Answer Key continued

Benchmark Pre-TestOBJECTIVE 8: (8.10)(B)

1. D Correct

If the ratio of two similar figures is a:b, then the ratio of their volumes is a3:b3. All cubes are similar. Since the given ratio of the edges of the larger cube to the smaller cube is 5:1, the ratio of their volumes is 53:13 or 125:1. This means the volume of cube 2 is 125 times the volume of cube 1.

TAKS DOCTOR: Students who answered A did not cube the ratio. Students who answered B multiplied the ratio by 3 instead of cubing it. Students who answered C squared the ratio instead of cubing it.

2. F Correct

The scale factor is 1 __ 3 so the change in

volume is � 1 __ 3 � 3, or 1 ___

27 . 1 ___

27 of 324 in.3

or 12 in.3.

TAKS DOCTOR: Students who

answered G divided the volume by

9, not 27. Students who answered

H divided the volume by 3, not 27.

Students who answered J reduced the

volume by 1 __ 3 � 2 __

3 � 324 � 216 � .

3. A Correct

The scale factor is 1 __ 5 so the change in

volume is � 1 __ 5 � 3, or 1 ____

125 . 1 ____

125 of 1,250

is 10 cm3.

TAKS DOCTOR: Students who answered B divided the volume by 25 instead of 125. Students who answered C divided the volume by 15 (5 � 3) instead of by 125 (53). Students who answered D divided the volume by 5 instead of by 125.

4. H Correct

The ratio of the dimensions of the cylinders is 4:1 so the ratio of the volumes will be 43:13 or 64:1.

TAKS DOCTOR: Students who answered F identified the ratio of the dimensions, not the ratio of the volumes. Students who answered G identified the ratio of the surface areas, not the ratio of the volumes. Students who answered J raised the ratio to the fourth power instead of to the third power.

5. C Correct

Since the volumes are in the ratio 8 to 1, the dimensions of the cones are in the ratio

3 ��

8 to 3 ��

1 or 2 to 1. This means the ratio of the areas is 22 to 12 or 4 to 1.

TAKS DOCTOR: Students who answered A identified the ratio of the dimensions, not the ratio of the areas. Students who answered B did not understand that they needed to cube root the given ratio and then square it. Students who answered D squared the ratio.

3 R D P R I N T

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Answer Key continued

Benchmark Pre-TestOBJECTIVE 9: (8.1)(B)

1. C Correct

Set up the proportion in the

form miles ______ gallons

� miles ______ gallons

. Since the car

can go 182 miles on 7 gallons, the left

side of the proportion is 182 ____ 7 . The right

side is miles on trip

_____________ gallons needed

� 455 ____ g . The

correct proportion is 182 ____ 7 � 455 ____ g .

TAKS DOCTOR: Students who answered A, B, or D did not keep the proportion in the correct ratios: they either mixed miles and gallons, or inverted the given values.

2. F Correct

Set up the proportion in the form

# tagged

____________ # of armadillos

� # tagged

____________ # of armadillos

.

Since the number with tags in the

second set of armadillos captured

was 3 out of 50, the left side of the

proportion is 3 ___ 50

. The total number

tagged was 40 and the total in the

park is unknown, so the right side is

40 ___ a . The correct proportion is 3 ___ 50

� 40 ___ a .

TAKS DOCTOR: Students who answered G, H, or J did not keep the proportion in the correct ratios: they either mixed tags and armadillos, or inverted the given values.

3. D Correct

Set up the proportion in the form

miles _____ days

� miles _____ days

. Since David bikes

26.5 per one day, the left side of the

proportion is 26.5 ____ 1 . The total number of

miles is unknown, and the total days is

30. So, the right side is m ___ 30

. The correct

proportion is 26.5 ____ 1 � m ___

30 .

TAKS DOCTOR: Students who answered A, B, or C did not keep the proportion in the correct ratios: they either mixed miles and days, or inverted the given values.

4. H Correct

Set up the proportion in the form

defective glasses

______________ number in batch

� defective glasses

______________ number in batch

.

Since each of the samples in the table

yield 17 defective glasses per 110,

the left side of the proportion is 17 ____ 110

.

The total number of defective glass

is unknown and the total produced is

2,000. So, the right side is d _____ 2000

. The

correct proportion is 17 ____ 110

� d _____ 2000

.

TAKS DOCTOR: Students who answered F, G, or J did not keep the proportion in the correct ratios: they either mixed defective glasses with number produced, or inverted the given values.

5. A Correct

Set up the proportion in the form

object height

____________ shadow height

� object height

____________ shadow height

.

Since the person is 5 feet tall and his

or her shadow is 11 feet long, the left

side of the proportion is 5 ___ 11

. The height

of the tree is 18 feet but the length of

its shadow is unknown. So, the right

side is 18 ___ s . The correct proportion is

5 ___ 11

� 18 ___ s .

TAKS DOCTOR: TAKS DOCTOR: Students who answered B, C, or D did not keep the proportion in the correct ratios: they either mixed up object height with shadow height, or inverted the given values.

3 R D P R I N T

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Answer Key continued

Benchmark Pre-TestOBJECTIVE 9: (8.3)(B)

1. B Correct

Since 28 players on the team have been fitted, 48 � 28 � 20 players on the team have not been fitted. To find the percent, divide 20 by 48 to arrive at approximately 42%.

