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TEST PREP for New York Grade 6 Mathematics Performance Indicators

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ISBN 13: 978-0-547-42223-7ISBN 10: 0-547-42223-7

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iii NY Test Prep Grade 6

Table of ContentsGrade 6 Mathematics in Brief . . . . . . . . . . . . . . . . . . . . . . . . . . . . v

Standardized Test-Taking Strategies for MathTips for Taking the Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .vii

Tips for Answering Multiple-Choice Questions . . . . . . . . . . . . . . . ix

Tips for Answering Short-Response and Extended-Response Questions . . . . . . . . . . . . . . . . . . . . . x

Strategies for Success . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi

Analyzing Word Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii

Learning Math Vocabulary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv

Math Anxiety . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvi

Troubleshooting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviii

Test Practice

Number Sense and OperationsWhole Number Place Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Commutative, Associative, and Distributive Properties . . . . . . . . 3

Properties of Addition and Multiplication . . . . . . . . . . . . . . . . . . . 5

Ratios and Proportional Reasoning . . . . . . . . . . . . . . . . . . . . . . . 7

Percents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Absolute Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Order Rational Numbers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Fractions with Unlike Denominators . . . . . . . . . . . . . . . . . . . . . . 15

Add, Subtract, Multiply, or Divide Mixed Numbers . . . . . . . . . . . 17

Fractions and Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Fractions, Decimals, and Percents . . . . . . . . . . . . . . . . . . . . . . . 21

Order of Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

Exponents. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

Estimation and Percents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

AlgebraAlgebraic Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

Writing Two-Step Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

Solving Two-Step Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

Proportions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

Evaluating Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37Cop

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iv NY Test Prep Grade 6

GeometrySimilar Triangles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

Areas of Triangles and Quadrilaterals. . . . . . . . . . . . . . . . . . . . . 41

Areas of Regular and Irregular Polygons . . . . . . . . . . . . . . . . . . 43

Circles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

Circles and Sectors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

Coordinate Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

MeasurementVolume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

Customary Units of Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

Metric Units of Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

Estimate Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

Statistics and ProbabilitySurveys and Samples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

Choosing Data Displays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

Mean, Median, Mode, and Range . . . . . . . . . . . . . . . . . . . . . . . 63

Interpreting Data Displays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

Predictions from Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

Probability and Counting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

Sample Test A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A1

Sample Test B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B1

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v NY Test Prep Grade 6

Grade 6 Mathematics Test in Brief

Question format Multiple Choice, Short-Response, Extended-Response

Time Limit 55 minutes � 2 days

Materials needed Bring two sharpened No. 2 pencils with erasers. Calculators are allowed during certain portions of the test.

Links www.emsc.nysed.gov/osa/

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vi NY Test Prep Grade 6

Standardized Test-Taking Strategies for Math

Standardized tests, such as the New York State Testing Program in Mathematics, are designed in order for you to demonstrate the content and skills you have learned. It is important to keep in mind that, in most cases, the best way to prepare for these tests is to pay close attention in class and take every opportunity to improve your mathematical, reading, and writing skills.

On the following pages, you will find tips and strategies to help you with the New York State Testing Program in Mathematics.

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vii NY Test Prep Grade 6

Tips for Taking the Test

Throughout the year

• Keep up with your homework. Homework is important practice that will help you learn the skills you need for the test. Practice will also help you answer questions more quickly, leaving more time for the difficult questions.

• Review your notes, homework, and tests on a regular basis to make sure that you maintain the skills you learned earlier in the year.

• Use flashcards to learn important formulas and vocabulary words. If you can, memorize formulas to save time on the test.

• Familiarize yourself with the format and content of the test.

• Make a timeline for reviewing materials in the time leading up to the test. Do not try to “cram” the night before the test.

• Practice without your calculator, because you will not be allowed to use a calculator on the test.

Before the test

• Be sure you are well rested.

• Eat a good breakfast.

• Be on time, and be sure that you have the necessary materials.

• Be sure to bring any assistive device that you need, such as glasses or a hearing aid.

• Try not to miss class the day before the test. Your teacher may be reviewing important content.

During the test

• Listen to the instructions of the teacher. It’s easy to miss important points that can affect your score.

• Read the directions carefully. If you do not understand a direction, raise your hand and ask for clarification immediately.

• Work the problem out in the test booklet. You are more likely to make a mistake when doing a problem in your head. You can also use your written work to help check your answer. Circle the answer and write the problem number next to your work so you can find it while you are reviewing your test.

• Read the entire question, including all answer choices, and think about your answer before you bubble in your answer.

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• Fill in the circle for each answer carefully and completely. Erase any stray marks on the page. If you change an answer choice, be sure to erase completely and carefully so that you do not tear a hole in the answer sheet.

• Make sure the number on the answer document matches the question number in the test booklet.

• Don’t spend too much time on any one question. If you cannot answer a question right away, fill in your best choice. If you have time at the end of the test, return to any questions you are unsure of.

• If questions contain negative wording such as NOT, read them carefully and be alert for the use of double negatives within a sentence.

• Understand the format of the test so that you can gauge your time according to what section of the test you are taking.

• If you finish early, review the test and make sure the answer sheet is filled out correctly. Remember, your first answer is usually the correct one, so don’t change an answer unless you can convince yourself that your original choice is wrong. Try solving the problem in a different way to see if you get the same answer.

• DON’T STRESS! Just remember what you have learned in class, and you should do well.

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ix NY Test Prep Grade 6

Tips for Answering Multiple-Choice Questions

• If there is a figure accompanying the question, review the figure carefully. Read the labels and make sure you understand what the figure represents. Remember, a figure may not be drawn to scale.

• If there is not a figure, it may be helpful to draw one on your scratch paper using the information provided.

• Read the multiple-choice question first for its general intent and then reread it carefully, looking for words that give clues or can limit possible answers to the question.

• If possible, work the question before looking at the answer choices. Then look for your answer among the given choices. If your answer is not one of the choices, read the question again. Be sure that you understand the problem. Remember, common errors are often used to generate incorrect answer choices. Be sure you work carefully.

• Make sure you answer the question being asked. A partial answer to the question may be used as an incorrect answer choice.

• Always read all of the possible answer choices—even if the first one seems like the correct answer. There may be a better choice farther down in the list.

• Think of what you already know about the math topic involved and use that information to help eliminate answer choices. You can also use estimation to eliminate answer choices.

• If you cannot work the question, you may be able to substitute the answer choices back into the question to find the correct choice. Start with the middle value. If the result is too large, then substitute a smaller value. If the result is too small, then substitute a larger value.

• Never leave a question blank. There is no penalty for guessing, so always choose an answer.

• When you are finished, reread the question and the selected answer to be sure that you made the best choice and that you marked it correctly on the answer sheet.

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x NY Test Prep Grade 6

Tips for Answering Short-Response and Extended-Response Questions

• Read the question first for its general intent and then reread it carefully. Make sure you understand exactly what is being asked. There is often more than one answer required, especially for extended-response questions.

• Use correct mathematical vocabulary and your best handwriting when answering the problem. Circle your answer.

• Show all work to get full credit. If you do a step in your head, write in words what you did and why.

• If you are unable to finish the problem, you may be able to get partial credit by writing down any information that you would use in solving the problem.

• If there is a figure accompanying the question, review the figure carefully. Read the labels and make sure you understand what the figure represents. Remember, a figure may not be drawn to scale.

• If a figure or graph is required in the answer, be sure that you draw the figure as accurately as possible and label all required parts.

• Never leave a question blank. There is no penalty for guessing, so always write an answer.

• When you are finished, reread the question. Check to make sure you answered all parts of the question.

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xi NY Test Prep Grade 6

Strategies for Success

There are various strategies you can employ ahead of time to help you feel more confident about answering questions on math standardized tests. Here are a few suggestions:

1. VISUALSNote the labels on the charts and graphs. For example, a scale on one axis may provide a valuable clue. Read all graphs twice.

When reading diagrams, read all labels and tick marks carefully, and read diagrams twice, also.

Label the figure with any information stated in the problem that is not in the diagram. Use the properties of the figure, for example, if it is stated that a figure is a square, you can label all the sides with the same length.

If a figure is not provided, it may be helpful to draw one. Be sure that you do not assume any information that is not included in the problem. Remember, the figure does not have to look perfect. It is only to help you understand the relationships in the problem.

2. CONCEPTSWhen answering questions about math concepts, don’t let a hard question stump you. You can always work with what you do know. It’s possible to answer a question when you know only a part of the concept being tested.

Another strategy to help you on difficult questions is to draw or sketch out the question’s concept. Often you can understand how to answer a question by listing what you know, sketching the process, and then identifying what you are supposed to solve.

If you do not understand a problem on the test, try to relate it to a problem you can solve. For example, you can substitute simpler numbers into a problem and figure out how to solve it. Then try again with the original values in the problem.

3. MATH SKILLSTo help you on the math sections of the tests, practice the skills as you are reading and discussing your textbook. For example, you could put the steps to a process in order in your mind. Also, sequencing a process can become a game you play with a friend who also has to take the test. Always ask yourself what the most important points are when studying sections. Some of the more common skills for studying math are

• Analyzing Information—the process of breaking something down into its parts and examining the relationships between them. Analyzing enables you to better understand the whole.

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xii NY Test Prep Grade 6

• Sequencing—the process of placing the steps in a process in order to better understand the steps and the process as a whole. When you analyze the sequence, you are determining what happens first, second, and so on.

• Categorizing—the process by which you group things together by the characteristics they have in common. Categorizing helps you to make comparisons and see differences among things.

• Identifying Cause and Effect—interpreting the relationships between events. A cause makes something happen. An effect is what happens as a result of the cause.

• Comparing and Contrasting—the process of examining situations or ideas, etc., for their similarities and differences.

• Summarizing—the process of taking a large amount of information and boiling it down into a short clear statement. To summarize a problem, you must analyze the problem to find the most important points and the supporting information.

• Paraphrasing—a paraphrase is a restatement of someone’s ideas or words. A paraphrase is usually about as long as the original; the ideas are just expressed in simpler terms. A paraphrase question might be stated like this, “According to the passage, which of these statements is accurate?”

• Visualizing—visualizing helps you see processes and procedures in your mind’s eye. Visualizing will help you be successful on a variety of math questions you could encounter on tests.

4. READING MATH

First, remember that what you have learned about math can help you in answering comprehension questions on tests. Also, though, remember the following points:

• Read the problem as if you were not taking a test.

• Look at the big picture. Ask yourself questions like, What is the question being asked? What do the diagrams or graphs tell me?

• Read the problem quickly first. This technique will help you know what information to look for as you read.

• Reread the problem and underline information related to the questions.

• Go back to the question and try to answer it in your mind before looking at the answers.

• Read all the answer choices and eliminate the ones that are obviously incorrect.

• If you can eliminate certain answers, getting the choice down to two, go ahead and pick one of the two responses. That’s an educated guess, and you are most likely better off making the choice.

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xiii NY Test Prep Grade 6

Analyzing Word Problems

Many students who are comfortable with basic skill problems are still stumped by word problems. These steps will help you work through word problems on standardized tests.

Step 1 Understand the problemRead the problem carefully and make sure you understand what is being asked. You may wish to rewrite the question in your own words.

List the given information or circle it in your test booklet, if you are allowed to write in it. Cross out any unnecessary information.

Step 2 Make a planThink about similar problems you have seen in the past, and how you solved them.

Determine a strategy or strategies that you will use to solve the problem, such as drawing a diagram, working backward, finding a pattern, or other problem-solving strategies.

Step 3 Solve the problemSolve the problem according to your plan. If the strategy you chose is not working, go back and revise. Write out all the steps on your scratch paper to avoid making careless mistakes.

Step 4 Look backMake sure you answered the question that was asked.

Check your answer in the words of the problem to make sure your answer is reasonable.

Make sure your answer is in the correct place on the answer document.

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xiv NY Test Prep Grade 6

Learning Math Vocabulary

Learning vocabulary is important in order to be successful on standardized tests. During the test, you will not be able to ask the meaning of a word, and you may not be able to answer a question that contains a word you do not know.

Spend time learning vocabulary throughout the year so that you are prepared for your test when the time comes.

Identify important terms:As you learn new concepts, keep a list of unfamiliar terms. Also, review the standards for your grade and write down any words you do not know.

Learn the meaning of each term:Look up the meaning of each new word in your glossary. It may help to use the Vocabulary Questioning Strategies shown on the next page. Another way to learn vocabulary is by using graphic organizers like the ones shown below.

Memory aids:Your lists of words may be used as memory aids, or it may be helpful to create flashcards with the term on the front and the definition and/or examples on the back. Review the flashcards frequently. As you learn the words, you may remove the flashcards from your stack, but keep them for occasional review before your exam.

Use context clues:If you do encounter an unfamiliar word on your test, don’t panic. Try to relate it to a familiar word or use context clues to determine the meaning of the word in the problem.

Term

Definition

Example Example Example

Definition Characteristic

Example Nonexample

Word

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xv NY Test Prep Grade 6

Vocabulary Questioning Strategies

Vocabulary term

Before you look up the word, predict its meaning. Some clues you can use are as follows:

• the way you have seen or heard the word used• the everyday meaning of the word• the meaning of the root word, prefix, or suffix

I think this word means

Look up the word in your glossary, and write its meaning here.

Write a question in your own words that contains the vocabulary term, and write the answer.

Question:

Answer:

Think of a strategy to remember the meaning of the word. Some possible strategies are as follows: draw a picture that represents the word, write a poem or song about the word, or relate the math meaning to the everyday meaning of the word. Write your strategy here.

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xvi NY Test Prep Grade 6

Math anxiety is a term used to describe fear and negative attitudes about working with numbers and taking math tests. Here are some suggestions to help alleviate math anxiety.

• Motivate yourself to learn math. Math class can be challenging, but it also has many rewards. Mathematics is a useful tool with a wide range of applications in nearly every field, as well as everyday life.

• Talk to your teacher about your anxiety. He or she may have suggestions or be able to help in other ways.

• Go to class every day! Research shows a strong correlation between attendance and math grades. Attending class should be a high priority.

• Make the most of your class time. Warm up for class by looking over the previous day’s notes and homework. Write out any questions you have. If possible, read ahead in the text. Be alert and attentive. You won’t get much benefit out of sleeping through class.

• Ask questions in class. If you just decide you can figure something out later, you may not understand the rest of the lecture, and fall further behind. Most often others will have the same question.

• Develop a note-taking system. If you are too busy writing every word the teacher says, you will not have time to comprehend much. Use abbreviations and shorthand during class, and re-work or re-write your notes soon after class to make sure you understand what was said.

• Do your homework as soon after class as possible. The longer you wait, the more you may forget. If you get behind, you will have a harder time understanding further material, and you may become frustrated.

• Find a study partner or group to work with. This will make math a more comfortable activity, maybe even fun!

• Find a place you are comfortable studying, where there are few distractions. If you have a certain place set aside for studying, you will find it easier to get into the right frame of mind to study there.

• Take breaks while studying. The mind works best in short periods of time, between 20 and 45 minutes. When you can’t concentrate, take 5–10 minutes to walk around, stretch, or have a snack, then return to your work refreshed.

• Get help when you are stuck. Don’t agonize for hours, ask your teacher, a tutor, a classmate, or a friend for help.

• Make a vocabulary list and a formula list. Use flashcards to memorize definitions and formulas. Remember, math is like a foreign language. You can’t speak it if you don’t know the words.

Math AnxietyC

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• To solidify your understanding, after you have done your homework, try the following: Check your answers against the answers in the back of the book. Do some extra problems from the book in areas you had trouble. Make up some practice problems and work them. Write out a general step-by-step procedure for solving each type

of problem.

• Learn relaxation techniques and practice them before the test so that if you get frustrated you will be able to relax during the test.

• Learn more about math anxiety in books or on the Internet. Many people have math anxiety, and there are a lot of resources out there.

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xviii NY Test Prep Grade 6

Taking practice tests can be helpful, but you will get more out of them if you analyze the tests after they have been scored to see where you made mistakes. Look at the table below to see some common types of mistakes. Use the blank rows to add in your own types with how you can avoid them in the future.

Type of mistake Ways to avoid it in the future

I was unfamiliar with the concept involved in the question.

Review the standards to make sure I know what will be covered on the test.

I knew how to do the problem, but I couldn’t remember.

Maintain skills throughout the year. Review old tests and homework to keep old topics fresh.

I misread the problem. Read the problem carefully, and check my answer against the words of the problem to make sure the answer makes sense.

I did not know the meaning of a word in the problem.

Make lists of vocabulary terms and use vocabulary strategies to learn their meanings.

I did not transfer the answer to the answer sheet correctly.

Check frequently that the answers are in the right place. Circle the answer in the answer booklet or on scratch paper so I can go back and check it.

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1 NY Test Prep Grade 6

Name _________________________________ Date ______________Class ______________

NUMBER SENSE AND OPERATIONSWhole Number Place Value

6.N.1 Read and write whole numbers to trillions.

Select the best answer for each question.