TAKS DOCTOR: Students who answered A found the number of players that have not been fitted rather than the percent. Students who answered C found the percent that have been fitted rather than the percent that have not been fitted. Students who answered D subtracted the number of players that have not been fitted from 100%.

2. H Correct

The total number of players is 8 � 4 � 2 � 14. The number of players that are in the 11th grade is 4, so the percent of the team that is in the 11th

grade is 4 ___ 14

� 0.286 � 28.6% .

TAKS DOCTOR: Students who answered F found the number of players rather than the percent. Students who answered G found the percent of players in the 10th grade rather than in the 11th grade. Students who answered J found the percent of players in the 12th grade rather than in the 11th grade.

3. D Correct

Express the given information using an algebraic equation: the question translates into “85% of what number is 17” which can be expressed as 0.85x � 17. Solve the equation by dividing both sides by 0.85:

17 ____ 0.85

� 20 questions.

TAKS DOCTOR: Students who answered A found the number of questions Maria answered incorrectly. Students who answered B multiplied 17 by 0.85 instead of dividing. Students who answered C found the percent answered incorrectly.

4. G Correct

According to the graph, 75% of the 240 people are under the age of 30. This means 0.75 � 240 � 180 people are under the age of 30. Five percent of those people are under 16, so 0.05 � 180 � 9 people.

TAKS DOCTOR: Students who answered F found 5% of 75, rather than 5% of the number of people (180). Students who answered H found 5% of the total number of people (240), rather than 5% of those under the age of 30. Students who answered J found the number of people under the age of 30, not the number of people under 16.

5. B Correct

Since 10 minutes is equivalent to

10 ___ 60

� 1 __ 6 of an hour, divide 24 by 6 to

arrive at 4 miles in 10 minutes.

TAKS DOCTOR: Students who answered A divided 24 by 10 instead of by 6. Students who answered C multiplied 24 by 6 instead of dividing. Students who answered D multiplied 24 by 10 instead of dividing by 6.

3 R D P R I N T

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Answer Key continued

Benchmark Pre-TestOBJECTIVE 9: (8.11)(A)

1. B Correct

Since there are 5 choices, the probability of randomly selecting the

correct answer is 1 __ 5 and the probability

of randomly selecting an incorrect

answer is 1 � 1 __ 5 � 4 __

5 . The probability

of missing two and then getting two correct is the product of the probabilities of each event:

4 __ 5 • 4 __

5 • 1 __

5 • 1 __

5 � 16 ____

625 .

TAKS DOCTOR: Students who answered A found the probability of getting all 4 correct. Students who answered C found the probability of getting all 4 wrong. Students who answered D multiplied the sums of the probability of getting 2 wrong and then 2 right.

2. F Correct

The total number of balls in the box is 12. The number that are red or blue is 5 � 4 � 9. The probability of getting a red or blue is equal to

number red or blue ________________ total number in box

� 9 ___ 12

� 3 __ 4 .

TAKS DOCTOR: Students who answered G found the probability of getting a red ball. Students who answered H found the probability of getting a blue ball. Students who answered J multiplied the probabilities of each event (“and”) rather than adding them (“or”).

3. C Correct

The probability of randomly choosing

a red apple is 5 __ 9 . Without replacing

the red apple, the number of apples remaining is 8 and the probability of randomly choosing a green apple from

those 8 is 4 __ 8 � 1 __

2 . The probability of

both events occurring is the product of

the two probabilities or 5 __ 9 • 1 __

2 � 5 ___

18 .

TAKS DOCTOR: Students who

answered A multiplied 1 __ 9 by 1 __

9 .

Students who answered B found the probability with replacement. Students who answered D added the probabilities instead of multiplying them.

4. J Correct

Odd numbers make up 25 � 12.5 � 12.5 � 50% of the spinner so the probability of getting an odd number is 0.5. The number 5 represents 12.5% of the spinner so the probability of spinning a 5 is 0.125. The probability of spinning an odd number and then the number 5 is the product of the two probabilities: 0.5 × 0.125 � 0.0625.

TAKS DOCTOR: Students who answered F added the probabilities instead of multiplying. Students who answered G found the probability of spinning an odd number. Students who answered H found the probability of spinning an odd on both spins.

5. A Correct

Since 12th graders make up 48% of the Pre-Calculus class, the probability of randomly selecting a 12th grader is 0.48 from that class. Since the 12th graders make up 70% of the Calculus class, the probability of randomly selecting a 12th grader is 0.7. The probability of selecting a 12th grader from both classes is the product of the two probabilities: 0.48 × 0.7 � 0.336.

TAKS DOCTOR: Students who answered B found the probability of selecting a 12th grader from the Pre-Calculus class. Students who answered C found the probability of selecting a 12th grader from the Calculus class. Students who answered D added the probabilities instead of multiplying them.

3 R D P R I N T

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Answer Key continued

Benchmark Pre-TestOBJECTIVE 9: (8.11)(B)

1. B Correct

The experimental probability of rolling a 3 on the next roll is equal to the ratio

# 3s rolled in experiment

_____________________ total # rolls in experiment

� 80 ____ 400

� 1 __ 5 .

TAKS DOCTOR: Students who answered A found the theoretical probability of rolling a 3 on the next roll, not the experimental probability. Students who answered C found the experimental probability of rolling a 4 rather than a 3 on the next roll. Students who answered D found the experimental probability of not rolling a 3 on the next roll.

2. F Correct

The theoretical probability of rolling a 3 on the next roll is equal to the ratio

#3s on a die _____________ total #s on a die

� 1 __ 6 . The difference

is 1 __ 5 (found in #1) minus 1 __

6 � 0.2 �

0.167 � 0.033.

TAKS DOCTOR: Students who answered G found the theoretical probability of rolling a 3, not the difference. Students who answered H found the experimental probability of rolling a 3, not the difference. Students who answered J found the sum of the two probabilities, not the difference.

3. B Correct

Since the data is given as percents, the experimental probability of tossing a heads on the next toss has already been calculated and is equal to the percent of tosses that were heads in the experiment, or 0.42.

TAKS DOCTOR: Students who answered A divided 42 by 150, instead of reading off the percent given. Students who answered C found the theoretical probability of tossing a heads, not the experimental probability. Students who answered D found the experimental probability of tossing a tails, not a heads.

4. J Correct

The theoretical probability of tossing

a heads is 1 __ 2 � 0.5 so the difference

between the two probabilities is 0.5 �0.42 � 0.08.

TAKS DOCTOR: Students who answered F found the sum of the two probabilities instead of the difference. Students who answered G found the theoretical probability of tossing a heads. Students who answered H found the experimental probability of tossing a heads.

5. B Correct

Based on Mike’s record, his experimental probability of bowling

a score of over 150 is 70 ______ 70�30

� 70 ____ 100

� 7 ___ 10

. If he bowls 1,000 games, he

can expect to bowl 1,000 � 7 ___ 10

� or 700

games with a score of over 150.

TAKS DOCTOR: Students who answered A subtracted 30 from 1000. Students who answered C found the correct expected value, but then subtracted 30 from it. Students who answered D found the number of games Mike could expect to score under 150, rather than over 150.

3 R D P R I N T

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Answer Key continued

Benchmark Pre-TestOBJECTIVE 9: (8.12)(A)

1. B Correct

Find each measures of central tendency to determine which is the most impressive: range � 9 � 4 � 5;

mean � 5 � 4 � 7 � 9 � 4 ________________ 5 � 5.8;

median � middle number when ordered least to greatest � 5; and mode � number that appears the most often � 4. The mean (5.8) is the greatest.

TAKS DOCTOR: Students who answered A, C, or D chose a measure whose value is less than the mean.

2. J Correct

Find each of the measures of central tendency to determine which has the highest value: range � 92 � 84 � 8;

mean � 443 ____ 5 � 88.6; median � middle

number when ordered least to greatest � 89; and mode � number that appears the most often � 92. The mode (92) has the highest value.

TAKS DOCTOR: Students who answered F, G, or H chose a measure whose value is less than the mode.

3. D Correct

The median and the mode of the data

set are both 25. The mean is 220 ____ 9 �

24. _ 4 . Therefore, the median and the

mode are both greater than the mean.

TAKS DOCTOR: Students who answered A chose a false statement since the median is also 25. Students who answered B chose a false statement since the mean is 24.4. Students who answered C chose a false statement since the range is 50 � 15 � 35 � 25 (mode), not less.

4. F Correct

The range of the original data was 100 � 80 � 20. If Maggie scored a 90 on Quiz 3, the range would not change since 88 was not the highest or the lowest score.

TAKS DOCTOR: Students who answered G chose a measure that would change since the original mean was 88 and the new mean would be 88.4. Students who answered H chose a measure that would change since the original median was 88 and the new median would be 90. Students who answered J chose a measure that would change since there was originally no mode and the new mode would be 90.

5. D Correct

In a stem-and-leaf plot, the stem represents the first digit in a value and the leaf represents the last digit. The first few test scores are 98, 94, 91, 89, and so on. There are a total of 17 scores represented in the stem-and-leaf plot. Of those, 9 are greater than 80. Nine out of 17 is approximately 53%, so more than 50% of the class scored above an 80.

TAKS DOCTOR: Students who answered A chose a false statement since the highest score was a 98, not a 92. Students who answered B chose a false statement since the median (middle) score was an 81, not an 80. Students who answered C chose a false statement since the range of the scores was 98 − 52 � 46, not 50.

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Answer Key continued

Benchmark Pre-TestOBJECTIVE 9: (8.12)(C)

1. C Correct

The height of each bar represents the number of people surveyed who answered in that category. The approximate number of people surveyed is 45 � 55 � 70 � 40 � 20 � 230.

TAKS DOCTOR: Students who answered A identified the minimum number of people in any one category. Students who answered B identified the maximum number of people in any one category. Students who answered D multiplied the maximum number of people in any one category (70) by the number of categories (5).

2. G Correct

To calculate the percentages, divide the number in each category by the total number of people:

200 ____ 800

� 0.25 � 25%; 318 ____ 800

� 0.4 �

40%; 160 ____ 800

� 0.2 � 20%; 122 ____ 800

� 0.15

� 15%.