1 Write the following number in standard form: two trillion, eight hundred thirty billion, twenty-four million

A 2,830,024,000

B 2,000,830,024,000

C 2,830,240,000,000

D 2,830,024,000,000

2 Write the number 1.678 trillion in standard form.

F 1,678,000

G 1,678,000,000

H 1,678,000,000,000

J 1,678,000,000,000,000

3 Which number below shows a 4 in the ten-billions place?

A 375,048,000

B 5,040,578,932

C 1,348,738,000,321

D 50,357,046,000,364

4 Which number represents one trillion?

F 1,000

G 1,000,000

H 1,000,000,000

J 1,000,000,000,000

5 Find the sum of 8.5 trillion and 1.5 billion. Write the sum in standard form.

A 8,501,500,000

B 10,000,000,000

C 8,501,500,000,000

D 10,000,000,000,000

6 Write 9,057,326,000,000 in word form.

F Nine billion, fifty-seven thousand, three hundred, twenty-six

G Nine billion, fifty-seven million, three hundred, twenty-six

H Nine trillion, fifty-seven million, three hundred, twenty-six thousand

J Nine trillion, fifty-seven billion, three hundred, twenty-six million

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Name _________________________________ Date ______________Class ______________

7 What is the place value of the digit 5 in the number 6,538,642,000,103

A hundred thousands

B hundred millions

C hundred billions

D hundred trillions

8 Which number is greater than 5.377 trillion?

F 5,380,000,000

G 5,000,380,000,000

H 5,377,000,000,000

J 5,377,050,000,000

9 How many times greater is the number 4 trillion than the number 4 billion?

A 100 times

B 1000 times

C 10,000 times

D 100,000 times

Short-Response: Show your work for each question.

10 An astronomer discovers a planet outside the solar system. The planet is approximately 130,000,000,000 miles from Earth. Write this number in word form.

11 The mayor of a city estimates that the town will spend 5.87 billion dollars on a new water treatment system. Write this number in standard form.

Extended-Response: Show your work for the following question.

12 Last year, the population of a small country was 195,229,300. This year, the population increased to 196,230,400. By how much did the population increase? Write your answer in standard form and in words.

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NUMBER SENSE AND OPERATIONSCommutative, Associative, and Distributive Properties

6.N.2 Define and identify the commutative and associative properties of addition and multiplication.6.N.3 Define and identify the distributive property of multiplication over addition.


1 Peter wants to show that 2x + 3 is equivalent to 3 + 2x. What property would he use?

A Associative

B Distributive

C Commutative

D Algebraic

2 The Associative Property of Addition is demonstrated by which equation?

F d × (e + f ) = d × d

G d + (e + f ) = (d + e) + f

H d × (e + f ) = (d × e) + (d × f ) J d + (e + f ) = (d + e) × (d + f )

3 Which is an example of the Distributive Property?

A 2 + 3 = 3 + 2

B (1 + 2) + 3 = 1 + (2 + 3) C 2 (1 + 3) = 2 × 1 + 2 × 3

D 2 × 0 = 0

4 Janice followed the steps shown to rewrite an expression.

4 (x + 5) = 4x + 20

= 20 + 4x

Which pro perties did she use?

F Associative and Distributive

G Associative and Commutative

H Distributive and Commutative

J Associative, Distributive, and Commutative

5 Dinish is given the expression 4 + (5 × 4). He wants to use the Commutative Property. Which expression is NOT equivalent to the original expression?

A (5 · 4) + 4

B (4 · 5) + 4

C 4 + (4 · 5) D (4 · 4) + (4 · 5)

6 The Distributive Property of Multiplication over Addition is demonstrated by which equation?

F a × (b + c) = a × a

G a × (b × c) = (a × b) × c

H a × (b + c) = (a × b) + (a × c) J a + (b + c) = (a + b) × (a + c)

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7 The Associative Property of Multiplication is demonstrated by which equation?

A a × ( b __ c ) = b × ( a __ c )

B a × b × c = (a × b) × c

C (a × b) × c = a × (b × c)

D (a × b) × c = a × (b) × c

8 Which property of multiplication allows the expression 4 (-3) (-25) to be rewritten as 4 (-25) (-3) ?

F Commutative

G Associative

H Inverse

J Identity

9 Which expression is equivalent to 5 + (2 + 3) and shows Associative Property?

A (5 + 2) + (5 + 3) B (5 + 2) + 3

C 5 + (3 + 2) D (2 + 3) + 5

10 Which is an example of the Commutative Property?

F 2 + 3 = 3 + 2

G (1 + 2) + 3 = 1 + (2 + 3) H 2 (1 + 3) = 2 × 1 + 2 × 3

J 2 × 0 = 0


11 Identify the property used.

75 + 12 + 25 = 75 + 25 + 12

12 Identify the property used.

4 × (3 × (-2) ) = (4 × 3) × (-2)


13 Prove that x (3 + 4) = 7x. Identify any properties that you use.

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NUMBER SENSE AND OPERATIONSProperties of Addition and Multiplication

6.N.4 Define and identify the identity and inverse properties of addition and multiplication.6.N.5 Define and identify the zero properties of multiplication.


1 Which of the following statements describes the rational number 3?

A It is the additive inverse of -3.

B It is the additive inverse of 1 __ 3 .

C It is the multiplicative inverse of - 1 __ 3 .

D It is the multiplicative inverse of -3.

2 Which of the following illustrates the Identity Property of Multiplication?

F 9 + (-9) = 0

G 3 × 1 = 3

H 12 × 1 = 0

J 5 × 1 __ 5 = 1

3 Which of the following illustrates the Inverse Property of Multiplication?

A 76 + (-76) = 0

B 1 × 0 = 0

C 14 × (-1) = -14

D 7 × 1 __ 7 = 1

4 Which one of the properties is shown here?

3 + 0 = 3

F Associative

G Commutative

H Distributive

J Identity

5 Which number represents the additive inverse for the number -3?

A -3

B 3

C - 1 __ 3

D 0

6 What property is illustrated in the equation?

(-7) + 7 = 0

F Associative Property of Addition

G Commutative Property of Addition

H Inverse Property of Addition

J Identity Property of Addition

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7 What property is illustrated in this equation?

88 × 0 = 0

A Associative Property of Multiplication

B Zero Property of Multiplication

C Inverse Property of Multiplication

D Identity Property of Multiplication

8 What is always the answer when you use the Zero Property of Multiplication?

F 0

G 1

H 2

J The number you are multiplying by zero.

9 What property is illustrated in this equation?

0 + 1,003 = 1,003

A Associative Property of Addition

B Identity Property of Addition

C Inverse Property of Multiplication

D Zero Property of Multiplication

10 Which of the following equations has the solution w = -3?

F 5 + w = 8

G 5 = w - 8

H w - 5 = 8

J 5 = w + 8


11 What is the value of d in the equation 4d = 36?

12 What is the value of k in the equation

6 = 3 __ 4 k ?


13 Evaluate the expression

-7 + (-2) + 2 __ 3 + 4 + 2 __

5 . Justify each

step of the solution by identifying the property used.

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NUMBER SENSE AND OPERATIONSRatios and Proportional Reasoning

6.N.6 Understand the concept of rate. 6.N.7 Express equivalent ratios as a proportion. Also 6.N.8, 6.N.9, 6.N.10


1 Mr. David’s class has 12 boys and 15 girls. What is the ratio of boys to girls?

A 4:5

B 12:27

C 15:27

D 12:1

2 Which ratio is equal to 5:3?

F 10:3

G 3:5

H 10:6

J 5:8

3 Which two ratios are equal to 2:8?

A 4:1 and 8:2

B 1:4 and 3:12

C 4:16 and 8:34

D 3:12 and 8:2

4 Al read 60 pages in 3 hours. Express this as a rate.

F 6 pages per hour

G 1 hour per page

H 20 pages per hour

J 30 pages per hour

5 Lauren paid $5.50 for 5 pounds of peaches. What is the cost of 10 pounds of peaches priced at the same unit cost?

A $5.00

B $5.50

C $10.00

D $11.00

6 A delivery truck can travel 240 miles on 30 gallons of gas. At that rate, how far could the truck travel on 15 gallons of gas?

F 8 miles

G 120 miles

H 240 miles

J 360 miles

7 Peggy reads every day of the week for one week and reads 210 pages. What is her average rate per day?

A 7 pages per day

B 30 pages per day

C 70 pages per day

D 210 pages per day

8 Lisa babysat for 12 hours and made $36. Roger babysat for 5 hours and made $30. Sinead babysat for 12 hours and made $60, Which person made the most money per hour?

F Lisa

G Sinead

H Roger

J Not enough information is given.

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9 If a package of 20 recordable CDs costs $16, how much do 5 of the recordable CDs cost?

A $4

B $5

C $8

D $10

10 If a 24-pack of canned juice costs $16, how much do 6 of the cans of juice cost?

F $4

G $6

H $8

J $9

11 Brandon can walk 3 miles in 2 hours. How many miles can he walk in 6 hours?

A 4

B 9

C 12

D 18

12 A honeybee can fly 15 miles in 1 hour. How many miles can it fly in 40 minutes?

F 4

G 5

H 6

J 10


In Questions 13–14, determine whether the ratios can be written in a proportion.

13 6 ___ 25

, 8 ___ 25

14 5 ___ 16

, 25 ___ 96

15 Drew uses 12 gallons of gas to drive 408 miles. How many gallons of gas would it take Drew to drive 1,224 miles?

16 This year, 3 out of every 5 children who signed up for day camp were girls. If 25 children signed up, how many of them were girls?

Extended-Response: Show your work for each question.

17 A printing company makes stickers. They printed 1,400 animal stickers and 4,600 stickers of funny sayings. If you bought a package of 120 stickers that were packaged in the same ratio, how many would be animal stickers? Explain your answer.

18 Explain what is meant by the words ratio and rate. Give an example of each.

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NUMBER SENSE AND OPERATIONSPercents

6.N.11 Read, write, and identify percents of a whole (0% to 100%). 6.N.12 Solve percent problems involving percent, rate, and base.


1 The students at South Middle School want to raise $2,500 for new playground equipment at the elementary school. To date, they have raised $1,700. What percent of their goal have they reached?

A 32%

B 45%

C 68%

D 75%

2 Ramon spent 40% of his savings on a new stereo system. If he had $275.50 in his savings account, how much did he spend on the stereo system?

F $40.00

G $110.20

H $120.20

J $165.30

3 In Mrs. Wilson’s class, 18 out of 24 students saw the new action movie. What percent of her class did NOT see the new movie?

A 25%

B 30%

C 70%

D 75%

4 The students at Scott Middle School either ride the bus, walk, or are driven by a parent. Look at the chart to find the percent of seventh graders who ride the bus.

How We Get to SchoolGrade Bus Walk Driven

6th 98 35 55

7th 88 23 42

8th 70 30 33

F 38%

G 42%

H 58%

J 65%

5 Ralph used 75% of his study time working on his research paper. If it took him 3 hours to work on his paper, how much time did Ralph have left to work on his science homework?

A 1 hour

B 2 hours

C 3 hours

D 4 hours

6 Miguel has a garden that has an area of 315 square feet. If the corn in his garden covers 190 square feet, what percent of the garden is corn?

F 50%

G 55%

H 60%

J 65%

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7 The baseball coach keeps track of his players’ at bats and hits. Use the chart to determine who had the greatest percent chance of getting a hit.

Player Batting StatisticsPlayer Hits At BatsBarry 16 55

Ken 33 80

Pete 19 62

Jose 22 59

A Barry

B Ken

C Pete

D Jose

8 Tarik left a 22% tip for the waitress who served his family. Without the tip, the bill for the meal was $67.62. What was the total amount, including the tip, that Tarik paid?

F $14.88

G $52.74

H $67.84

J $82.50


9 Mrs. Daley waited to buy a new washing machine until they went on sale. She got a $849.00 washer for only $568.83. What amount of money did she save? What percent of the original price was this amount?

10 In 1926, Babe Ruth played in 152 baseball games, had 495 turns at bat, and held a 37.2% batting average. How many hits did he have?


11 Katie saves 50% of the money she earns. If she earns $300 a week and works 3 weeks, how much money does she save?

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NUMBER SENSE AND OPERATIONSAbsolute Value

6.N.13 Define absolute value and determine the absolute value of rational numbers (including positive and negative).


1 Which number is equal to ⎪-4⎥

A 4

B -4

C (-4)

D 4 -1

2 Which of the following values is equal to -11?

F ⎪-11⎥

G ⎪11⎥

H - ⎪-11⎥

J - (-11)

3 The Cougars football team started on the 30-yard line and fell back to the 19-yard line. Which represents the change in their position?

A ⎪30 - 19⎥ yards

B ⎪30 + 19⎥ yards

C ⎪19⎥ - ⎪30⎥ yards

D - ⎪30 - 19⎥ yards

4 What is the value of this expression? 52 - ⎪-15⎥

F 37

G 38

H 67

J 82

5 The chart shows the change in the value of some stocks. Which stock showed the greatest change?

Stock Value ChangeABC Corporation $52.93 +$3.42

BiggieMart $74.16 -$1.98

GoCar Company $61.98 -$8.13

FlyRight Airline $12.55 +$0.45

A ABC Corporation

B BiggieMart

C GoCar Company

D FlyRight Airline

6 What is the distance on a number line between 10 and -5?

F -15

G -5

H ⎪-5⎥

J 15

7 What is the distance on a number line between -20 and -2?

A -22

B -18

C ⎪-18⎥

D ⎪-22⎥

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8 Which of the following pairs of numbers are shown on the number line below?

321 102223 2

F ⎪-3⎥ and ⎪3⎥

G - ⎪-3⎥ and - ⎪3⎥

H -3 and (-3)

J - ⎪-3⎥ and ⎪3⎥

9 A skydiver jumped out of an airplane at 7,000 feet above ground level. The wind blew him off course and he landed on a hill 84 feet above ground level. Which expression shows the change in the skydiver’s altitude beween the landing and the jumping points?

A ⎪7,000⎥ + ⎪84⎥ feet

B 7,000 - (-84) feet

C ⎪7,000 - 84⎥ feet

D ⎪84⎥ + ⎪7,000⎥ feet

10 The chart shows the temperature at noon in Portland, Maine, and the change from the previous day. Which is the greatest amount of change?

Day 1 2 3 4 5Temp. 2° 6° -3° 0° -8°

DegreesChange

0° +4° -9° +3° -8°

F -9°

G -8°

H +3°

J +4°


11 Simplify this expression.

8 - ⎪-15⎥

12 What is the value of the expression?

⎪-3⎥ - 8 + ⎪-5⎥


13 Which value is greater: ⎪-15⎥ or ⎪15⎥ ? Explain your reasoning.

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NUMBER SENSE AND OPERATIONSOrder Rational Numbers

6.N.14 Locate rational numbers on a number line (including positive and negative). 6.N.15 Order rational numbers (including positive and negative).


1 The lengths in miles of some major rivers are shown in the chart.

Heilong River2,758 miles

Irtish River2,704 miles

Parana River2,795 miles

Zaire River2,716 miles

Which of the following shows these lengths in order from least to greatest?

A 2,704, 2,716, 2,795, 2,758

B 2,795, 2,758, 2,716, 2,704

C 2,704, 2,758, 2,716, 2,795

D 2,704, 2,716, 2,758, 2,795

2 Jacob collected some rocks for a rock garden. The rocks had masses of 13.05, 13.55, 13.055, and 13.5 kilograms. Which shows the masses of the rocks in order from greatest to least?

F 13.55, 13.5, 13.055, 13.05

G 13.55, 13.055, 13.5, 13.05

H 13.05, 13.055, 13.5, 13.55

J 13.05, 13.5, 13.055, 13.55

3 Which of the following shows the mixed numbers in order from least to greatest?

A 2 3 __ 4 , 2 5 __

8 , 2 4 __

7 , 2 7 ___

10

B 2 4 __ 7 , 2 5 __

8 , 2 7 ___

10 , 2 3 __

4

C 2 3 __ 4 , 2 4 __

7 , 2 5 __

8 , 2 7 ___

10

D 2 4 __ 7 , 2 7 ___

10 , 2 3 __

4 , 2 5 __

8

4 Which list of numbers is in order from least to greatest?

F - 22 __ 7 , -0.75, 1.8, 2 1 __

5

G -0.75, - 22 __ 7 , 1.8, 2 1 __

5

H -0.75, 1.8, 2 1 __ 5 , -

22 __ 7

J - 22 __ 7 , 2 1 __

5 ,1.8, -0.75

Use the following number line to answer questions 5 –6.

0 1 2 3�3 �2 �1

A B C D

5 Which point on the number line

corresponds with 7 __ 2 ?

A C

B D

C E

D F

6 Which point on the number line corresponds with -2.5?

F A

G B

H C

J D

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7 Which of the following shows the decimals in order from greatest to least?

A 0.07, 0.67, 0.067, 0.607

B 0.067, 0.67, 0.07, 0.607

C 0.607, 0.67, 0.07, 0.067

D 0.67, 0.607, 0.07, 0.067

8 The team of scientists in the Arctic recorded the following temperatures at their base camp.

Day 1 Day 2 Day 3 Day 4-34° -24° -29° -36°

Which day was the warmest day?