The correct percentages are 25%, 40%, 20%, and 15%.

TAKS DOCTOR: Students who

answered F or H did not divide the

number in each category by 800:

200 ____ 800

� 0.25 � 15%; 200 ____ 800

� 0.25 �

30%. Students who answered J used

the number in each category, not the

percent.

3. C Correct

In a bar graph, the height of the bar usually represents the number of data values that fall into a certain category. Multiply 240 by 37.5% (0.375) to find the number of votes Charlene received: 240 � 0.375 � 90.

TAKS DOCTOR: Students who answered A chose the percent of votes Charlene received, not the number of votes she received. Students who answered B chose the percent of votes Charlene did not receive, not the number of votes she did receive. Students who answered D chose the number of votes Charlene did not receive, not the number she did receive.

4. H Correct

Since the sum of the numbers in the circle graph is 100, the numbers can either represent the percent of households in a certain category or the number of households in that category. This means the height of the bars in the bar graph will be the same. The heights should be, from left to right, 12, 25, 30, 18, and 15. Instead, the heights are 18, 25, 30, 12, and 15. The bars for “under 20” and “60–79” were switched.

TAKS DOCTOR: Students who answered F chose an incorrect pair since the height of the “80-99” category is correct. Students who answered G chose an incorrect pair since the height of the “80–99” category is correct. Students who answered J chose an incorrect pair since the height of the “20–29” category is correct.

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Answer Key continued

Benchmark Pre-TestOBJECTIVE 9: (8.13)(B)

1. C Correct

The percentage of red cars sold was 15% and the percentage of white cars was 35%. Therefore, more than twice as many white cars were sold as red cars, not the reverse. This statement is false.

TAKS DOCTOR: Students who answered A chose a true statement since black cars represent the smallest section of the circle graph (10%). Students who answered B chose a true statement since silver cars represent the largest section of the circle graph (40%). Students who answered D chose a true statement since 35% (white cars) is more than the total of 15% and 10% (red and black cars).

2. F Correct

Since silver cars represent 40% of the sales and black cars represent 10% of the sales, the ratio of silver to black is 40 to 10, or 4 to 1. So, silver cars outsold black cars by a ratio of 4 to 1.

TAKS DOCTOR: Students who answered G did not realize that there were more silver cars sold than white cars. Students who answered H did not understand that the pie graph does not provide information about sales growth, but rather only about the sales for a particular month. Students who answered J did not understand that one month’s sales is not an indication that a color will be discontinued.

3. A Correct

The number of students enrolled in Algebra 1 is approximately 370. The number of students enrolled in all the other math classes together is approximately 250 � 180 � 140 � 570. Since 370 is not greater than 570, this statement is false.

TAKS DOCTOR: Students who answered B chose a true statement since the bar for Pre-Calculus is the shortest and therefore represents the lowest enrollment. Students who answered C chose a true statement since enrollment in Algebra 1 (� 370) is more than twice the enrollment in Pre-Calculus (� 140). Students who answered D chose a true statement since the enrollment in Algebra 2 (� 180) is slightly less than half of the

enrollment in Algebra 1 (� 370 ____ 2

� 185).

4. J Correct

Since the bar lengths decrease as the level of difficulty increases, it is reasonable to conclude that fewer students choose to take the more difficult classes.

TAKS DOCTOR: Students who answered F did not understand that the bar graph only provides information about the students enrolled in math classes, not about all the students in the school. Students who answered G chose a conclusion that is not necessarily supported by the information. The graph does not provide reasons for the different enrollments. (The same teacher may teach both classes.) Students who answered H chose a conclusion that is not supported by the information provided. The bar graph does not provide information about how many Algebra 1 teachers the school has or needs.

3 R D P R I N T

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Answer Key continued

Benchmark Pre-TestOBJECTIVE 10: (8.14)(A)

1. B Correct

Although the question asks for the original price, consider the more common strategy for finding the sales price of an item: when determining sales price, begin with the original price and subtract the % off of that price: sales price � original � % of original. Since 20% is equivalent to one fifth and the sales price is given as x, this equation becomes

x � p � 1 __ 5

p or p � 1 __ 5 p � x.

TAKS DOCTOR: Students who answered A chose an incorrect equation since the sales price plus a percent of the sales price equals slightly less than the original price. Students who answered C chose an incorrect equation since subtracting a percent from the sales price decreases the price even more. Students who answered D chose an incorrect equation since subtracting one-fifth from the sales price decreases the price even more.

2. H Correct

Let David’s unknown age be represented by x and then translate Tasha’s age into an algebraic expression: “3 more than twice David’s age” can be written as 3 � 2x. Since Tasha is 19 years old, set the expression equal to 19: 3 � 2x � 19. Since addition is commutative, this is equivalent to 2x � 3 � 19.

TAKS DOCTOR: Students who answered F chose an equation that would represent the expression “twice the quantity of 3 more than David’s age” rather than 3 more than twice David’s age. Students who answered G added 3 years to Tasha’s age rather than to twice David’s age. Students who answered J subtracted 3 years from twice David’s age instead of adding it.

3. A Correct

To increase an amount by a percent over time, you must know the original amount, so the average price of lumber in 1998 is needed.

TAKS DOCTOR: Students who answered B did not understand that the future price would not determine the past price. Students who answered C did not understand that knowing the range of the prices would not provide the information needed. Students who answered D did not understand that knowing the amount of lumber sold would not provide the information needed to find the price in 2004.

4. F Correct

Since each tile measures 12 in. by 12 in., the area of the tile is 1 ft2. If Mr. Hennessey knows the square feet he is tiling and how many tiles are in a box, he can divide to determine how many boxes he needs.

TAKS DOCTOR: Students who answered G did not realize that the size of the tile is already provided. Students who answered H did not understand that the amount of tax will not affect the number of boxes. Students who answered J did not understand that the weight of the boxes will not affect the number of boxes.

5. C Correct

Since the price per box is already known, as well as the shipping and handling fee, the only missing information is how many boxes will be purchased and what the tax rate will be.

TAKS DOCTOR: Students who answered A understood that the number of boxes is needed, but did not realize that the tax rate is needed. Students who answered B or D did not understand that the box weight is not needed since there is a flat shipping rate.

3 R D P R I N T

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Answer Key continued

Benchmark Pre-TestOBJECTIVE 10: (8.14)(B)

1. C Correct

Divide 20 by 5 to get a rate of 4 gallons per minute. Since there are 60 minutes in an hour, this is equivalent to a rate of 240 gallons per hour. Divide 2,400 gallons by 240 to arrive at 10 hours to empty the tanker.

TAKS DOCTOR: Students who answered A found the number of minutes to empty the tanker, rather than the number of hours. Students who answered B divided 2,400 by the product of 20 and 5. Students who answered D divided 2,400 by the product of 20 and 60.

2. F Correct

Subtract 30% of 150 from 150 to get the pre-tax price of 150 � (150)(0.3) � $105. Then add 6.25% of 105 to 105 to get the price with tax: 105 � (105)(0.0625) � $111.56. Since Ellen paid 3($50) � $150, her change is $150 � $111.56 � $38.44.

TAKS DOCTOR: Students who answered G forgot to include the sales tax. Students who answered H used 30% of the original price, instead of taking 30% off the original price. Students who answered J found the cost of the coat, not the amount of change.

3. C Correct

First find the perimeter of the yard by adding the lengths of the sides: 25.4 � 19.2 � 38.4 � 16 � 99 ft. Since the fence itself costs $6.50 per linear foot, multiply the cost by the number of feet: 99 � $6.50 � $643.50. To find the cost to install the fence, divide 99 by 6 (since the cost is per 6-foot panel) and then multiply by the cost: (99 � 6) � 4.25 � $70.13. Add the two amounts to find the total cost: $643.50 � $70.13 � $713.63.

TAKS DOCTOR: Students who answered A divided the perimeter by 6 before finding the cost of the fence even though the price of the fence itself was not per 6-foot panel. Students who answered B only found the cost of the fence itself; they did not find the cost of the installation as well. Students who answered D did not divide the perimeter by 6 before finding the cost of installation.

4. G Correct

Find the distance around the roller by calculating the circumference of a circle with radius 4.5 (since the diameter is 9): C � 2�(4.5) � 28.27. Since the roller went around 52 times, multiply 28.27 � 52 � 1,470. This is the distance around the lake in inches; divide by 12 to find the distance in feet: 1470 � 12 � 122.5 or approximately 123 ft.

TAKS DOCTOR: Students who answered F multiplied 52 by 9 and divided by 12. Students who answered H used the diameter of the roller instead of the radius. Students who answered J found the distance in inches instead of in feet.

5. A Correct

Find the total cost if Pierre uses high octane gas: 580(2.19) � $1,270.20. Then find the total cost if Pierre uses regular gas: 580(1.97) � $1,142.60. The savings is the difference between the amounts or $127.60. As a percent,

127.60 _______ 1270.20

is approximately 10%.

TAKS DOCTOR: Students who answered B, C, or D chose an

incorrect percent since 127.60 _______ 1270.20

11%, 12%, or 13%.

3 R D P R I N T

Copyright © by Holt, Rinehart and Winston. 162 Holt Mathematics Grade 9All rights reserved.

Answer Key continued

Benchmark Pre-TestOBJECTIVE 10: (8.14)(C)

1. C Correct

Since Janet has 4 more thimbles than Allie, let the number of thimbles Allie has be represented by x. This means the number that Janet has will be 4 more than x, or x � 4. Since Carissa has 3 times as many as Janet, the number Carissa has will be 3 times (x � 4) or 3(x � 4). The equation is Allie � Janet � Carissa � 121 or x � (x � 4) � 3(x � 4) � 121.

TAKS DOCTOR: Students who answered A did not understand that “4 more than” means 4 � x, not 4 times x. Students who answered B did not understand that the number Carissa has will be 3 times (x � 4) not just 3 times x. Students who answered D did not understand that “4 more than” means 4 � x, not 4 times x.

2. J Correct

Since the lobby is a square, use the equation A � s2. Since the area is known, the equation is 576 � s2. To solve this equation, take the square root of both sides of the equation. So, to find the length, find the square root of the area.