F Day 1

G Day 2

H Day 3

J Day 4

9 Which point on the number line could

represent -2 1 __ 4 ?

0 1 2 3�3 �2 �1

A B C D

A Point A

B Point B

C Point C

D Point D

10 Marco collects stamps. He has stamps

that are 3 __ 4 inches wide, 3 __

5 inches wide,

5 __ 8 inches wide, and 4 __

7 inches wide. Which

shows the stamps in order from least to greatest width?

F 4 __ 7 , 3 __

5 , 5 __

8 , 3 __

4

G 3 __ 4 , 3 __

5 , 4 __

7 , 5 __

8

H 3 __ 4 , 3 __

5 , 5 __

8 , 4 __

7

J 4 __ 7 , 5 __

8 , 3 __

5 , 3 __

4


11 Steve received scores of 9.88, 9.78, 9.86, 9.79, and 9.87 for his 10-meter platform diving. What was his highest score?


12 Which of the following numbers is farthest from zero when the numbers are graphed on a number line? Which number has the greatest value? Which has the least value?

-1.5, 2 __ 5 , 1.2, 1 1 __

4

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NUMBER SENSE AND OPERATIONSFractions with Unlike Denominators

6.N.16 Add and subtract fractions with unlike denominators. 6.N.17 Multiply and divide fractions with unlike denominators.


1 Which fraction is equivalent to 4 ___ 15

+ 7 ___ 20

?

A 11 ___ 60

B 11 ___ 35

C 11 ___ 20

D 37 ___ 60

2 Which fraction is equivalent to 1 ___ 18

+ 1 __ 8 ?

F 1 ___ 72

G 1 ___ 36

H 1 ___ 13

J 13 ___ 72

3 What is 1 __ 2 + 1 __

3 + 1 __

4 written in simplest

form?

A 1 __ 9

B 1 __ 4

C 11 ___ 12

D 13 ___ 12

4 What is the value of 4 __ 5 + 5 ___

24 - 1 __

2 ?

F 1 ___ 15

G 111 ____ 120

H 8 ___ 17

J 29 ___ 30

5 Which expression has a value that is

greater than 1 __ 2 ?

A 13 ___ 30

- 27 ___ 70

B 5 __ 6 - 4 ___

54

C 49 ___ 50

- 3 __ 5

D 5 ___ 16

+ 1 __ 9

6 Which fraction is equivalent

to 2 __ 7 + 1 ___

14 + 3 ___

10 ?

F 3 ___ 35

H 1 __ 5

G 6 ___ 31

J 23 ___ 35

7 Simplify 5 __ 6 - 2 __

3 - 1 ___

15

A 1 ___ 30

C 1 __ 6

B 1 ___ 10

D 1 __ 3

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8 Jan wants to add 3 __ 8 and 1 __

3 . What is the

least common denominator?

F 24

G 16

H 8

J 3

9 Hector is asked to add 1 __ 4 , 1 __

6 , and 1 __

8 . What

is the least common denominator?

A 24

B 48

C 96

D 192

10 Add the fractions: 1 __ 5 + 4 __

6 . What is the sum

in simplest form?

F 13 ___ 15

G 5 __ 6

H 26 ___ 30

J 22 ___ 30

11 Subtract: 4 __ 5 -

3

__ 8

.

A 7 __ 8

B 1 __ 3

C 17 ___ 40

D 7 ___ 20

12 Deborah wants to add 2 __ 5 , 7 ___

10 , and 5 __

6 .

What is the least common denominator?

F 30

G 50

H 60

J 300

13 Three of the fractions below are

equivalent to 8 ___ 10

- 12 ___ 24

. Which fraction is

NOT equivalent?

A 72 ____ 240

B 36 ____ 120

C 6 ___ 20

D 5 ___ 10

Short-Response: Show your work for the following question.

14 Jennie wants to add 3 __ 8 , 4 __

9 , and 5 ___

11 . What

is the answer? Show your work.


15 Isaac uses 1 __ 2 cup of milk for a recipe,

3 __ 4 cup of buttermilk, and 2 __

3 cup of water.

When these liquids are combined, how many cups of liquid are there?

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NUMBER SENSE AND OPERATIONS

Add, Subtract, Multiply or Divide Mixed Numbers

6.N.18 Add, subtract, multiply, and divide mixed numbers with unlike denominators. Also 6.N.19


1 Add.

12 2 __ 3 + 7 3 __

4 =

A 19 1 __ 2

B 20 1 __ 4

C 20 5 ___ 12

D 21

2 Subtract

19 1 __ 2 - 11 1 __

3 =

F 8 1 __ 6

G 8 1 __ 2

H 9

J 9 1 __ 6

3 Sarah’s book bag weighs 18 1 __ 3 pounds.

When she removes textbook, the book

bag weighs 16 3 __ 8 pounds. How much does

Sarah’s math textbook weigh?

A 1 23 ___ 24

pounds

B 2 1 ___ 24

pounds

C 2 3 __ 8 pounds

D 2 23 ___ 24

pounds

4 When Nick entered the fifth grade, he

was 58 1 __ 2 inches tall. When he entered

sixth grade, Nick had grown 4 3 __ 4

inches.

How tall was Nick when he entered sixth grade?

F 62 1 __ 4 inches

G 62 1 __ 2 inches

H 62 inches

J 63 1 __ 4 inches

5 The art teacher found partially used

boxes of clay that weighed 2 3 __ 4

pounds,

1 __ 3 pound, 1 5 __

6 pounds, and 7 ___

12 pound.

About how much clay did she find in all?

A 5 1 __ 4 pounds

B 5 1 __ 2 pounds

C 5 3 __ 4 pounds

D 6 pounds

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6 It took Stephen 3 1 __ 2 hours to do the

yardwork. He spent 2 __ 3 of that time

mowing the grass. How long did it take Stephen to mow the grass?

F 1 2 __ 3 hours

G 2 hours

H 2 1 __ 3 hours

J 3 hours

7 What is 3 __ 4 of 1 5 __

6 ?

A 5 __ 8

B 1 1 __ 8

C 1 3 __ 8

D 2 7 __ 12

8 Bill made a vegetable garden that had a

total area of 5 3 __ 4 square meters. The area

of the vegetable garden was 1 1 __ 2 times as

great as the area of Bill’s flower garden. What was the area of the flower garden?

F 3 5 __ 6 square meters

G 4 1 __ 4 square meters

H 7 1 __ 4 square meters

J 8 5 __ 8 square meters


9 The 6th grade classes at one school collected cans for a fund drive. The chart shows the number of pounds of cans each class collected.

Room 203

Room 210

Room 214

Room 218

56 5 __ 16

pounds

47 7 __ 12

pounds

59 1 __ 4

pounds

52 3 __ 8

pounds

How many pounds were collected in all?

10 Subtract and find the answer in simplest form.

7 5 __ 8 - 1 1 __

6 =

11 Give the multiplicative inverse of each of

these numbers: 5, 1 __ 3 , 0.7, 4 1 __

2 . Explain

how you know that your answers are correct.


12 You have 3 3 __ 4 cups of walnuts. You use

1 1 __ 2 cups in a recipe. You then divide the

remaining nuts evenly into three separate bags and freeze them. What is the amount of walnuts in each bag? Explain why your answer is reasonable.

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NUMBER SENSE AND OPERATIONSFractions and Decimals

6.N.20 Represent fractions as terminating or repeating decimals.


1 Sandy lost 1 3 __ 8 pounds training for

basketball season. What is that number in decimal form?

A 0.375 pounds

B 1.3 pounds

C 1.375 pounds

D 1.40 pounds

2 Agnes got 43 of 50 questions on the math test correct. What is her score expressed as a decimal?

F 0.07

G 0.43

H 0.5

J 0.86

3 What is the number 33 _____ 1,000

expressed as a decimal?

A 0.0033

B 0.033

C 0.33

D 3.3

4 Which of these lists does NOT show a set of equivalent numbers?

F 0.4, 10 ___ 25

, 0.40

G 1 __ 4 , 5 ___

20 , 0.25

H 1.64, 1 32 ___ 50

, 1 16 ___ 25

J 5 2 ___ 50

, 5.06, 5 6 ____ 100

5 Which of these shows a set of equivalent numbers?

A 3.09, 3 9 ___ 10

, 39 ___ 10

B 2 42 ___ 50

, 2.84, 2 21 ___ 25

C 8 ____ 100

, 0.8, 20 ___ 25

D 16 ___ 25

, 64 ____ 200

, 0.64

6 Which number is equivalent to 28 ____ 700

?

F 0.004

G 0.04

H 0.4

J 4.0

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7 When 7 ____ 110

is written as a decimal, how

many digits repeat?

A 2

B 3

C 7

D 11

8 A gas station received a shipment of 2,875 gallons of gas. The tank holds 3,000 gallons in all. Which decimal shows the fraction of the tank that was filled by the shipment?

F 0.958

G 0.9583

H 0.95833

J 0.958 _ 3

9 Which shows 1. −

8 written as a fraction?

A 1 ___ 18

B 5 __ 9

C 8 __ 9

D 17 ___ 9

10 Which of the following fractions is NOT a repeating decimal?

F 1 __ 3

G 3 __ 8

H 1 __ 6

J 1 ___ 11


11 Express 11 __ 12

as a repeating decimal.

Then round the decimal to the nearest thousandth.

12 What is 0.625 written as a fraction in simplest terms?


13 What digit is in the hundred-thousandth’s place of 0.32

−− 48 . Explain your reasoning.

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NUMBER SENSE AND OPERATIONSFractions, Decimals, and Percents

6.N.21 Find multiple representations of rational numbers (fractions, decimals, andpercents 0 to 100).


1 Sandy lost 1 1 __ 8 pounds training for

basketball season. What is that number in decimal form?

A 0.125 pounds

B 1.1 pounds

C 1.125 pounds

D 1.2 pounds

2 Which is NOT another way to write the part of a kilogram that this container of yogurt holds?

F 7 ___ 10

G 0.170

H 1 ___ 10

+ 7 ____ 100

J 17 ____ 100

3 Olivia got 57 out of 60 questions on the math test correct. What is her score expressed as a percent?

A 5%

B 57%

C 90%

D 95%

4 The label on a gallon of whole milk says that the milk contains 3.3% fat. What is that number expressed as a decimal?

F 0.0033

G 0.033

H 0.33

J 3.3

5 The trip meter on Mr. Nesmith’s car shows the number of miles he drove to work.

Which shows another way to describe this distance?

A 12 2 __ 5 miles

B 12 4 __ 5 miles

C 12 1 __ 8 miles

D 12 2 ___ 25

miles

6 Which of these lists does NOT show a set of equivalent numbers?

F 0.35, 14 ___ 40

, 35%

G 3 ___ 10

, 30%, 6 ___ 20

H 1.64, 1 32 ___ 50

, 1 16 ___ 25

J 52%, 0.52, 13 ___ 24

yogurt

0.17 kg

12.8

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7 The scale shows the weight of Beth’s dog in pounds.

Which is another way to describe this weight?

A 24 3 __ 5 pounds

B 24 1 __ 6 pounds

C 24 3 __ 8 pounds

D 24 3 ___ 50

pounds

8 Three fifths of the players on Jake’s football team are on the honor roll. What percent of the team is on the honor roll?

F 3.5%

G 35%

H 60%

J 70%

9 During the championship baseball game, DeWayne hit the ball 12 times. Nine of those hits were foul balls. What percent of his hits were foul balls?

A 3%

B 12%

C 75%

D 120%

10 Which of these shows a set of equivalent numbers?

F 3.09, 3 9 ___ 10

, 3.9%

G 2 42 ___ 50

, 2.84, 2 21 ___ 25

H 8%, 0.8, 20 ___ 25

J 16 ___ 25

, 32%, 0.64


11 In a survey, eighty people were asked to name their favorite sport. The results of the survey are shown in the table.

Sport Number of PeopleBaseball 27Football 45Soccer 8

What percent of those surveyed chose football as their favorite sport?

12 Sixty-eight percent of those surveyed chose blue as their favorite color. What is that number expressed as a decimal?


13 About 41% of all cars in a lot are silver. Write this value as a decimal and as a fraction in simplest form.

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NUMBER SENSE AND OPERATIONSOrder of Operations

6.N.22 Evaluate numerical expressions using order of operations (may includeexponents of two or three).


1 Doreen bought 5 cakes for $12 each and 3 cartons of milk for $2 each. Which expression shows how much Doreen spent in dollars?

A 5 × 12 × 3 × 2

B 5 × 12 + 3 × 2

C (5 + 3) × (12 + 2)

D (5 + 2) × (12 + 3)

2 Insert parentheses to make this number sentence true.

20 ÷ 5 × 2 + 3 = 5

F (20 ÷ 5) × 2 + 3 = 5

G 20 ÷ (5 × 2) + 3 = 5

H 20 ÷ 5 × (2 + 3) = 5

J 20 ÷ (5 × 2 + 3) = 5

3 Use order of operations to simplify.

22 - 6 ÷ 2 + 3

A 11

B 22

C 10

D 16


2 3 + 8 ÷ 4

F 64

G 10

H 4

J 2.5

5 Which is the correct order of operations?

A Simplify inside parentheses, simplify exponents, add and subtract, multiply and divide

B Simplify inside parentheses, multiply and divide, add and subtract, simplify exponents

C Simplify exponents, simplify inside parentheses, multiply and divide, add and subtract

D Simplify inside parentheses, simplify exponents, multiply and divide, add and subtract

6 Insert brackets to make this number sentence true.

6 + 6 + 10 ÷ 11 = 2

F (6 + 6 + 10) ÷ 11 = 2

G 6 + 6 + (10 ÷ 11) = 2

H (6 + 6) + 10 ÷ 11 = 2

J 6 + (6 + 10) ÷ 11 = 2

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7 Which expression below is equal to this expression?

(7 - 3) × 6 ÷ 2

A (7 - 3 × 6) ÷ 2

B 7 - (3 × 6) ÷ 2

C 7 - (3 × 6 ÷ 2)

D None of the above.

8 Which of the following sentences is true according to order of operations?

F Multiply before dividing

G Add before multiplying

H Divide before multiplying

J Multiply and divide from left to right

9 Which of the following sentences is true according to order of operations?

A Simplify inside parentheses before simplifying exponents.

B Simplify parentheses before simplifying inside brackets.

C Add before subtracting.

D Add before simplifying exponents.



18 - 3 × 2 - 2 3


3 × ( 4 3 + 8)


12 Insert parentheses to make this number sentence true. Explain your answer.

2 × 6 2 - 8 = 56

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NUMBER SENSE AND OPERATIONSExponents

6.N.25 Evaluate expressions having exponents where the power is an exponent ofone, two, or three. Also 6.N.23, 6.N.24


1 Rewrite 2 × 2 × 2 × 2 × 2 using exponents.

A 2 × 105

B 55

C 25

D 2-5

2 Which expression is equal to 4 5 ?

F 4 × 4

G 4 × 4 × 4

H 4 × 4 × 4 × 4

J 4 × 4 × 4 × 4 × 4

3 Rewrite 2,000 using exponents.

A 2 × 103

B 2 × 106

C 25

D 2-5

4 Which of the following is NOT equal to 9 cubed?

F 9 × 9 × 9

G 9 3

H 729

J 9 × 3

5 Which of the following represents the prime factorization of 36?

A 22 × 32

B 62

C 33

D 2 × 3 × 3 × 3

6 Caleb found that the area of his dog’s pen was 122 square feet. Which number is equivalent to 122?

F 12 × 2

G 6 × 6

H 12 × 12

J 12 × 12 × 12

7 Jamie has 2 8 raisins. If she eats half every hour, how many raisins will she have at the end of 2 hours?

A 2 × 2

B 2 × 2 × 2

C 2 × 2 × 2 × 2

D 2 × 2 × 2 × 2 × 2 × 2

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8 Which pair of expressions are both equal to 32?

F 2 5 , 2 × 4 4

G 2 6 , 2 × 4 2

H 2 5 , 2 × 4 2

J 2 6 , 2 × 4 4

9 42 • 35 • 25

_________ 42 • 34 • 26

=

A 3 __ 2

B 8 __ 3

C 3

D 12

10 Which expression is equivalent to

53 × 55?

F 52

G 58

H 515

J 2515


11 Simplify this expression.

52 + 83 – 23

12 Evaluate. Rewrite the answer using an exponent.

1,000

_____ 10


13 Jared says that 43 + 33 = (4 + 3)3. Is he correct? Explain.

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NUMBER SENSE AND OPERATIONSEstimation and Percents

6.N.26 Estimate a percent of a quantity.


1 A meal at a restaurant costs $15.95. Jared wants to leave a 15% tip. Estimate the amount he should leave as a tip.

A $1.60

B $2.00

C $2.40

D $3.20

2 Ramon spent 40% of his savings on a new stereo system. If he had $275.50 in his savings account, about how much did he spend on the stereo system?

F $40

G $110

H $120

J $170

3 In Mrs. Wilson’s class, 75% of the students saw a new action movie. If there are 25 students in the class, about how many students saw the movie?