TAKS DOCTOR: Students who answered F did not understand that to solve an equation involving the square of a variable you must find the square root, not divide by 2. Students who answered G confused perimeter and area; if the perimeter were given, you would divide by 4 to find the length of the side. Students who answered H did not understand that to solve an equation involving the square of a variable you must find the square root, not the square.

3. B Correct

To arrive at the second step, distribute the 6 to both of the terms in the

parentheses: 6(3x � 8) � 6(3x) � 6(8) � 18x � 48 so the second step is 18x � 48 � 2 � �10.

TAKS DOCTOR: Students who answered A did not distribute the 6 to the �8. Students who answered C distributed the 6 to the 2, even though the 2 is not in the parentheses. Students who answered D added the �8 and the 2, even though the 2 is not in the parentheses.

4. H Correct

There are several different rectangles that have an area of 36. However, only one of these will also have a perimeter of 30. Try each of the choices to determine the correct answer. A rectangle with dimensions 3 by 12 will have an area of (3)(12) � 36 and a perimeter of 3 � 3 � 12 � 12 � 30.

TAKS DOCTOR: Students who answered F chose a rectangle with the correct area but whose perimeter is 74 cm. Students who answered G chose a rectangle with the correct area but whose perimeter is 40 cm. Students who answered J chose a rectangle with the correct area but whose perimeter is 26 cm.

5. C Correct

In some situations, the best strategy to solve a problem is to draw a picture. Graph the given points and then graph each of the choices. The only point that completes the picture of the square is (1, �1). Each of the other points forms a quadrilateral, but not a square.

TAKS DOCTOR: Students who answered A, B, or D chose a point that forms a quadrilateral with the other three points, but not a square.

3 R D P R I N T

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Answer Key continued

Benchmark Pre-TestOBJECTIVE 10: (8.15)(A)

1. C Correct

To cover the box, you need to know the area of each of the sides, the top, and the bottom. In other words, you need to know the area of the surface, or the surface area.

TAKS DOCTOR: Students who answered A did not understand that perimeter is the distance around a two-dimensional figure. Students who answered B did not understand that circumference is the distance around a circle. Students who answered D did not understand that volume is the capacity of a three-dimensional figure.

2. J Correct

The capacity of a three-dimensional figure is its volume. Since the amount of water needed to fill the pool is another way of saying the pool’s capacity, volume is the correct answer.

TAKS DOCTOR: Students who answered F did not understand that perimeter is the distance around a two-dimensional figure. Students who answered G did not understand that lateral area is a two-dimensional measurement that measures the area of the sides of a three-dimensional figure. Students who answered H did not understand that surface area is a two-dimensional measurement that measures the area of the sides, top, and bottom of a three-dimensional figure.

3. A Correct

Since all the angles of the figure are right angles, the figure is a rectangle, which is also a parallelogram and a quadrilateral. However, since the sides are different lengths (x � y ), the figure is not a square or a rhombus. Choice A is correct.

TAKS DOCTOR: Students who answered B, C, or D did not recognize the figure as a rectangle or did not understand that a rectangle also meets the definition of both a quadrilateral (has 4 sides) and a parallelogram (has 2 pairs of equal-length parallel sides).

4. G Correct

Since the equation for the area of

a rectangle is A � � � w, find the

correct ratio by dividing both sides

of the equation by �: A __ � � � � w _____

� so

w � A __ � . As a comparison, the width of

a rectangle is the quotient of its area

divided by its length.

TAKS DOCTOR: Students who answered F inverted the ratio. Students who answered H or J identified a ratio that does not include the variable A, and therefore cannot compare the rectangle’s area to its length.

5. C Correct

Use key words to describe the equation: minus means “the difference” or “less than”; plus means “the sum” or “more than”; and 2( ) means “two times”, “the product”, or “twice.” The only choice that accurately arranges these meanings is choice C.

TAKS DOCTOR: Students who answered A arranged the meanings correctly but inverted the fraction. Students who answered B did not distribute the 2 to the 3 and came up with an inaccurate description. Students who answered D described x � 5 as “5 times x ” instead of “5 more than x ” or “the sum of 5 and x.”

3 R D P R I N T

Copyright © by Holt, Rinehart and Winston. 164 Holt Mathematics Grade 9All rights reserved.

Answer Key continued

Benchmark Pre-TestOBJECTIVE 10: (8.16)(A)

1. B Correct

Use each set of values of a, b, and c to test the properties until you find one that does not meet the requirements: 42 � 52 � 16 � 25 � 41 � 82. So, the set of integers 4, 5, and 8 are not a Pythagorean Triple.

TAKS DOCTOR: Students who answered A, C, or D chose a set of numbers for which both of the given properties are true. Each set of numbers is a Pythagorean Triple.

2. G Correct

According to the table, the ones digit follows the pattern 3, 9, 7, 1, 3, 9, 7, 1. This pattern repeats in sets of 4, with every fourth one being a 1. So, consider multiples of 4. The closest multiple of 4 to 46 is 44, which means 344 has a 1 in the ones place. Since 46 is two more than 44, move down the pattern two places. The digit in the ones place of 346 is a 9.

TAKS DOCTOR: Students who answered F identified the digit in the ones place of 345 rather than 346. Students who answered H identified the digit in the ones place of 347 rather than 346. Students who answered J identified the digit in the ones place of 348 rather than 346.