A 6

B 12

C 15

D 19

4 At Scott Middle School, 30% of the 6th graders walk to school, and 40% of the seventh graders walk to school. There are 102 sixth graders and 96 seventh graders. What is the approximate number of sixth and seventh graders who walk to school?

F 30

G 40

H 70

J 200

5 Dough used 70% of his study time to work on his research paper. If his total study time was 2 hours, about how much time did he have for other subjects?

A 0.6 hour

B 1 hour

C 1.4 hours

D 1.8 hours

6 Charlie has a garden that has an area of 305 square feet. About 60% of the area is planted with beans, and Charlie calculates that this is 183 square feet. How can he check his estimate?

F Find 10% of 300 and multiply this amount by 6.

G Find 50% of 300 and add 10% of 300 to this amount.

H Divide 190 by 300 to see if the result is close to 0.60.

J All of the above.

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7 About 48% of the students at Highland Middle School buy lunch. There are 402 students at the school, and each lunch costs $2.95. Which of the following is the best estimate of the total amount spent on lunches each day?

A $50

B $200

C $400

D $600

8 A CD costs $19.95. Jake gets a 10% discount. About how much does he pay for the CD?

F $2

G $18

H $20

J $22

9 Sales tax in Kathy’s state is 6.25%. Estimate the total price of a $29.98 toaster, including sales tax.

A $2.00

B $25.00

C $32.00

D $40.00


10 A quality-control company found that 2% of a certain shipment was defective. If the shipment contained 23,865 pieces, how many pieces were defective?


11 Beth wants to buy a shirt that is being sold at 60% of its original price. The original price is $57.00 and Beth calculates that she will pay $34.20. Describe how she can use estimation to check the reasonableness of her calculation.

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ALGEBRAAlgebraic Expressions


1 Write the phrase 6 less than the quotient of 4 and a number as a variable expression.

A 4 - 6n

B 6 - 4n

C 4 __ n - 6

D 6 - 4 __ n

2 This sign is shown in a restaurant window.

“Spaghetti Special”

All you can eat for $4.50 per person.

Meatballs .75 cents each

Suppose a large group of people buy the special. The total number of meatballs ordered by the group is 20. Which expression gives the total amount paid by the group of people?

F 4.50 • n + 20 • 0.75

G 4.50 • n + 0.75 • n + 20

H 4.50 • 20 + 0.75 • 20

J 4.50 • n + 0.75 • n

3 Mike attends the county fair. Admission is $5 and ride tickets cost $.75 each. If Mike buys x tickets, which expression represents the total amount Mike spends on admission and tickets?

A 0.75x

B 5 + 0.75x

C 0.75 + 5x

D 5 - 0.75x

4 If q = 5, x = –4, and y = 2, what is 6q + 4x – y?

F -15

G -12

H 12

J 15

5 If w = 10, x = -2, and y = 2,

what is xw ___ y ?

A -10

B - 5 __ 2

C 5 __ 2

D 10

6 Which expression represents the phrase 3 times the difference of 12 and y?

F 3(12 - y)

G 3(y - 12)

H 3 - (12 - y)

J 3 – 12y

7 If r = 5, s = -4, and y = 2, what is r(3s + 7y)?

A -46

B -10

C 10

D 52

6.A.1 Translate two-step verbal expressions into variable expressions.6.A.2 Use substitution to evaluate algebraic expressions (may include exponents of one, two, and three).

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8 If w = 7, x = 5, and y = 6,

what is 4w – 3y

_______ x ?

F 2

G 9.2

H 24.4

J 30

9 If j = 3 and k = 1, what is j 2 - k 3 ?

A 3

B 6

C 8

D 9

10 Which expression represents the phrase the quotient of a number and 6, increased by 10?

F n _ 6+10

G n __ 6 + 10

H 6n + 10

J 6 __ n + 10

11 The sign shows the cost of renting a canoe.

CANOE RENTALSBasic Fees $9.00

Hourly Rate $4.50

Which expression can be used to find the cost in dollars of renting the canoe for h hours?

A 4.5(9 + h)

B 9h + 4.5

C 9 + 4.5h

D (9 + 4.5)h


12 Write an expression to represent each of the following phrases. Then tell which expression has a greater value when n = 20.

17 plus the quotient of a number n and 5

60 minus the product of 2 times a number n

13 Evaluate the following expression for x = 5:

x 2 + 2x + x 3 - 25 ___ x


14 It costs $5 to rent skates at the skating rink, and $2.50 per hour to skate. Write an expression to show the total amount of renting skates and skating for h hours. How much money will you need if you want to skate for 3 hours? If you take $15 to the skating rink and skate for 3 hours, how much money will you have left over for snacks?

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ALGEBRAWriting Two-Step Equations

6.A.3 Translate two-step verbal sentences into algebraic equations.


1 Which equation represents this sentence: Five plus the quotient of a number and 6 equals 9.

A 5 + 6x = 9

B 5 + x __ 6 = 9

C 5 + 6 __ x = 9

D 5 + x + 6 = 9

2 Which equation represents this sentence: Twenty-seven is equal to the sum of 3 and the product of 4 and a number n.

F 27 = 3n + 4

G 27 = 3 + 4 + n

H 27 = 3 + 4 _ n

J 27 = 3 + 4n

3 The cost of renting a mountain bike is a basic fee of $6 plus an additional $2 for each hour that the bike is rented. Which equation can be used to find c, the cost of renting a bike for h hours?

A c = 2(h + 6)

B c = 6(h + 2)

C c = 2h + 6

D c = 6h + 2

4 Maria bought 3 posters at the regular price of $16 each. Then she got the same discount on each poster. Which equation can be used to find t, the total price of the 3 posters with the discount, d?

F t = 16 - d

G t = (3 × 16) - d

H t = 3d + (3 × 16)

J t = (3 × 16) - 3d

5 Jamal had 14 CDs. He gave 3 of his friends each an equal number of a few of his CDs. Then Jamal bought 4 new CDs. Which equation can be used to find n, the number of CDs Jamal has now after giving away x CDs to each of his friends?

A n = 14 + x - 4

B n = 14 - x + 4

C n = 14 - 3x + 4

D n = 14 + 3x - 4

6 David is 3 times as old as his brother, plus 4 years. Which equation can be used to find David’s age d when his brother is b years old?

F d = b + (3 · 4)

G d = 3b + 4

H d = 3b – 4

J d = b + 4

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7 George was involved in a swim-a-thon fundraiser. He contributed $10 of his own money and his parents promised to pay him $3 for every lap that he swam. Altogether, he raised $97. Which equation can be used to find the number of laps, n, he swam?

A 97 = 3n

B 10 = 97 + 3n

C 3n - 97 = 10

D 3n + 10 = 97

8 Julia has $100 in an account at school. She uses the account to pay for school lunch every day. Every day, $4 is deducted from the account to pay for Julia’s lunch. When the amount in the account is $20, she likes to add money to it. Which equation can be used to determine how many days, d, she can buy lunch before adding more money to the account?

F 4d = 100

G 4d - 20 = 100

H 20 = 100 + 4d

J 20 = 100 - 4d

9 A health club charges $32 each month and a one time registration fee of $120. Miguel has spent a total of $280. Which equation can be used to determine the number of months m Miguel has been a member of the health club?

A 120 + 32m = 280

B 120 - 32m = 280

C 120 × 32m = 280

D 280 + 32m = 120


10 An amusement park charges $15 for admission and $3 for each ride. Write an equation that can be used to find the total cost for different numbers of rides taken.


11 One side of an isosceles triangle is 12 centimeters long. The other two sides are congruent and have the same length. The perimeter of the triangle is 48 centimeters. Write an equation that can be used to find one of the unknown side lengths of the triangle.

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ALGEBRASolving Two-Step Equations

6.A.4 Solve and explain two-step equations involving whole numbers using inverse operations. Also 6.A.5


1 Which equation has a solution of x = 6?

A 3x - 2 = 20

B 1 __ 3 (x) + 4 = 10

C 3x + 4 = 22

D 2 __ 3 (x) + 5 = 17

2 Jenny has $15.00 to buy drinks for the team. Drinks are priced as follows:

How many sports drinks can she buy if she buys 3 waters?

F 3 sports drinks

G 4 sports drinks

H 5 sports drinks

J 6 sports drinks

3 In the equation x __ 2 + 5 = 15, what is the

first step in isolating the variable?

A Add 5 to both sides.

B Multiply both sides by 1 __ 2 .

C Subtract 5 from both sides.

D Subtract 15 from both sides.

4 What is the solution to this equation?

5x + 16 = 41

F x = 2

G x = 3

H x = 5

J x = 11.4

5 Rob’s first step in solving an equation was to add 5 to each side. Then he multiplied each side by 3. Which equation could he have been solving?

A 3x + 5 = 10

B x __ 3 + 5 = 10

C 10 = x __ 3 - 5

D 10 = 3x - 5

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6 What is the solution to this equation?

5 + 4m + 7 = 28

F m = 3

G m = 4

H m = 5

J m = 6

7 Which value of s is the solution to this equation?

36 = 27 + s __ 3

A 3

B 9

C 12

D 27

8 Which equation has the solution x = 1?

F 3x - 2 = 4

G 6x + 9 = 15

H 10 + 3x = 7

J 11 - 5x = 3

9 Which of the following equations has the same solution as the equation 8x = 24?

F 5x + 1 = 21

G 13 = 3 + 3x

H 15 = 24 ___ x + 12

J 8x - 8 = 24


10 What value of y makes this equation true?

450 + 15y = 630

11 Solve this equation for z.

z __ 5 + 22 = 157


12 Sue wants to solve the following equation.

x __ 6 - 5 = 12

What step should she take first? Solve the equation for x.

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ALGEBRAProportions

6.A.5 Solve simple proportions within context. Also 6.G.1


1 A grocery store has a sale on red grapes of 2 pounds for $3. How much do 6 pounds of grapes cost?

A $1

B $1.50

C $4

D $9

2 Mr. Ortez is driving 240 miles from Dallas to Houston. The fuel efficiency of his car is 40 miles per gallon. How many gallons of gas will Mr. Ortez use to make this trip?

F 4 gallons

G 6 gallons

H 6.7 gallons

J 8 gallons

3 Trevor reads 6 pages of a novel in 18 minutes. How long would it take him to read 150 pages?

A 30 minutes

B 50 minutes

C 300 minutes

D 450 minutes

4 What is the solution of the proportion

12 _ x = 6 _ 18

?

F x = 15

G x = 24

H x = 36

J x = 48

5 A catering company offers dinner selections that include fish and beef. From experience, the caterers know that fish dinners and beef dinners will

be ordered in a ratio close to 2 __ 5

. At one

dinner, 156 people ordered fish and 375 people ordered beef. Were the dinners ordered in the expected ratio?

A Yes.

B No, they would have expected 380 beef dinners.

C No, they would have expected 390 beef dinners.

D No, they would have expected 404 beef dinners.

6 The Smiths paid Heidi $60 for 5 hours of babysitting. If the Smiths pay Heidi the same hourly wage for 3 hours of babysitting, how much money will she make?

F $12

G $15

H $30

J $36

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7 Sylvie paid $30 for 8 pairs of socks. Which proportion can she solve to find the amount d, in dollars, that she will pay for 20 pairs of socks?

A 8 ___ 30

= 20 ___ d

B 8 ___ 20

= d ___ 30

C 30 ___ 8 = d ___

20

D 20 ___ d = 30 ___

8

8 A biscuit recipe calls for 5 cups of milk per 25 cups of flour. If the recipe is reduced, how much flour should be used with 1 cup of milk?

F 1 __ 5 cup

G 1 cup

H 5 cups

J 25 cups

9 A paint store recommends mixing 5 liters of purple paint with 8 liters of white paint to make a particular shade of lavender. How many liters of purple paint should be used with 12 units of white paint to get the same shade of lavender?

A 3.25 liters

B 7.5 liters

C 5 liters

D 9.2 liters


10 Michael can read 18 pages of a novel per hour. At this rate, how many hours will it take him to read a 315-page novel?


11 Mr. Olson thinks that the larger container of laundry detergent shown below is a better buy. Write a proportion that you could use to see if he is correct. Tell whether you agree with Mr. Olson and explain your reasoning.

Sudz

96 oz.

$6 $4

Bubbles

64 oz.

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ALGEBRAEvaluating Formulas

6.A.6 Evaluate formulas for given input values (circumference, area, volume, distance, temperature, interest, etc.)


1 A rectangular prism has a length of 9 cm, a width of 6 cm, and a height of 5 cm. What is its volume?

A 129 cm 3

B 258 cm 3

C 270 cm 3

D 540 cm 3

2 Naji saw this sign as she rode past the

bank. She knows that the number of

degrees Fahrenheit is 9 __ 5 the number

of degrees in Celsius, plus 32. About

what is the temperature in degrees

Fahrenheit?

F 50°F

G 65°F

H 75°F

J 92°F

3 A playground has a circular field that is 20 ft in diameter. What is the approximate area of the field?

A 31.4 ft 2

B 62.8 ft 2

C 314 ft 2

D 1,256 ft 2

4 The radius of a cylinder is 3 cm, and its height is 4 cm. What is the volume? Use 3.14 for π.

F 84.78 cm 3

G 113.04 cm 3

H 131.88 cm 3

J 299.96 cm 3

5 The seat on a stool is a semicircle.The straight part of the seat is 30 cm long. What is the area of the seat?

A 125.5 cm 2

B 250 cm 2

C 353.25 cm 2

D 425 cm 2

6 A hoop is made by bending plastic into a circle. If the diameter of the circle needs to be 0.79 m, what is the approximate length of plastic needed to make the hoop?

F 0.5 m

G 1.3 m

H 2.5 m

J 3.14 m

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7 Jodi bikes at an average speed of 20 miles per hour. If she bikes for 3 hours and 30 minutes without stopping, how far will she travel?

A 60 miles

B 66 miles

C 70 miles

D 660 miles

8 A jet is traveling at a speed of 525 miles per hour. How long will it take the jet to travel 2100 miles?

F 4 hours

G 5 hours

H 40 hours

J 50 hours

9 Five years ago, Maria deposited $500.00 in a simple interest account. The interest rate is 7.25%. How much money is in Maria’s account now?

A $181.25

B $581.50

C $681.25

D $2,312.50

10 Ray is planning to fence in a circular garden. The distance from the center of the garden to the edge of the garden is 15 feet. What is the approximate area of the garden?

F 94.25 square feet

G 225.00 square feet

H 706.5 square feet

J 756.14 square feet

11 About how many feet of fencing should Ray purchase for the garden in Question 10?

A 47.12 feet

B 94.25 feet

C 141.37 feet

D 188.50 feet


12 Ray put a circular fountain at the center of the garden described in Question 10. The fountain has a radius of 2 feet. What is the remaining area of the garden? Round to the nearest square foot.


13 Cecilia Park is shaped like a circle with diameter 50 yards. Rogers Park is a rectangle that is 50 yards long and 40 yards wide. Tappan Park is shaped like a right triangle with side lengths 30 yards, 40 yards, and 50 yards. Which park has the greatest area? Which park has the greatest perimeter (or circumference)?

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GEOMETRYSimilar Triangles

6.G.1 Calculate the length of corresponding sides of similar triangles, usingproportional reasoning.


1 Triangles ABC and FDE are similar. Which are corresponding sides?

B

C

E

FDA

A −−

AB and −−

EF

B −−

AB and −−

BC

C −−

AB and −−

FD

D −−

AB and −−

ED

2 Triangles PQR and STV are similar. What is x?

x

P

V

T

S

R

3 cm

6 cm

1.4 cm

F 4.2 centimeters

G 19.3 centimeters

H 5.6 centimeters

J 2.8 centimeters

3 Triangles ABC and MNP are similar.AB = 7 cm, MN = 21 cm, and BC = 3 cm. What is the length of the side of MNP that corresponds to side

−− BC ?

A 4 centimeters

B 9 centimeters

C 7 centimeters

D 3 centimeters

In the diagram, triangles EFG and HJK are similar. Use the diagram to answer questions 4–6. Side lengths are given in centimeters.

x

H

G

K

J

10 8

4

E

F

4 What is the ratio of corresponding sides?

F 8 to 4

G 3 to 8

H 8 to 10

J 10 to 4

5 Which proportion can you use to find the length of side x?

A x __ 4 = 10 ___

8

B x __ 4 = 8 ___

10

C x ___ 10

= 8 __ 4

D x ___ 10

= 4 __ 8

6 What is the length of side x?

F 8 centimeters

G 10 centimeters

H 5 centimeters

J 12 centimeters

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Triangles TVU and XYZ are similar. Use the triangles to answer questions 7–9.

T U

V

X Z

Y

7 Which statement shows the sides of the triangles are proportional?

A TU ___ XY

= TV ___ XZ

= VU ___ YZ

B TU ___ XZ

= TV ___ XY

= VU ___ YZ

C TU ___ YZ

= TV ___ XZ

= VU ___ XY

D TU ___ YZ

= TV ___ XY

= VU ___ XZ

8 Suppose TU = 5 cm, XZ = 9 cm, and TV = 4 cm. What is XY?

F 2.7 centimeters

G 7.2 centimeters

H 2.2 centimeters

J 4.5 centimeters

9 What is the ratio of corresponding sides?

A 2.7 to 5

B 4 to 5

C 4 to 9

D 5 to 9


10 The side lengths of two similar triangles are in the ratio 5 : 4. One side of the smaller triangle is 16 cm. What is the length of the corresponding side in the larger triangle?