3. C Correct

Since all of the numbers in the pattern are the consecutive powers of 4 and they all end in either a 4 or a 6, it is reasonable to conclude that all powers of 4 end in either a 4 or 6.

TAKS DOCTOR: Students who answered A did not realize that the ones digit does not always increase by 2: it increases by 2 and then decreases by 2 and then increases

by 2 and so on. Students who answered B did not recognize that the information provided concerns the powers of 4, not the multiples of 4. Some multiples of 4, such as 8, do not end in a 4 or 6. Students who answered D did not recognize the pattern of the digits in the ones place.

4. G Correct

Find the width of the first square by dividing the perimeter by 4: 16 � 4 � 4. Then use the pattern described to find the width of the fifth square: 4, 4 � 1, 4 � 1 � 1, 4 � 1 � 1 � 1, and finally 4 � 1 � 1 � 1 � 1. So the width of the fifth square is 8. This means the perimeter of the fifth square is 4(8) � 32 units.

TAKS DOCTOR: Students who answered F found the perimeter of the fourth square in the pattern, not the fifth square. Students who answered H found the perimeter of the sixth square in the pattern. Students who answered J found the perimeter of the seventh square in the pattern.

5. D Correct

Since each of the numbers in the choices is a perfect square number and since each one ends in a 1, all three choices provide a counterexample to Joe’s conjecture.

TAKS DOCTOR: Students who answered A did not realize that B and C also provide valid counterexamples to Joe’s conjecture. Students who answered B did not realize that A and C also provide valid counterexamples to Joe’s conjecture. Students who answered C did not realize that A and B also provide valid counterexamples to Joe’s conjecture.

3 R D P R I N T

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Answer Key continued

Benchmark Pre-TestOBJECTIVE 10: (8.16)(B)

1. A Correct

A counterexample can be used to prove that a statement is not true. Consider the values x � 3 and y � 2 and test the truthfulness for each portion of the statement: 3 � 2

but 1 __ 3 1 __

2 (not �).

TAKS DOCTOR: Students who answered B, C, or D chose statements that are true statements. Any positive integer values of x and y will result in true statements; that is, no counterexamples can be found so the statements are all true.

2. J Correct

The only statement for which a counterexample cannot be found is choice J. Therefore, this statement is the only one that must be true.

TAKS DOCTOR: Students who answered F chose a statement that could be false; if x � �3 and y � �2, then x2 � y2 but x is not greater than y. Students who answered G chose a statement that could be false; if x � 3 and y � 2, then x2 � y2 but y is not greater than x. Students who answered H chose a statement that could be false; if x � 3 and y � 2, then x2 � y2 but y is not a negative number.

3. D Correct

In a parallelogram, opposite angles are equal and adjacent angles are supplementary. This means that or m�A � 180° � m�B or m�A � 180° � m�D. However, m�A � 180° � m�C since angle A and C are opposite angles, not adjacent angle.

TAKS DOCTOR: Students who answered A chose a valid conclusion since opposite angles are equal. Students who answered B chose a

valid conclusion since each pair of adjacent angles are supplementary and the sum of the two pairs is 360°. Students who answered C chose a valid conclusion since C and D are adjacent angles and adjacent angles are supplementary.

4. G Correct

Since all three angles in the first triangle have a measure of x°, the triangle is equiangular and therefore equilateral. Since the second triangle is a right triangle, the hypotenuse must be longer than the two legs and is therefore not an equilateral triangle. Since the third triangle has three equal sides, it is equilateral. Therefore, only one of the triangles is not equilateral.

TAKS DOCTOR: Students who answered F did not realize that two of the triangles are equilateral triangles, not just one. Students who answered H did not realize that the right triangle cannot be an equilateral triangle. Students who answered J did not realize that the perimeter of the first triangle cannot be determined.

5. C Correct

The diagonals of a rectangle and a square have equal lengths. Since the diagonals of figure ABCD are not of equal length, the figure cannot be a rectangle or a square. The only choice that agrees with this analysis is choice C.

TAKS DOCTOR: Students who answered A or B did not understand that a rectangle must have diagonals of equal length and that figure ABCD therefore cannot be a rectangle. Students who answered D did not understand that a square must have diagonals of equal length and that figure ABCD therefore cannot be a square.

3 R D P R I N T

Copyright © by Holt, Rinehart and Winston. 166 Holt Mathematics Grade 9All rights reserved.