11 A triangle has sides 8.3 cm, 2.9 cm, and 5.6 cm. What could be the dimensions of a larger similar triangle? Explain.


12 The lengths of corresponding sides of two similar triangles are in the ratio 3 : 2. The perimeter of the smaller triangle is 28 cm. What is the perimeter of the larger triangle? Explain your answer.

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1 What is the area of the parallelogram?

5 m

12 m

6 m

A 36 m 2

B 60 m 2

C 72 m 2

D 360 m 2

2 What is the area of the largest triangle in the diagram below?

10 cm

5.8 cm8.5 cm6.9 cm

A 29 cm 2

B 34.5 cm 2

C 58 cm 2

D 69 cm 2

3 The diagram shows the dimensions of Emily’s hallway. How much carpet does she need to completely cover the floor?

4 ft

12.5 ft

A 16.5 ft 2

B 20.5 ft 2

C 33 ft 2

D 50 ft 2

4 A window is shaped like an isosceles triangle. The height of the triangle is 36 inches, the base of the triangle is 14 inches. What is the area of the window?

F 50 in . 2

G 252 in . 2

H 360 in . 2

J 504 in . 2

5 The two parallel sides of a trapezoid are 12 feet long and 15 feet long. The distance between the parallel sides is 14 feet. What is the area of the trapezoid?

A 41 ft 2

B 189 ft 2

C 378 ft 2

D 2,520 ft 2

6 A triangle has a 16 centimeter base and a height of 9 centimeters. If both the base and the height are reduced by half, what will be the new area of the triangle?

F 18 square centimeters

G 36 square centimeters

H 65.875 square centimeters

J 72 square centimeters

GEOMETRYAreas of Triangles and Quadrilaterals

6.G.2 Determine the area of triangles and quadrilaterals (squares, rectangles, rhombi,and trapezoids) and develop formulas.

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7 The height of a rhombus is half the length of one of its sides. If the length of one of its sides is 10 inches, what is the area of the rhombus?

A 5 square inches

B 15 square inches

C 50 square inches

D 100 square inches

8 What is the area of a triangle with a base of 7 inches and a height of 8.4 inches?

F 14.7 square inches

G 22.7 square inches

H 29.4 square inches

J 58.8 square inches


9 The base of a triangle is 12 centimeters and the height is 6 centimeters. How many times as great is its area than the area of a rectangle with base 6 centimeters and height 3 centimeters?


10 Tom drew two congruent right triangles, each with lengths of 6, 8, and 10 inches. He cut the triangles out and joined them together to form a quadrilateral. His friend Joan drew the same triangles as Tom, but formed a different quadrilateral. What types of quadrilaterals did Tom and Joan form? What were the areas of the two quadrilaterals?

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GEOMETRYAreas of Regular and Irregular Polygons

6.G.3 Use a variety of strategies to find the area of regular and irregular polygons.


1 A square with side length s has a triangle with height h attached to one side. The base of the triangle is the same length as the side length of the square. Which expression can be used to find the area of this shape?

A 4s + 1 __ 2 • s • h

B s 2 + 1 __ 2 • s 2

C s 2 + 1 __ 2 • s • h

D s 2 + s • h

2 The diagram represents Stanley’s yard. Find the area of Stanley’s yard?

96 ft

64 ft

66 ft116 ft

F 4,224 ft 2

G 7,704 ft 2

H 10,368 ft 2

J 11,136 ft 2

3 What is the area of the shape?

A 6 square units

B 8.5 square units

C 11 square units

D 12 square units

4 What is the area of this shape?

F 15 square units

G 17.5 square units

H 18 square units

J 24 square units

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5 Janice’s living room makes an L-shape with a V-shaped bay window on one end. What is the area of the living room, including the bay window?

18 ft

4 ft

12 ft

6 ft

9 ft

F 49 ft 2

G 162 ft 2

H 174 ft 2

J 216 ft 2

6 Julia wants to find the area of a regular hexagon by subdividing it into smaller polygons and using familiar area formulas. She knows the measure of the side length of the hexagon and the distance across the widest part. Which of the subdivisions shown could she use without making any other measurements or finding any other lengths?

A

B

C

D


7 The quadrilaterals in the diagram are both rectangles. What is the area of the shaded region?

9 m

15 m

8 m

12 m


8 A polygon has vertices A(1, 2), B(4, 4), C(4, –2), D(–2, –2), and E(2, 3). Find its area.

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GEOMETRYCircles

6.G.5 Identify radius, diameter, chords, and central angles of a circle.6.G.6 Understand the relationship between the diameter and radius of a circle.


Use the following figure to answer questions 1–3. Point C is the center of the circle.

E

BC

DF

1 Which line segment forms a radius of the circle?

A −−

DB

B −−

BC

C −−

DE

D −−

DF

2 Which line segment forms a chord, but not a diameter, of the circle?

F −−

CE

G −−

BC

H −−

DE

J −−

DF

3 Which of the following angles is NOT a central angle of the circle?

A ∠ECD

B ∠FDC

C ∠DCB

D ∠ECB

4 What is the longest chord you can draw inside any circle?

F The radius

G The diameter

H A chord that does NOT go through the center.

J None of the above.

5 Which line segment forms a diameter of the circle?

A

B

F

E

D

C

A −−

AB

B −−

BC

C −−

DE

D −−

BF

6 The diameter of a circle is 12 centimeters. How long is the radius?

F 24 centimeters

G 18 centimeters

H 12 centimeters

J 6 centimeters

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7 How many central angles are drawn in the circle below? What is the measure of each one?

A one; 180°

B one; 360°

C two; 90°; 90°

D two; 180°; 180°

8 The radius of a circle is 14 yards. Find the diameter of the circle.

A 7 yards

B 28 yards

C 196 yards

D 44 yards


9 Draw a central angle that measures 90° on the circle shown.


10 Scott drew 2 diameters in the circle below. The 2 diameters divided the circle into 4 congruent central angles. Then his friend Mary drew 2 more diameters in the circle. After Mary drew these diameters, there were 8 congruent central angles in the circle. What was the measure of one of these 8 congruent central angles? Explain.

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GEOMETRYCircles and Sectors

6.G.7 Determine the area and circumference of a circle, using the appropriate formula.6.G.8 Calculate the area of a sector of a circle, given the measure of a central angle and the radius of the circle. Also 6.G.9


1 What is another name for the perimeter of a circle?

A area

B diameter

C circumference

D radius

2 Which statement is NOT true?

F The circumference of a circle is equal to π times the diameter.

G The circumference of a circle is equal to π times two times the radius.

H The area of a circle is equal to π times the radius squared.

J The area of a circle is equal to π times the diameter squared.

3 A scientist is recording the types of animals that live within a 6 mile radius of a natural spring. Which expression could you use to find how many square miles this is?

A 6 × π

B 3 × 3 × π

C 6 × 6 × π

D 12 × 12 × π

Use the drawing of a pizza to answer questions 4–5.

4 Which of the following equations can be used to find the approximate circumference of the pizza below?

F C = 2 × 3.14 × 14

G C = 3.14 × 14

H C = 3.14 × 142

J C = 3.14 × 72

5 As shown, the pizza is divided into 8 congruent pieces. What is the approximate area of one of these pieces?

A 5.5 in . 2

B 19 in . 2

C 44 in . 2

D 77 in . 2

6 The radius of a circle is 28 cm. The measure of a central angle drawn in the circle is 60°. Which expression can be used to find the approximate area of the sector?

F 1 __ 3 × π × 28 2

G 1 __ 6 × π × 28 2

H 1 __ 3 × π × 14 2

J 1 __ 6 × π × 14 2

14 in.14 in.14 in.

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Use the circle below for Exercises 7–8.

5 cm

7 Which expression could you use to find the circumference of the circle in centimeters?

A 2.5 × π

B 5 × π

C 2 × 5 × π

D 5 × 5 × π

8 Which expression could you use to find the area of the circle in square centimeters?

F 5 × π

G 2.5 × 2.5 × π

H 5 × 5 × π

J 10 × 10 × π

9 A dinner plate has a diameter of 10 inches. Which expression could you use to find the area of the dinner plate in square inches?

A 10 × π

B 5 × 5 × π

C 10 × 10 × π

D 20 × 20 × π

10 A circular arena has a diameter of 250 feet. Which expression can you use to find the distance around the arena in feet?

F 250 × π

G 500 × π

H 250 × 250 × π

J 500 × 500 × π


11 A bicycle tire has a diameter of 20 inches. About how much ground will it cover in one full rotation?

diameter = 20 in.

12 Jessica draws a circle graph with a diameter of 3 inches. The measure of one of the sectors on the circle graph is 45°. What is the area of this sector? Round to the nearest tenth.


13 The area of a clock face is 16π square inches. What is the radius of the clock face? What expression can you use to find the circumference of the clock face in inches? What is the circumference of the clock face, rounded to the nearest tenth of an inch? C

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MEASUREMENTSelect Appropriate Measuring Tools

6.G.10 Identify and plot points in all four quadrants. Also 6.G.11


Use this graph for questions 1–3.

1

10

2345678910

2 3 4 5 6 7 8 9 10

P

R

S

x

y

1 Which point is located at the coordinates (8, 6)?

A Point P

B Point Q

C Point R

D Point S

2 Which of these ordered pairs is a vertex of the pentagon?

F (4, 8)

G (5, 6)

H (8, 9)

J (10, 8)

3 Which ordered pair represents a point located inside the triangle and outside the pentagon?

A (2, 5)

B (6, 8)

C (8, 4)

D (8, 6)


K

P

S

H

M

E

4

3

2

1

21

22

23

24

2 3 4121222324 O x

y

4 Which points have positive coordinates?

F Points E and H

G Points P and E

H Points H and K

J Points K, H, and M

5 Points E, H, and P are three vertices of a parallelogram. Where is the fourth vertex?

A (-2, 0)

B (-1, -2)

C (0, -2)

D (1, -2)

6 Points E, H, and K form the vertices of a triangle. What is the area of triangle EHK?

F 4 square units

G 4.5 square units

H 9 square units

J 12 square unitsCop

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1

3

5

7

1 3 5 7

2

4

6

2 4 6O

U V

Z

Y

W

X

x2121222324252627

222324252627

y

7 List all the points that have one positive coordinate and one negative coordinate.

A U and Z

B V, W, and Y

C U, X, and Z

D U, V, W, and Z

8 What polygon can you form by connecting the points U, V, X, and Z?

F pentagon

G parallelogram

H trapezoid

J triangle

9 What is the area of the shape whose vertices are U, V, X, and Z?

A 20 square units

B 42 square units

C 60 square units

D 84 square units



2

4

2 4O x

22

24

2224

y

10 Graph the points A(–3, –2), B(0, 2), C(3, 2) and D(0, –2). Connect points A, B, C, and D to form quadrilateral ABCD.

11 Classify quadrilateral ABCD from Exercise 10. Then find the area of the quadrilateral.


12 A rectangle drawn in a coordinate plane has vertices at points (–3, 2), (4, 2), and (4, –3). What are the coordinates of the fourth vertex, and what is the area of the rectangle? Explain your answer.

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MEASUREMENTVolume

6.M.1 Measure capacity and calculate volume of a rectangular prism. Also 6.G.4


1 What is the volume of a 5.5 foot tall, 2.75 foot wide, and 2.5 foot deep refrigerator to the nearest tenth?

A 10.8 cubic feet

B 15.1 cubic feet

C 37.8 cubic feet

D 71.6 cubic feet

2 What is the volume of a 5 foot long, 3 foot wide, and 2 foot deep rectangular toy chest?

F 10 cubic feet

G 15 cubic feet

H 30 cubic feet

J 60 cubic feet

3 The area of the base of a cube-shaped packing box is 36 square inches. What is the volume of the box in cubic inches?

A 72 cubic inches

B 96 cubic inches

C 216 cubic inches

D 360 cubic inches

4 A cube-shaped packing box is 30 inches deep. What is the volume in cubic inches of the box?

F 270 cubic inches

G 2,700 cubic inches

H 27,000 cubic inches

J 270,000 cubic inches

5 Which of the following is a method that can be used to find the volume of the rectangular prism shown?

A Count 4 cubes on the bottom layer and multiply by 4, the number of layers.

B Count all the cubes in the prism.

C Count 8 cubes on the front face of the cube and multiply by 2.

D All of the above.

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6 A rectangular prism is 4 inches by6 inches by 8 inches. Another rectangular prism has dimensions that are twice as long. How many times as great is the volume of the second prism than the volume of the first prism?

F 2 times

G 4 times

H 6 times

J 8 times

7 Maria is wrapping a present. The shipping box measures 10 inches by 5 inches by 5 inches. A small gift box inside the shipping box measures 2 inches by 2 inches by 2 inches. How much space is left inside the shipping box for packaging material?

A 8 cubic inches

B 242 cubic inches

C 250 cubic inches

D 258 cubic inches

8 What is the volume of a rectangular prism that has a length of 15 centimeters, a width of 25 centimeters, and a height of 32 centimeters?

F 72 cubic centimeters

G 216 cubic centimeters

H 1944 cubic centimeters

J 12,000 cubic centimeters


9 A rectangular prism is 2 inches by 4 inches by 6 inches. Another rectangular prism has dimensions that are three times as long. How many times as great is the volume of the second prism than the volume of the first prism?

10 A rectangular prism has a 3 feet by 3 feet square base and a height of 4.5 feet. What is the volume of the prism?


11 The volume of a cube is 125 cubic centimeters. What is the length of one edge of the cube? Explain your answer.

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MEASUREMENTCustomary Units of Capacity

6.M.2 Identify customary units of capacity (cups, pints, quarts, and gallons).6.M.3 Identify equivalent customary units of capacity (cups to pints, pints to quarts, and quarts to gallons). Also 6.M.6


1 Samantha is measuring cooking oil for a recipe. She pours up to the line shown on the measuring cup below.

CUPS2

How many ounces of cooking oil does Samantha pour into the measuring cup?

A 4 oz

B 8 oz

C 12 oz

D 16 oz

2 Which unit of measure would you use to find out how much water is in a swimming pool?

F inches

G pounds

H ounces

J gallons

3 Mark mixed 30 pints of blue paint with 26 pints of yellow paint to make green paint. How many gallons of green paint did he make?

A 3.5 gallons

B 7 gallons

C 14 gallons

D 448 gallons

4 A caterer is making lasagna to serve at a banquet. To make one pan of lasagna, the caterer needs 4 cups of tomato sauce. How many quarts of tomato sauce will the baker need to make 25 pans of lasagna?

F 25 quarts

G 50 quarts

H 75 quarts

J 100 quarts

5 A caterer prepares 12 gallons of fruit punch for a large wedding. How many pints is this?

A 24 pints

B 48 pints

C 96 pints

D 192 pints

6 The school cafeteria makes 3 gallons of soup each day. The cafeteria sells the soup at a price of $.75 per cup. What is the maximum amount of money the cafeteria can make from selling soup on any given day?

F $12

G $18

H $36

J $48

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7 Which amount is greater than 12 pints?

A 2 gallons

B 6 quarts

C 20 cups

D 24 cups

8 Which bottle has the smallest capacity?

F 1 3 __ 4 gallon bottle

G 6 quart bottle

H 13 pint bottle

J 32 cup bottle

9 How many paper cups can Gloria fill with this container of juice?

A 6

B 16

C 24

D 32


10 The football team members drank 2.5 gallons of water at the last game. How many quarts did they drink?

11 Teresa filled 28 one-quart jars with chili to sell at a farmer’s market. How many gallons of chili did Teresa make?


12 Jon has a recipe that calls for 3.5 cups of milk. Jon wants to triple the recipe, but has only 1 quart of milk. Does he need to buy more milk? If so, how many additional quarts should he buy? Explain.

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MEASUREMENTMetric Units of Capacity

6.M.4 Identify metric units of capacity. 6.M.5 Identify equivalent metric units of capacity (milliliter to liter and liter to milliliter). Also 6.M.6


1 Which unit of measure would you use to determine the volume of a teacup?.

A millimeters

B milligrams

C milliliters

D kiloliters

2 Which measurement is equivalent to 2.8 liters?

F 0.28 milliliter

G 28 milliliters

H 280 milliliters

D 2,800 milliliters

3 Ms. Parker has 6 L of juice. She wants to serve the juice to her students. If each serving is 300 mL, how many students can have juice?

A 15 students

B 20 students

C 25 students

D 30 students

4 541 milliliters is equivalent to which amount?

F 0.541 liters

G 5.41 liters

H 54,100 Liters

J 541,000 Liters

5 To make some fruit punch, Karen added 50 mL of lemon juice, 3.1 L of orange juice, and 0.8 L of limeade to 2 L of seltzer water. About how much fruit punch did she make?

A about 3 L

B about 4 L

C about 5 L

D about 6 L

6 Yesterday the cafeteria sold a total of 88 L of milk. If each serving was 400 mL, how many servings of milk did the cafeteria sell?

F 200 servings

G 210 servings

H 220 servings

J 230 servings

7 A bottle contains 2 L of liquid and 40 mL of air. What fraction of the total capacity of the bottle is air?

A 1 _____ 5,000

B 1 ____ 500

C 1 ___ 50

D 1 __ 5

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8 Enoch’s thermos can hold 500 mL ounces of liquid. How many times can he fill his thermos from 2.5 L container of juice?

F 2 times

G 4 times

H 5 times

J 6 times

9 Dan’s little brother has a lemonade stand. If he charges $.50 for each 250 mL serving of lemonade, what is the maximum amount he can make from selling 3.5 L of lemonade?

A $7

B $14

C $17.50

D $125

10 An Olympic sized swimming pool holds approximately 2,500,000 liters of water. About how many milliliters is that?.

F 2,500

G 250,000

H 250,000,000

J 2,500,000,000


11 How many child’s doses are contained in a full bottle of this cough medicine?


12 Kerry cooked 2.5 liters of tomato sauce. How many 400 mL jars can he fill with the sauce? How much sauce will be left over after the jars are filled?

CoughMedicine

Dosage: Children 6 to 12 yrs.5mL every 6 hours as needed 0.15L

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MEASUREMENTEstimate Measures

6.M.8 Justify the reasonableness of estimates.6.M.9 Determine personal references for capacity.


1 Estimate the volume of this cube.

6.5 inches

A 36 cubic inches

B 100 cubic inches

C 275 cubic inches

D 1,500 cubic inches

2 A rectangular box has dimensions 14.2 inches by 8.8 inches by 15.6 inches. What is the approximate volume of the box?

F 96 cubic inches

G 200 cubic inches

H 550 cubic inches

D 2,000 cubic inches

3 What is the approximate surface area of the box described in Question 2?

A 400 square inches

B 1,000 square inches

C 2,016 square inches

D 4,032 square inches

Use this rectangular prism for questions 4–5.

2.4 m

3.5 m

7 m

4 Estimate the surface area of the prism.

F 16 square meters

G 20 square meters

H 32 square meters

J 100 square meters

5 Estimate the volume of the prism.

A 16 cubic meters

B 30 cubic meters

C 48 cubic meters

D 60 cubic meters

6 Emma’s yard is shaped like a right triangle. She measures one leg of the triangle and finds that it is 42 feet long, and the other leg is about twice as long as that. Estimate the area of her yard.

F 80 square feet

G 800 square feet

H 1600 square feet

J 3200 square feet

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7 Susan estimated the area of her bedroom floor. She wrote down 12 as her estimate, but forgot to include units. Which of the following is most likely to be the units she forgot to include?

A feet

B meters

C square feet

D square meters

8 Matt measured several features of his bedroom. However, when he recorded his findings, he forgot to record the units of measure he used. One measurement he recorded is 34. What feature’s measurement would this most likely be?

F the area of the window in square feet

G the height of the room in feet

H the length of the room in yards

J the width of the door in inches

9 A scientist estimates that the diameter of a circular crater on the moon is about 20 meters. What is the approximate circumference of the crater?.

A about 3.1 meters

B about 6.3 meters

C about 31 meters

D about 63 meters

10 Which of the following best describes how a liter compares to a gallon?

F It is less than a gallon.

G It is about the same as a gallon.

H It is more than a gallon.

J None of the above.


11 Sheila filled the water cooler with 3 gallons of water. She then served 16 glasses of water from the cooler. About how much water remains in the cooler?

12 A wheel on a toy truck is about 2 inches wide. If the truck is pushed 3 feet across the floor, about how many times will the wheel turn around? Explain your thinking.

Extended-Response: Show your work for the each question.

13 The gallon milk jug shown is about two-thirds full. About how many 8 oz glasses of milk can be poured from the jug? Explain.

14 One base of a trapezoid is the same length as the height of the trapezoid. The other base is three times as long as the height of the trapezoid. If the height of the trapezoid is 4.1 cm, estimate the area of the trapezoid.

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Name _________________________________ Date ______________Class ______________

STATISTICS AND PROBABILITYSurveys and Samples

6.S.1 Develop the concept of sampling when collecting data from a population anddecide the best method to collect data for a particular question.


1 A scientist collects weekly rainfall data from 42 random sites throughout the desert. What is the sample?

A The 42 sites

B The entire desert

C The average rainfall

D The length of the study

2 Some researchers wanted to estimate the percent of students at a school who chew gum. The researchers watched students walking to school in the morning and counted the number who were chewing gum. Which answer is NOT a potential problem with this sampling method?

F More students who drive or get rides may be chewing gum in their cars.

G More students may be chewing gum at other times of the day.

H Students may have a first-period exam.

J Students may not want to chew gum heading to school because they will have to throw it out when they get there.

3 A researcher watched students at a block party in his neighborhood to see how many were chewing gum. Why is this sometimes called a “convenience sample”?

F It is convenient for students to go to a party in their own neighborhood.

G It is convenient for the researcher to use nearby subjects.

H Because gum is often purchased at a convenience store.

J Gum would be conveniently available to people at a party.

4 For which situation would it make sense to use a sample rather than the population?

F Determining how many students in Mr. Sperry’s class need extra help with reading

G Determining which television show your friends will watch Tuesday night

H Determining how many members of the basketball team practiced during the summer

J Determining the number of students in your school who will attend Friday’s swim meet

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5 What is a problem with an inference based on a convenience sample?

A It is too easy and convenient.

B People may not be honest in their answers.

C A sample of fewer than 24 people is not valid.

D The sample may not reflect the overall population.

6 A candidate for mayor wants to poll voters to see how well her campaign is doing. What is the biggest problem with posting signs asking people to call the pollsters with their opinions?

F People will not see the signs.

G Self-selected responders are not a random sample.

H There may be too many male callers.

J Callers may not tell the truth.

7 A doctor wants to know how much time people spend in the waiting room. Which sampling method will be the most representative?

A Survey the last 2 patients of the day

B Survey the first 4 patients of the day

C Survey 1 out of every 10 patients seen during a week

D Survey all the patients who scheduled appointments at the last minute


8 Omar wants to find the percent of students at his school who participate in at least one after-school activity. He asks all the students on one of the buses after school. Tell whether this sample is likely to be representative of the population. If not, describe a method Omar could use to collect data.


9 The mayor of a town wants to know how many town residents support a new law. The clerk called 100 people who voted for the mayor in the last election. Of those called, 38 like the new law, 50 do not like the new law, and 12 have no opinion. Identify the population and the sample. Is the sample representative? If not, explain how to make it more representative of the population.

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Name _________________________________ Date ______________Class ______________

STATISTICS AND PROBABILITYChoosing and Constructing Data Displays

6.S.4 Determine and justify the most appropriate graph to display a given set of data(pictograph, bar graph, line graph, histogram, or circle graph). Also 6.S.2, 6.S.3


Use the following chart to answer questions 1–2.

Williams P.S.

Grade Boys Girls

5 15 19

6 25 14

7 17 16

8 12 21

1 Which type of graph gives the BEST representation of this data?

A Venn diagram

B line graph

C circle graph

D double bar graph

2 Dave made a frequency table showing the total number of students in grades 5–6, and the total number of students in grades 7–8. What was the frequency for each of these?

F Grades 5–6: 34

Grades 7–8: 33

G Grades 5–6: 40

Grades 7–8: 29

H Grades 5–6: 33

Grades 7–8: 40

J Grades 5–6: 73

Grades 7–8: 66

3 An environmental protection group tracked the population of bald eagles in a national park over three years. Their results appear in the table below.

Year Eagles

1 27

2 20

3 17

Which graph best represents these data?

A

0

153045607590

1

27

2

47

3

64

B

2

1

3

C

0

5

10

15

20

25

30

1 2 3

D 21 3

20 1727

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4 Adults living near the town of Bayside can choose to join one or both of two hockey leagues. The table shows the number of adults in each league.

League Players

Raiders 62

Tigers 48

Both 14

Which type of graph would BEST represent the data in the table?

F histogram

G circle graph

H line graph

J Venn diagram

5 In Lisa’s math class, 6 students received test scores in the 91–100% range, 12 students received scores in the 81–90% range, and the other 2 students received scores in the 71–80% range. Which type of display would BEST represent the data?

A histogram

B line graph

C pictograph

D Venn diagram

6 Which data could best be represented by this graph?

F Change in distance over time

G Height of major mountain ranges

H High temperature each day

J Number of students playing various musical instruments


7 During a snowstorm, it snowed all afternoon and evening. Kayla measured the amount of snow on the ground at three different times, as shown in the table. What type of display can she use for the data? Justify your choice.

Time 2 PM 3 PM 5 PM

Snowfall 1 in. 3 in. 7 in.


8 According to the Venn diagram, which favorite color is NOT shared by at least 2 friends? Explain your answer.

Jane

green

yellowblue

red

Mary

Stacy

Our Favorite Colors

9 Sam asks 20 students to choose their favorite sport. Half the students choose football, 5 choose soccer, 2 choose swimming, and 3 choose other sports. Sam wants to use a circle graph for the data. Is that a good choice for a data display? Why or why not?

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Name _________________________________ Date ______________Class ______________

STATISTICS AND PROBABILITYInterpreting Data Displays

The circle graph below shows the daily sales at Sal’s Market during one week. Use the circle graph for Exercises 1–3.

1 On what day did Sal’s Market sell the least?

A Wednesday

B Thursday

C Sunday

D Saturday

2 About what percentage of the sales occurred on Saturday?

F 25%

G 33%

H 50%

J 90%

3 Sal’s Market had $150,000 in sales that week. Which is a good estimate of the store’s sales on Friday?

A $25,000

B $50,000

C $75,000

D $100,000

Use the following graph to answer questions 4–6.

10

8

6

4

2

0

Test Scores (%)

Nu

mb

er

of

Stu

den

ts

60 70 80 90 100

Math Test Scores

4 According to the graph, how many students took the math test?

F 9

G 11

H 21

J 23

5 How many students got a test score below 90%?

A 6

B 15

C 9

D 21

6 Which test score was most common?

F 100%

G 80% and 90%

H 70%

J 80%

6.S.7 Read and interpret graphs.

Saturday

Friday

Sunday

Monday

Tuesday

Wednesday

Thursday

Sales at Sal’s Market

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In the line graph below, the amount of books read by a student for each week is the combined total for that week and all the preceding weeks. Use the graph for questions 7–9.

Total Books Read

8

6

4

2

01

Miguel

2 3 4 5 6

Bo

oks R

ead

WeeksAnna

7 How many books did Anna and Miguel read in all in the 6 weeks?

A 6

B 7

C 12

D 14

8 Who was ahead after 5 weeks and by how much?

F Anna by 2 books

G Miguel by 2 books

H Anna by 1 book

J Miguel by 1 book

9 At what point or points were they tied for the number of books read?

A weeks 3 and 6

B weeks 1 and 2

C never

D week 6 only


10 Amy surveyed two classes, “Which game do you prefer: checkers, chess, or backgammon? The responses are displayed in the bar graph. How many more students preferred chess in Class A than in Class B?


11 Use the graph below. In what year did the girls’ basketball have its greatest number of wins? In what year did the boys’ team have its greatest number of wins? In what year was the difference between the number of wins by the girls’ team and the number of wins by the boys’ team the greatest?

02003 2004 2005 2006

Year

Gam

es W

on

Games Won by Grady School

Girls’ basketball team

Boys’ basketball team

5

10

15

20

25

Checke

rs

Chess

Backg

amm

on

Game

Game Preference

02468

1012

Stu

den

ts

Class A

Class B

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A1 NY Test Prep Grade 6

Name _________________________________ Date ______________Class ______________


1 Find the sum of 3.7 trillion and 4.6 million. Write the sum in standard form.

A 3,700,000,004,600

B 3,700,004,600,000

C 3,700,000,000,004,600

D 3,704,600,000,000,000

2 Eric pulls one marble from the box without looking. Without replacing the first marble, he draws another marble. What is the probability that both marbles are white?

F 1 __ 9

G 1 __ 3

H 5 ___ 54

J 5 ___ 51

3 Which equation is an example of the associative property of multiplication?

A 5 × 6 × 8 = 5 × 8 × 6

B (5 × 6) × 8 = 5 × (6 × 8)

C 5 × 6 × 8 = 240

D (5 × 6) × 8 = 8 × (5 × 6)

4 The perimeter of ΔABC is 43 inches. Triangle A'B'C' is a similar triangle with side lengths three times the lengths of the sides of ΔABC. What is the perimeter of ΔA'B'C'?

A A� B�B

C

C�

F 14.3 inches

G 46 inches

H 86 inches

J 129 inches

5 Four students tried to use the distributive property. Only only one student used the property correctly. Which of the following equations is correct?

A 5(20 + n) = 5(20) + n

B 4(3n + 1) = 12n + 4

C 7(5 + n) = 12 + 7n

D 8(2n + 4) = 16n + 8

Sample Test AC

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A1-A14_NY_G6.indd A1A1-A14_NY_G6.indd A1 1/4/10 12:54:39 PM1/4/10 12:54:39 PM


Name _________________________________ Date ______________Class ______________

6 Gilda completed 60% of her assignment. Which shows another way to describe this number?

F 0.06

G 60 ___ 10

H 3 __ 5

J 6.0

7 A librarian wants to know how often people in a town use the library. Which sampling method will be the most representative?

A Survey 1 out of every 10 people who use the library on one day.

B Survey all the people who enter the library first thing in the morning.

C Conduct a survey by randomly calling 100 of the town’s citizens.

D Conduct a survey by randomly calling 100 people who currently have books checked out.

8 What would be the area of the circle if the radius were halved? Use 3.14 for π.

8 m

F 200.96 m 2

G 100.48 m 2

H 50.24 m 2 J 25.12 m 2

9 Sheila made punch by mixing 12 cups of fruit juice with 4 pints of soda water and 1 quart of lemonade. How many gallons of punch did she make?

A 1.5

B 6

C 12

D 24

10 The bar graph shows the sixth grade class size at a middle school from 2002 to 2007. In which year was the class size exactly twice that of 2003?

0

10

20

30

40

50

60

70

80

90

100

110

120

130

2002

2003

2004

2005

2006

2007

Year

Stu

den

ts

40

50

60

100

120

95

F 2003 H 2006

G 2005 J 2007

11 The two parallel sides of a trapezoid are 50 cm and 40 cm. The distance between these two sides is 60 cm. What is the area of the trapezoid?

A 2400 cm 2

B 3000 cm 2

C 2700 cm 2

D 5400 cm 2

12 Carlos read 30 pages in 20 minutes. Assume he continues at the same rate. Use a proportion to find the number of pages he could read in 80 minutes.

F 60 pages

G 100 pages

H 120 pages

J 240 pages

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13 Find the difference: 3 4 __ 5 - 2 1 ___

20 .

A 1 3 ___ 20

B 1 3 __ 5

C 1 3 __ 4

D 2 3 ___ 10

14 Lydia has already spent 30 hours at volleyball practice this year. She plans to attend practice 6 hours a week for the rest of the year. Let w be the number of weeks in the rest of the year. Which expression describes the total number of hours Lydia will spend at volleyball practice this year?

F 30 + 6

G 36w

H 36 + w

J 30 + 6w

15 What is the value of the expression 11r + 3s when r = 5 and s + 7?

A 65

B 76

C 92

D 152

16 Nigel filled an eyedropper with water. He wrote down “5” as an estimate of the amount of water in the eyedropper, but forgot to use units. Which of the following are most likely to be the units he forgot to include?

F milliliters

G liters

H cups

J pints

17 What is the sum of 12 and its additive inverse?

A –12

B 0

C 1

D 1 ___ 12

18 Which of the following numbers CANNOT be written as a proportion?

F 3 __ 8 and 9 ___

24

G 12 ____ 100

and 3 ___ 25

H 27 ___ 49

and 4 __ 7

J 1 ___ 12

and 5 ___ 60

19 It costs $5 to get into an amusement park plus $2 per ride, and Carter has $80 to spend. Which equation can be used to find the number of rides n that he can afford?

A 5n + 2 = 80

B 2n + 5 = 80

C 7n + 80

D 5n + 80 + 2

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20 Jamal wrote down the equation 9 × 0 = 0. Which of the following properties does his equation illustrate?

F inverse property of zero

G zero property of multiplication

H zero property of identity

J identity property of zero

21 It is recommended that a person eat no more than 2,400 grams of sodium per day. Andy ate 864 grams of sodium for lunch. What percent of the recommended daily amount does this represent?

A 33%

B 36%

C 37%

D 41%

22 At a pet store, 60% of the birds are parakeets. If there are 45 birds, how many are parakeets?

F 3

G 27

H 30

J 75

23 An artist wants to cut a paper that is

15 3 __ 4 inches long into pieces that are

2 1 __ 4 inches long. How many pieces can

be cut?