Answer KeyBenchmark Post-TestOBJECTIVE 1: (A.1)(A)

1. C

2. H

3. B

4. H

5. A

OBJECTIVE 1: (A.1)(B)

1. D

2. J

3. A

4. G

5. D

OBJECTIVE 1: (A.1)(C)

1. D

2. F

3. B

4. H

5. B

OBJECTIVE 1: (A.1)(D)

1. C

2. H

3. C

4. J

5. B

OBJECTIVE 1: (A.1)(E)

1. C

2. F

3. D

4. G

5. D

OBJECTIVE 2: (A.2)(A)

1. B

2. G

3. D

4. F

5. C

OBJECTIVE 2: (A.2)B

1. B

2. H

3. C

4. G

5. D

OBJECTIVE 2: (A.2)(C)

1. B

2. C

3. H

4. D

OBJECTIVE 2: (A.2)(D)

1. B

2. H

3. B

4. G

5. A

OBJECTIVE 2: (A.3)(A)

1. B

2. J

3. B

4. F

5. D

3 R D P R I N T

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Answer Key continued

Benchmark Post-TestOBJECTIVE 2: (A.3)(B)

1. D

2. H

3. B

4. G

5. D

OBJECTIVE 2: (A.4)(A)

1. D

2. F

3. B

4. F

5. C

6. H

OBJECTIVE 2: (A.4)(B)

1. A

2. H

3. A

4. J

5. B

6. F

OBJECTIVE 2: (A.4)(C)

1. D

2. G

3. A

4. J

5. C

OBJECTIVE 3: (A.5)(A)

1. B

2. H

3. D

4. J

OBJECTIVE 3: (A.5)(C)

1. D

2. G

3. B

4. H

5. C

OBJECTIVE 3: (A.6)(A)

1. C

2. G

3. B

4. H

5. D

OBJECTIVE 3: (A.6)(B)

1. C

2. F

3. B

4. J

5. B

OBJECTIVE 3: (A.6)(C)

1. A

2. G

3. A

4. J

5. B

OBJECTIVE 3: (A.6)(D)

1. A

2. H

3. A

4. G

5. C

3 R D P R I N T

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Answer Key continued

Benchmark Post-TestOBJECTIVE 3: (A.6)(E)

1. A

2. J

3. D

4. J

5. D

OBJECTIVE 3: (A.6)(F)

1. A

2. F

3. B

4. H

5. D

OBJECTIVE 3: (A.6)(G)

1. C

2. G

3. D

4. H

5. A

OBJECTIVE 4: (A.7)(A)

1. B

2. G

3. C

4. J

5. B

OBJECTIVE 4: (A.7)(B)

1. A

2. F

3. B

4. G

5. A

6. J

OBJECTIVE 4: (A.7)(C)

1. C

2. H

3. B

4. H

5. A

OBJECTIVE 4: (A.8)(A)

1. A

2. F

3. C

4. H

5. C

OBJECTIVE 5: (A.9)(C)

1. D

2. G

3. B

4. H

5. D

OBJECTIVE 5: (A.11)(A)

1. C

2. J

3. B

4. H

5. A

OBJECTIVE 6: (8.6)(A)

1. B

2. F

3. A

4. F

5. A

3 R D P R I N T

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Answer Key continued

Benchmark Post-TestOBJECTIVE 6: (8.6)(B)

1. A

2. J

3. C

4. G

5. B

OBJECTIVE 6: (8.7)(D)

1. B

2. F

3. D

4. J

5. A

OBJECTIVE 7: (8.7)(A)

1. B

2. J

3. C

4. H

5. A

OBJECTIVE 7: (8.7)(B)

1. C

2. J

3. A

4. J

5. C

OBJECTIVE 7: (8.7)(C)

1. A

2. G

3. C

4. F

OBJECTIVE 8: (8.8)(A)

1. C

2. G

3. B

4. G

5. C

OBJECTIVE 8: (8.8)(B)

1. A

2. H

3. C

4. J

5. B

OBJECTIVE 8: (8.8)(C)

1. B

2. G

3. D

4. G

5. B

OBJECTIVE 8: (8.9)(A)

1. A

2. J

3. B

4. F

5. B

OBJECTIVE 8: (8.9)(B)

1. C

2. G

3. D

4. F

5. A

3 R D P R I N T

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Answer Key continued

Benchmark Post-TestOBJECTIVE 8: (8.10)(A)

1. C

2. J

3. B

4. F

5. B

OBJECTIVE 8: (8.10)(B)

1. A

2. J

3. B

4. G

5. C

OBJECTIVE 9: (8.1)(B)

1. A

2. G

3. A

4. J

5. C

OBJECTIVE 9: (8.3)(B)

1. C

2. G

3. A

4. H

5. C

OBJECTIVE 9: (8.11)(A)

1. C

2. H

3. B

4. F

5. D

OBJECTIVE 9: (8.11)(B)

1. A

2. J

3. D

4. F

5. C

OBJECTIVE 9: (8.12)(A)

1. A

2. G

3. C

4. H

5. B

OBJECTIVE 9: (8.12)(C)

1. B

2. J

3. B

4. H

OBJECTIVE 9: (8.13)(B)

1. B

2. H

3. D

4. G

OBJECTIVE 10: (8.14)(A)

1. D

2. G

3. C

4. J

5. B

3 R D P R I N T

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Answer Key continued

Benchmark Post-TestOBJECTIVE 10: (8.14)(B)

1. B

2. J

3. B

4. H

5. C

OBJECTIVE 10: (8.14)(C)

1. D

2. H

3. D

4. F

5. B

OBJECTIVE 10: (8.15)(A)

1. D

2. G

3. C

4. F

5. D

OBJECTIVE 10: (8.16)(A)

1. C

2. F

3. B

4. G

5. C

OBJECTIVE 10: (8.16)(B)

1. D

2. F

3. B

4. F

5. B

3 R D P R I N T