A 6

B 7

C 8

D 9

24 Flor wants to solve the equation 5x - 4 = 16. What step should she take first?

F Subtract 4 from each side.

G Add 4 to each side.

H Divide both sides by 5.

J Multiply each side by 5.


|-4| + 12 - |-5|

A 3

B 11

C 13

D 21

26 The lengths of some boards in inches are: 58, 68, 70, 48, 60, 64, 62, 58. If another board 62 inches long were added to the list, what would happen to the median length?

F It would stay the same.

G It would increase by 1 __ 2 .

H It would increase by 1.

J It would decrease by 1.

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27 For each of the first three weeks on her job, Joyce earned $875, $915, and $850. For the fourth week, she earned $20 more than the mean of her earnings for the first three weeks. What was the range of her earnings for the first four weeks?

A 25

B 35

C 50

D 65

28 The graph below shows the length in miles of some tunnels. Which is the BEST estimate of the difference in the lengths of the Seikan and the Delaware Aqueduct?

Tunnel Lengths

0 20 40 60 80 100

Seikan

DelawareAqueduct

Miles

Brooklyn-Battery

St. Gotthard

F 30 miles

G 50 miles

H 60 miles

J 80 miles

29 Which would be the most appropriate way to display this data?

Which is your dominant hand?

Right 62

Left 24

Ambidextrous 14

A circle graph

B box-and-whisker plot

C line graph

D scatterplot

30 Raul goes on a three-day hiking trip with his father. Each day they hike for 6 hours at an average speed of 3 miles per hour. After three days, how many miles have Raul and his father hiked?

F 9 miles

G 18 miles

H 27 miles

J 54 miles

31 Judi commutes 1 1 __ 8 miles to school.

Cesar commutes 3 3 __ 4 times as far as Judi.

How far does Cesar commute?

A 2 5 __ 8 miles

B 3 3 ___ 32

miles

C 3 21 ___ 32

miles

D 4 7 ___ 32

miles

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32 To find the area of a regular hexagon, Lisa divided it into two congruent polygons. She measured the lengths shown in the diagram Use her measurements to find the area of the regular hexagon.

3 cm

1.5 cm

2.6 cm

F 2.925 cm 2

G 5.85 cm 2

H 11.7 cm 2

J 15.6 cm 2

33 Evaluate 4 2 + 5 3 + 10 3 .

A 53

B 141

C 1041

D 1141

34 Which point on the number line BEST

shows the location of –5 ___ 8 ?

21 2 0 1

A B C D

12

12

F Point A

G Point B

H Point C

J Point D

35 Write a • a • a • a • a • a • a • a • a using an exponent.

A a 7

B a 8

C a 9

D a 10

36 Which unit of measure would you use to find out how much pancake batter is in a small mixing bowl?

F inches

G pounds

H cups

J gallons

37 A pizza is cut into 8 identical slices, as shown below. The diameter of the pizza is 16 inches. Which of the following is equal to the area of one slice?

A 8 • π

B 32 • π

C 64 • π

D 256 • π

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38 Which expression is equivalent to 5 7 ?

F 5 • 7

G 7 • 7 • 7 • 7 • 7

H 5 • 5 • 5 • 5 • 5 • 5 • 5

J 5 • 5 • 5 • 5 • 5 • 5 • 5 • 5

39 What number is the multiplicative inverse of 0.3?

A – 10 ___ 3

B – 0.3

C 10 ___ 3

D 1

40 Which number is equivalent to 8 ___ 11

?

F 0.72

G 0.7 −

2

H 0. −−

72

J 0.727

41 Use the formula C = (F - 32) • 5 __ 9

to convert 89°F to an equivalent

temperature in degrees Celsius. Round to

the nearest whole number.

A 18°C

B 32°C

C 49°CD 71°C

42 Derek’s father drove for 5 hours at an average speed of 55 miles per hour. Derek’s mother drove for 4 hours at an average speed of 65 miles per hour. Who drove a greater distance, and how much farther did he or she drive?

F Derek’s father; 10 miles farther

G Derek’s father; 15 miles farther

H Derek’s mother; 10 miles fartherJ Derek’s mother; 15 miles farther

Tim, Ann, Beth, and Zak went bowling. The following chart shows their scores for the first five frames. Use the chart for Exercises 43–44.

Tim Ann Beth Zak9 8 7 65 8 8 66 8 9 83 8 8 99 8 7 9

43 If the bowling score data were represented in a frequency table, what would be the frequency for a score of 9?

A 4

B 5

C 6 D 7

44 If the data were represented in a frequency table, which of the following woiuld be the best choice of a data display for the data in the frequency table?

F scatter plot

G histogram

H circle graph

J line graph

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45 A rectangular box has dimensions 31 cm, 19.5 cm, and 15.2 cm. Julia rounds each dimension to the nearest whole centimeter and estimates that the volume of the box is about 9000 cm3. Which statement is true?

A Her estimate is greater than than the actual volume.

B Her estimate is less than than the actual volume.

C Her estimate is off by about 1000 cubic centimeters.

D Her estimate is off by about 500 cubic centimeters.

46 Bob drew a circle and measured its circumference and diameter using a piece of string and a ruler. About how many times as long as the diameter was the circumference?

F 31.4 times as long

G 3.14 times as long

H 3.41 times as long

J Not enough information given.

47 The diameter of a wheel on a toy train is 10.2 centimeters. Estimate how far the wheel travels along a straight wooden track if it makes 5 complete turns.

A about 30 centimeters

B about 50 centimeters

C about 150 centimeters

D about 300 centimeters

48 The base of a triangular sail is 4 feet long, and its height is 15 feet. What is the area of the sail?

F 15 square feet

G 30 square feet

H 38 square feet

J 60 square feet

49 The baseball coach keeps track of his players’ at bats and hits. Use the chart to determine who had the greatest percent chance of getting a hit.

Player Batting Statistics

A Barry

B Ken

C Pete

D Jose

50 What is the approximate circumference of the circular pool?

18 ft

F 9 feet H 113 feet

G 57 feet J 314 feet

51 Subtract: 4 __ 5 - 3 __

8 .

A 7 __ 8

B 1 __ 3

C 17 ___ 40

D 7 ___ 20

Player Hits At BatsBarry 16 55Ken 22 59Pete 19 62Jose 33 80

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52 Which point is NOT the same distance from the origin as (-3, 4)?

F (3, -4)

G (-3, -4)

H (3, 4)

J (-3, 0)

53 What is the y-coordinate of the ordered pair (1, -2)?

A -2

B -1

C 0

D 1

54 Louisa randomly pulls one block from the box. Without putting the first block back, she draws another block. What is the probability that the first block is white and the second block is gray?

F 2 ___ 33

H 1 __ 6

G 1 ___ 18

J 1 __ 3

55 A bag contains 5 orange, 4 green, and 6 red marbles. Two marbles are pulled at random from the bag. How many different outcomes are in the sample space for this experiment?

A 1

B 3

C 6

D 12

56 In the figure below, which of the following segments is NOT a chord of the circle?

E

BC

DF

F _

FD

G _

CD

H _

ED

J _

EF

57 Which two ratios are equal to 2:8?

A 4:1 and 8:2

B 1: 4 and 3:12

C 4:16 and 8:34

D 3:12 and 8:2

58 Which shows the following numbers in order from greatest to least?

0.001, -0.01, -0.11, -0.101, 1.01, -1.11

F -1.11, -0.11, -0.101, -0.01, 0.001, 1.01

G -1.11, 1.01, -0.11, -0.101, -0.01, 0.001

H 1.01, 0.001, -0.01, -0.101, -0.11, -1.11

J 1.01, 0.001, -1.11, -0.11, -0.101, -0.01

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59 There are 11 lunch tables and 132 students at a middle school. What is the ratio of lunch tables to students?

A 1 to 11

B 1 to 12

C 11 to 12

D 11 to 13

60 Jolie has a total of 8 reptiles in her aquarium. Exactly 6 of the reptiles are lizards. What percent of the reptiles in the aquarium are lizards?

F 48%

G 60%

H 68%

J 75%

61 During a go-cart race, DeWayne passed 3 out of the 12 other cars in the race. What percent of cars did DeWayne pass?

A 25%

B 30%

C 40%

D 45%

62 Catherine bikes 3.5 miles to work each day in 25 minutes. If she bikes at the same speed, how long will it take her to bike 14 miles?

F 100 minutes

G 196 minutes

H 4 hours

J 10 hours

63 What is the area of this shape?

2 4 6O x

y

2

4

6

A 11 square units

B 12 square units

C 14 square units

D 18 square units

64 Which of the following shows the mixed numbers in order from least to greatest?

F 3 1 __ 3 , 3 2 __

5 , 3 3 __

7 , 3 7 __

9

G 3 1 __ 3 , 3 7 __

9 , 3 2 __

5 , 3 3 __

7

H 3 2 __ 5 , 3 7 __

9 , 3 3 __

7 , 3 1 __

3

J 3 3 __ 7 , 3 2 __

5 , 3 1 __

3 , 3 7 __

9

65 Alejandro has read 102 pages. Milo has read 103 pages. How many more pages has Milo read than Alejandro?

A 1,100

B 1,000

C 900

D 90

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66 What is the solution of the equation?

72 = 18 + 9n

F n = 6

G n = 8

H n = 10

J n = 54

67 The population of Nevada in 2005 was reported to be 2,241,154. Nevada covers about 110,000 square miles in area. On average, about how many people live per square mile?

A 20 C 200

B 40 D 400

68 What is the decimal equivalent or an approximation to the nearest hundredth

for 5 ___ 12

?

F 2.4 H 0.24

G 0.42 J 0.125

69 Vera’s mother is 40 years old, which is 5 less than 3 times Vera’s age. Which equation could represent this sentence?

A 40 = 5v – 3

B 40 = 3v – 5

C v = 40 + 3v – 5

D 3v + 5 = 40

70 Find the area of the triangle below.

24 cm

15 cm

F 39 cm H 240 cm

G 180 cm J 360 cm

71 The table shows the cost of different sized boxes of pancake mix available at a grocery store. Which brand of pancake mix is the BEST buy?

Brand Size (ounces) Price

A 12 ounces $1.89

B 18 ounces $2.37

C 24 ounces $2.65

D 54 ounces $6.99

A Brand A C Brand C

B Brand B D Brand D

72 Marie has 3 different colored blouses, and 2 different colored vests. One of the blouses is blue and one of the vests is blue. If she randomly chooses a blouse and vest combination, what is the probability that she chooses the blue blouse and blue vest?

F 1 __ 6 H 1 __

5

G 1 __ 3 J 1 __

2

73 At a bakery, 1 __ 3 of the bagels served on

Saturday were raisin bagels, and 4 __ 5

of

these raisin bagels were served with cream cheese. What fraction of the bagels served on that Saturday were raisin bagels with cream cheese?

A 4 ___ 15

C 12 ___ 15

B 5 ___ 15

D 17 ___ 15

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74 What is the quotient?

3 __ 28

÷ 4 __ 7

F 3 ___ 49

G 3 ___ 16

H 19 ___ 28

J 3 __ 4

75 Which measurement is equivalent to 3.2 liters?

A 0.32 milliliters

B 32 milliliters

C 332 milliliters

D 3,320 milliliters

76 What is the value of q in the following equation?

q __

4 - 3 = 9

F 3 H 16

G 8 J 48


77 Every morning Ian jogs exactly four times around a circular reservoir. The total distance he jogs is 5 kilometers. Find the diameter of the reservoir to the nearest hundredth of a kilometer.

78 The table shows how many goals Alvin scored in 8 soccer games.

2

Gam

e 1

0

Gam

e 2

1

Gam

e 3

2

Gam

e 4

1

Gam

e 5

2

Gam

e 6

2

Gam

e 7

2

Gam

e 8

What is the mode of this list of numbers?

79 What is the value of the following expression?

3 + 6 × 4 - (5 - 2)2

80 The radius of a circle is 14 inches. What is the diameter of the circle?

81 While in France, Paulo rented a car that uses the metric system. When he bought gasoline for the car, what unit of measurement was used?

82 At a bakery, one cookie costs $.38. Caroline estimates that a dozen cookies will cost $3.80. Is this a reasonable estimate? If not, what is a better estimate of the cost? Justify your answer.

83 Write the whole number that has the digit 7 in the trillions, millions, and tens places, and the digit 0 in every other place.

84 A map has a scale of 1 inch =

3 kilometers. What is the actual distance

from Lampley to Valleyville if the distance

on the map is 4 inches?

85 Ramon spent $110.20 on some new clothes. The amount he spent was 40% of the amount he had in his wallet. How much did he have in his wallet?

86 A store offers a 20% discount on T-shirts. The amount Christine paid for a T-shirt after the discount was applied was $12. What was the amount of the discount on the T-shirt Christine bought?

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87 Oliver has a cube with the numbers 1 through 6 on its faces. What are all of the possible outcomes of rolling the cube two times in a row?

88 Plot the points (-3, 2) and (4, -1) on the coordinate grid below.

10

10O x

210

210

y

89 Plot the numbers 3 __ 4 and – 1 __

2 on a number

line.

90 Randy mixes 1 __ 8 pound of walnuts,

1 __ 2 pound of pecans, and 1 __

4 cup of

almonds. Write and solve a mathematical

equation that gives the total weight of the

mixed nuts.

91 One milliliter of water fits exactly inside one cubic centimeter of space. How many millimeters of water will fit inside the rectangular prism? How many liters of water will fit inside the prism?

92 A random survey of 100 people before a town election showed that 45 people were planning to vote for Smith and 55 were planning to vote for Dreiser. If all 3000 people in town vote for one of the two candidates, how many do you predict will vote for Dreiser? Justify your prediction.

93 Margaret is an architect who is making a plan for her client’s new porch. She drew the figure shown on the grid below. What is the area of the entire figure?

16 ft

.

26 ft.

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94 Allison made a list of the types of books she owns. The table shows the total number of books of each type. Name two different displays you could use to represent the data. Explain your thinking.

95 For a PTA fundraiser, people can buy giftwrap, greeting cards, or both. According to the Venn diagram, how many people bought greeting cards?

greetingcards

giftwrap

15

3529

96 A circle with center O is shown below. Name all the line segments that have

lengths that are exactly 1 __ 2 the length

of segment FJ. If the circumference of the circle is 10 centimeters, what is the length of one of the segments you listed? Round the length to the nearest tenth of a centimeter.

F

G

O

H

J

Type of book Number

Biographies 25

How-to 60

Reference 108

Novels 59

Short Story Anthologies 62

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B1 NY Test Prep Grade 6

Name _________________________________ Date ______________Class ______________

1 Find the sum of 5.8 trillion and 2.3 million. Write the sum in standard form.

A 5,800,000,002,300

B 5,800,002,300,000

C 5,800,000,000,002,300

D 5,802,300,000,000,000

2 Rasheed pulls one marble from the box without looking. Without replacing the first marble, he draws another marble. What is the probability that both marbles are gray?

F 4 ___ 17

G 1 __ 4

H 4 __ 9

J 1 __ 2

3 Which equation is an example of the associative property of multiplication?

A 2 × 5 × 9 = 2 × 9 × 5

B (2 × 5) × 9 = 2 × (5 × 9)

C 2 × 5 × 9 = 90

D (2 × 5) × 9 = 9 × (2 × 5)

4 Two-thirds of the students at Culver Middle School participate in a club or sport. If half of those students are in two or more clubs and sports, what fraction of all students at Culver Middle School participate in two or more clubs or sports?

F 1 __ 6

G 1 __ 3

H 1 __ 2

J 4 __ 3

5 Four students tried to use the distributive property. Only one student used the properly correctly. Which of the following equations is correct?

A 8(10 + n) = 8(10) + n

B 3(2n + 1) = 6n + 3

C 2(9 + n) = 11 + 2n

D 6(2n + 3) = 12n + 3

Sample Test BC

opyr

ight

© H

ough

ton

Miff

lin H

arco

urt P

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hing

Com

pany

.

B1-B14_NY_G6.indd B1B1-B14_NY_G6.indd B1 1/4/10 12:55:53 PM1/4/10 12:55:53 PM


Name _________________________________ Date ______________Class ______________

6 A book store owner wants to know how often people in a town buy books. Which sampling method will be the most representative?

F Survey 1 out of every 10 people who visit the book store on one day.

G Conduct a survey by randomly calling 100 of the town’s citizens.

H Conduct a survey by randomly calling 100 people who have bought books recently at the book store.

J Survey all the people who enter the book store first thing in the morning.

7 Objects on Neptune weigh 1 1 __ 8 times

as much as they weigh on Earth.

How much would a 9 1 __ 3 -lb backpack

weigh on Neptune?

A 10 1 __ 2 lbs

B 10 lbs

C 9 1 ___ 24

lbs

D 8 8 ___ 24

lbs

8 What are all the possible results when you perform an experiment of tossing a coin and then spinning a spinner divided into three equal sections labeled A, B, and C?

F H, T, A, B, C

G HA, TB, HC

H HA, TA, HB, TB, HC, TC

J HH, TT, HT, TH, AB, BC, AC, AA, BB, CC

9 Gino filled a bottle cap with water. He wrote down 6 as an estimate of the amount of water in the bottle cap, but forgot to use units. Which of the following are most likely to be the units he forgot to include?

A liters

B milliliters

C cups

D gallons

10 Which equation illustrates the zero property of multiplication?

F 5 × 0 = 0 × 5

G 5 + 0 = 0 + 5

H 5 × 0 = 5

J 5 × 0 = 0

11 To find the area of a regular hexagon, Paul divided it into two congruent polygons. He measured the lengths shown in the diagram Use Paul’s measurements to find the area of the regular hexagon.

60 cm

30 cm

52 cm

A 2340 cm 2

B 1170 cm 2

C 585 cm 2

D 293 cm 2

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12 At Ted’s sandwich shop, all sandwiches are made with a combination of bread, meat and cheese. There are 3 different choices of bread, 4 different choices of meat, and 2 different choices of cheese. One type of sandwich that can be ordered is beef and swiss on rye bread. If a customer orders a sandwich, what is the probability that it is beef and swiss on rye? Assume that all sandwich combinations are equally likely to be ordered.

F 1 ___ 24

G 1 ___ 12

H 1 __ 4

J 1 __ 3

13 Roberta wants to buy 64 ounces of sour cream. She priced the sour cream at four stores. Which is the BEST buy?

A Store A: 16 ounces for $1.50

B Store B: 32 ounces for $2.74

C Store C: 8 ounces for $0.55

D Store D: 4 ounces for $0.43

14 Dante planted a bean and measured the growth of the bean plant that sprouted from it. After 2 weeks, the bean plant was 3 centimeters tall. After 4 weeks, the bean plant was 6 centimeters tall. Predict the height of the bean plant after 5 weeks.

F 4.5 centimeters

G 7.5 centimeters

H 8 centimeters

J 9 centimeters

15 Kendra paid $48 for a sweater. If she bought it on sale at a 40% discount, what was the original price??

A $19.92

B $28.80

C $67.20

D $80.00

16 The speed limit near Bev’s house is 55 miles per hour. Which table shows the number of miles (m) driven in 1, 2, 3, and 4 hours (h) if a constant speed of 55 miles per hour is maintained?

m = 55h

F h 1 2 3 4

m 55 110 165 220

G m 1 2 3 4

h 25 50 100 150

H h 1 20 3 4

m 55 60 65 70

J h 1 2 3 4

m 55 85 115 145

17 What property does this equation illustrate?

5 × 7 = 7 × 5

A associative property

B commutative property

C identity property

D inverse property

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18 On Friday, 4 __ 6 of Ms. Shiu’s students

will be on a field trip. Which decimal is

equivalent to 4 __ 6 ?

F 0.6

G 0.66

H 0. −

6

J 0.67

19 A park is in the shape of a trapezoid, as shown. Find the area of the park.

0.75 mi

1.5 mi

1 mi0.5 mi

A 0.5625 mi 2

B 0.75 mi 2

C 0.375 mi 2

D 3.75 mi 2

20 Use the order of operations to simplify the expression below.

24 + 2 × (36 ÷ 9) - 5

F 27

G 35

H 56

J 99

21 What is the value of the expression 7k + 11r when k = 2 and r = 1?

A 25

B 29

C 38

D 45

22 Which equation represents the following statement?

3 is 12 less than two times the number n.

F 3 = 12 - 2n

G 3 = 2n - 12

H 3 - 12 = 2n

J 3 = 12(2n)

23 The time it takes to cook a turkey is proportional to its weight. It takes 4 hours to cook a 10 pound turkey. How long will it take to cook a 15 pound turkey?

A 5 hours

B 6 hours

C 7 hours

D 8 hours

24 What is the solution to the equation 9 + 5x = 24?

F x = 2.67

G x = 3

H x = 4.8

J x = 15

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25 The scale on a map is 4 centimeters 5 50 miles. If two cities are 5 centimeters apart on a map, what is the actual distance between the cities?

A 45 miles

B 55 miles

C 62.5 miles

D 72 miles


⎪-8⎥ + 11 - ⎪-4⎥

F -1

G 7

H 15

J 23

27 Use the formula C = (F -32) • 5 __ 9

to convert 79°F to an equivalent temperature in degrees Celsius. Round to the nearest whole number.

A 26°C

B 44°C

C 47°C

D 85°C

28 The diameter of a wheel on a toy truck is 8.1 centimeters. Estimate how far the wheel travels along a straight line if it makes 4 complete turns.

F about 25 centimeters

G about 50 centimeters

H about 100 centimeters

J about 150 centimeters

29 Which expression is equivalent to 4 8 ?

A 4 • 8

B 8 • 8 • 8 • 8

C 4 • 4 • 4 • 4 • 4 • 4 • 4 • 4

D 4 • 4 • 4 • 4 • 4 • 4 • 4 • 4 • 4

30 What number is the multiplicative inverse of 0.9?

F - 10 ___ 9

G -0.9

H 10 ___ 9

J 1

31 Which of the following numbers CANNOT be written as a proportion?

A 5 __ 7 and 15 ___

27

B 15 ___ 49

and 2 __ 7

C 3 ___ 12

and 15 ___ 60

D 35 ____ 100

and 7 ___ 20

32 At Hatfield Middle School, students can be in band or choir or both. According to the Venn diagram, how many students are in the choir?

ChoirBand

12

2036

F 12

G 20

H 32

J 36

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33 For each of the first three weeks the school store was open, the weekly sales were $85, $95, and $108. For the fourth week, the store’s weekly sales figure was $18 more than the mean of the sales figures for the first three weeks. What was the range of the weekly sales figures for the first four weeks?

A 28

B 29

C 113

D 114

34 What is the y-coordinate of the ordered pair (4, -3)?

F 4

G 2

H 1

J -3

35 Which point on the number line BEST

shows the location of - 1 __ 8

21 2 0 1

A B C D

12

12

A point A

B point B

C point C

D point D

36 Which list shows the numbers in order from least to greatest?

F 0.03, 0.003, -0.03, -0.33

G -0.03, -0.33, 0.003, 0.03

H -0.33, -0.03, 0.003, 0.03

J -0.33, -0.03, 0.03, 0.003

37 A gumball machine contains 5 red gumballs, 7 green gumballs, and 12 yellow gumballs. Two gumballs are dispensed from the machine at random when a quarter is put into the machine. How many different outcomes are possible?

A 3

B 4

C 6

D 9

38 Which would be the most appropriate way to display this data?

Transportationto School

Percent of Students

Bus 65

Car 15

Bike 8

Walk 12

F circle graph

G line graph

H scatterplot

J box-and-whisker plot

39 Kerry’s restaurant bill came to $12.50. If he wants to leave a 15% tip, how much should he leave?

A $1.50

B $1.88

C $2.01

D $2.41

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Name _________________________________ Date ______________Class ______________

40 At a fish counter there are 23 salmon, 12 grouper, and 15 cod. What is the ratio of cod to total number of fish?

F 2 to 3

G 1 to 4

H 3 to 10

J 3 to 2

41 The perimeter of ΔABC is 15 inches. Triangle A'B'C' is a similar triangle with side lengths twice the lengths of the sides of ΔABC. What is the perimeter of ΔA'B'C'?

A

C

B A�

C�

B�

A 15

B 30

C 45

D 60

42 Natasha uses 6 teaspoons of powdered drink mix for every 64 ounces of water. How much mix would be needed for 16 ounces of water?

F 1.5 teaspoons

G 2 teaspoons

H 2.5 teaspoons

J 3 teaspoons

A circle with center at point O is shown below. Use the circle for Exercises 43–45.

SO

R

P

Q

43 Which segment is exactly twice the length of the radius?

A Segment QP

B Segment OP

C Segment RP

D Segment QR

44 Which of the following is NOT a chord?

F Segment QP

G Segment RP

H Segment OQ

J Segment RQ

45 If the radius of the circle is 5 cm and the measure of angle SOR is 45°, what is the area of sector SOR?

A 3.125 cm 2

B 6.25 cm 2

C 9.8125 cm 2

D 78.5 cm 2

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46 Write the number 0.184 as a fraction in simplest form.

F 184 _____ 1000

G 46 ____ 250

H 23 ____ 125

J 23 ____ 100

47 A local newspaper plans to survey a small group of voters in the community to determine if the fire levy is likely to pass. What is this called?

A rounding

B sampling

C experimenting

D probability

48 Ilana’s new puppy was born weighing

7 5 ___ 16

pounds. After four weeks the puppy

had gained 1 7 __ 8 of a pound. How much

did the puppy weigh after four weeks?

F 6 3 ___ 16

pounds

G 7 3 ___ 16

pounds

H 8 3 ___ 16

pounds

J 9 3 ___ 16

pounds

49 What can be said about the product when a rational number is multiplied by one?

A The product is zero.

B The product is the original number.

C The product depends on the original number.

D The product has the opposite sign of the original number.

50 Keith recorded the amount of time he spent on homework each day for a month. If he wants to find the median of the data, which of the following must he find?

F the average amount of time spent

G the middle amount of time spent, when the amounts are ordered from least to greatest

H the amount of time he spent most often

J the difference between the greatest amount of time he spent and the least amount

51 Alan made punch by mixing 8 cups of fruit juice with 6 pints of seltzer and 2 quarts of lemonade. How many gallons of punch did he make?

A 1.5

B 1.75

C 2

D 4

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52 What is the area of this triangular sail in square inches?

8 in.

10 in.

F 10 square inches

G 20 square inches

H 30 square inches

J 40 square inches

53 Evaluate 6 2 + 4 3 + 10 2 .

A 44

B 152

C 200

D 380

54 What is the approximate circumference of a bicycle tire that has a radius of 11 inches?

r � 11 in.

F 34 inches

G 50 inches

H 69 inches

J 76 inches

55 Write b • b • b • b • b • b • b • b using an exponent.

A b 6

B b 7

C b 8

D b 9

56 Nicole ate 3 __ 5 of a pizza. Which decimal

value is equivalent to this fraction?

F 0.3

G 0.4

H 0.6

J 0.8

57 On a typical Saturday, about 60% of the skaters at the town skating rink rent their skates. Last Saturday, 55 people at the skating rink rented skates. About how many people skated last Saturday?

A 33

B 92

C 109

D 115

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58 Mrs. Hanover makes scarves from fleece

fabric. She has 8 1 __ 2 yards of fleece.

Each vest uses 1 1 __ 4 yard of fleece. How

many vests can Mrs. Hanover make?

F 4

G 5

H 6

J 7

59 There were 76 people waiting for baseball tickets. Only 25 people got tickets. Estimate the percent of the people waiting who actually got tickets.

A 26%

B 33%

C 40%

D 50%

60 Walking 10 blocks will consume approximately 80 calories. About how many calories will be consumed if 30 blocks are walked?

F 27 calories

G 90 pages

H 240 calories

J 375 calories

61 Yvonne has already saved $200 for a trip to Alaska. She plans to save an additional $50 each month for the rest of the year. Let m be the number of months left in the year. Which expression describes the total amount of money Yvonne will save for the trip?

A 200 + 50

B 50m

C 200 + m

D 200 + 50m

62 A cabinet is made of two rectangular prisms, as shown. What is the volume of the cabinet?

40 in.

30 in.

34 in.

20 in.50 in.

F 24,000 in. 3

G 34,000 in. 3

H 58,000 in. 3

J 64,000 in. 3

63 Katie drew a circle with diameter 14 inches. She also drew a circle with diameter 12 inches. What is the approximate difference in the areas of the two circles?

A about 22 in. 2

B about 40 in. 2

C about 113 in. 2

D about 154 in. 2

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64 About 92% of the students voted in a recent student council election. Write this number as a fraction in simplest form.

F 23 ___ 25

G 47 ___ 50

H 92 ____ 100

J 9 ___ 10

Use the graph below for Exercises 65 and 66

0

2003

2004

2005

2006

1

2

3

4

5

6

7

8

Year

Pro

fit

(th

ou

san

ds o

f d

ollars

)

65 About how much more did the company make in 2005 than in 2004?

A $1000 C $4000

B $2000 D $6000

66 In which year did the company’s profits increase the most compared to the previous year?

F 2003 H 2005

G 2004 J 2006

67 The low temperatures for the last five years in Oakdale on January 1st have been 38°, 44°, 36°, 48°, and 33°. What has been the mean low temperature over the last five years in Oakdale on January 1st?

A 44° C 38°

B 39.8° D 36°

68 Marlys has 5.5 L of juice. Each of the paper cups she bought will hold 250 mL. How many paper cups can she fill?

F 22

G 23

H 24

J 25

69 Andy wants to solve the equation 21 = 3 + 6m. What step should he take first?

A Add 3 to each side.

B Subtract 3 from each side.

C Multiply each side by 6.

D Divide each side by 6.

70 What is the area of the polygon?

1

100

2345678910

2 3 4 5 6 7 8 9 10 x

y

F 32 square units

G 42 square units

H 50 square units

J 64 square units

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71 You need 0.05 liters of water for a science experiment. How many milliliters is this?

A 5 mL

B 50 mL

C 500 mL

D 5000 mL

72 The bar graph below compares the heights of some tall buildings.

0

100

50

0DCBA

150

Hei

ght (

m)

Building

300

250

200

350

How many buildings are more than 175 meters tall?

F 1 H 3

G 2 J 4

73 Diego’s bill for dinner at Java and Jive was $8.60. How much would he pay altogether if he adds a 15% tip?

A $12.90

B $9.89

C $7.31

D $1.29

74 The temperature is 86°F. What is the temperature in degree Celsius?

( F = 9 __ 5 C + 32)

F 30°C

G 65.6°C

H 97.2°C

J 212.4°C

75 What is the area of a parallelogram that has a side length of 6 centimeters, a base length of 12 centimeters, and a height of 4 centimeters?

12 cm

4 cm 6 cm

A 72 square centimeters

B 48 square centimeters

C 24 square centimeters

D 12 square centimeters

76 According to the graph, about how many students watch fewer than 3 hours of sports per week?

Hours of Television SportsWatched Each Week

05

10152025303540

0 to 2 3 to 5 6 to 8 9 to 11 12 or more

Hours

Num

ber

of S

tude

nts

Girls

Boys

F 7

G 35

H 44

J 52

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77 Nina deposits $7200 in a bank account that pays 3% simple interest. Use the formula I = Prt, where P is the amount deposited, r is the interest rate, and t is the time in years, to find how much interest she earns after 4 years.

78 The table shows the temperatures for a week in Albuquerque. All temperatures are in degrees Fahrenheit.

Mon. Tues. Wed. Thurs. Fri. Sat. Sun.

85 75 90 91 82 89 91

What is the median of these data?

79 What is the value of the following expression?

20 3 + 20 2 - 4(5 × 20)

80 The circumference of a circle is 314 centimeters. What is the approximate diameter?

81 Evaluate: 6 2 __ 3 • (6 4 __

7 + 4).

82 A bag of 36 apples costs $4.32. What is the cost per apple?

83 At North Branch Library, 55% of the 220 books checked out last week were fiction. At South Branch Library, 60% of the 215 books checked out last week were fiction. At which library were a greater number of fiction books checked out?

84 Greg drives 230 miles in 4 hours. At this rate, how far can he drive in 6 hours?

85 Solve 16t + 11 = 43

86 A rectangular box has dimensions dimensions 19.9 cm, 19.7 cm, and 14.8 cm. Amanda rounds each dimension to the nearest whole centimeter and estimates that the volume of the box is about 6,000 cm 3 . Predict whether this estimate is greater than or less than the actual volume. Is it a reasonable estimate? Explain.


87 Demarcus has one quarter. He flips it three times in a row and records the result as one event. List all of the possible outcomes.

88 Plot the points (3, 22) and (24, 24) on the coordinate grid below.

5

5O x

25

25

y

89 Find the quotient: 5 1 __ 3 ÷ 2 1 __

6 .

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90 Maria buys 1 __ 3 yard of red velvet, 7 __

8 yard

of green velvet, and 1 __ 4 yard of white

velvet. Write and solve a mathematical

equation that gives the total yardage of

velvet that Maria bought.

91 Juan rolled a six-sided cube 30 times. He kept track of the results of the rolls in the frequency table shown, but forgot to record the frequencies for the outcomes 5 and 6. He recalls that the frequencies for these two outcomes were equal. If that’s true, what numbers should he record in the table? Explain.

Roll Outcome Frequency

1 3

2 7

3 4

4 6

5 ?

6 ?

92 A store offers a 15% discount on sweatshirts. The amount Josie paid for a sweatshirt after the discount was applied was $24. What was the amount of the discount on the T-shirt Christine bought?

93 What is the area of the parallelogram below?

20 m

6 m 8.5 m

94 A random survey of 100 people before a town election showed that 32 people were planning to vote for Sullivan and 68 were planning to vote for Inman. If all 3600 people in town vote for one of the two candidates, how many do you predict will vote for Inman? Justify your prediction.

95 Write the whole number that has the digit 8 in the trillions, billions, and hundreds places, and the digit 0 in every other place.

96 Plot the numbers - 3 __ 4 and 1 __

2 on a

number line.

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