Final Exam Review - Weeblymrsduprey.weebly.com/uploads/2/3/4/1/23411986/math... · 1 Final Exam...

Name: ________________________ Class: ___________________ Date: __________ ID: A

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Final Exam Review

Multiple ChoiceIdentify the choice that best completes the statement or answers the question.

1. The opposite expression for −2g 2 + 4gh − 3h 2 + 6 isA) −2g 2 + 4gh − 3h 2 + 6 B) 2g 2 + 4gh + 3h 2 + 6 C) 2g 2 − 4gh + 3h 2 − 6 D) −2g 2 − 4gh − 3h 2 − 6

2. Solve the following: 3(2x + 3) = 12.A) x = 0.5 B) x = 1.5 C) x = 2.0 D) x = 3.5

3. Stockbrokers can report money lost or gained in the price of stocks using decimal numbers. In one day, five stocks made the following losses or gains.

Stock A +5.25Stock B –4.38Stock C +0.75Stock D –1.21Stock E –0.52

Determine which choice represents the stocks in order from the one which lost the most to the one which gained the most.A) A, B, C, D, E B) A, C, E, D, B C) B, A, D, C, E D) B, D, E, C, A

4. When this object sits on a table, how many exposed faces does it have?

A) 56 B) 96 C) 100 D) 112

Name: ________________________ ID: A

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Pentagonal tables can be joined together to form larger tables. Use the tables to answer the following question(s).

5. Which statement describes the relationship between the table number and the number of seats at that table?A) The number of people at each table is two more than three times the number of tables. B) The number of people at each table is three more than two times the number of tables. C) The number of people at each table is four times the number of tables plus one. D) The number of people at each table is five times the number of tables.

6. Which linear equation represents the number of people who can be seated at each combination of tables?A) y = 4x + 1 B) y = 6x − 1 C) y = 2x + 3 D) y = 3x + 2

7. Which table of values can be used to represent the number of people that can sit at different table numbers?

A) C)

B) D)

Name: ________________________ ID: A

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Use the figures to answer the following question(s).

8. Following the pattern above, how many dots will Figure 5 contain?A) 10 B) 11 C) 12 D) 13

9. Which equation represents the relationship between the figure number (f) and the number of dots (n) in the figure?A) n = 2f + 5 B) n = 8f − 1 C) f = 7n + 1 D) n = f + 7

10. Which table of values describes the pattern?

A) C)

B) D)

11. Which statement describes the number of dots in each figure?A) The number of dots is four more than two times the figure number. B) The number of dots is seven more than the figure number. C) The number of dots is three more than four times the figure number. D) The number of dots is two more than fives times the figure number.

12. How many dots are in the ninth figure?A) 16 B) 23 C) 64 D) 71

13. Which figure number will have 42 dots?A) 28 B) 35 C) 37 D) 61

14. Which of these numbers is not a perfect square?A) 121 B) 99 C) 64 D) 36

Name: ________________________ ID: A

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15. Add the following polynomials. (2c2 d 2 − 4cd + 4) + (4c2 d 2 + 2cd − 6)A) 6c2 d 2 − 2cd − 2 B) −2c2d 2 − 2cd + 10 C) 4c2 d 2 − 4cd − 6 D) 6c2 d 2 + 2cd + 2

16. Solve 4 f = 11.A) f = 0.28 B) f = 0.36 C) f = 2.5 D) f = 2.75

17. What is the side length of a square with an area of 196 m2?A) 9 m B) 14 m C) 49 m D) 98 m

18. Jag has 4 large bags of popcorn, which he divides among some smaller bags. The smaller bags are 23 of the size of

the large bags. How many smaller bags of popcorn can Jag make?A) 4 B) 6 C) 8 D) 12

19. Solve the following: 34 x − 3.2 = 5.3 − 2x

3 .

A) x = 6 B) x = 8.5 C) x = 17 D) x = 102

20. Which decimal number is equivalent to 38?

A) 0.125 B) 0.250 C) 0.375 D) 0.500

21. Which division expression do the algebra tiles represent?

A) 4x2 + 2x2x + 1 B) 4x2 + 2x

−2x − 1 C) 4x2 + 2x−2x + 1 D) 4x2 + 2x

2x − 1

22. What is 8t − 2 = 5t + 7?A) t = 0.69 B) t = 1.67 C) t = 2 D) t = 3

Name: ________________________ ID: A

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23. Determine the surface area of the rectangular prism.

A) 960 units2 B) 128 units2 C) 44 units2 D) 40 units2

24. Expand −3y

4y + 1

using the distributive property.

A) −7y2 − 3y B) −12y2 − 3y C) −7y + 1 D) −12y − 1

25. Evaluate (–5.2) + 3.6 ÷ 0.5.A) –0.32 B) –3.2 C) 2.0 D) 17.6

26. Evaluate 70.A) 0 B) 1 C) 7 D) 70

27. In the figure shown below, the hole in the front surface extends straight through the object. The total surface area of the figure is

A) 82.15 cm2 B) 88.43 cm2 C) 97.85 cm2 D) 99.42 cm2

Name: ________________________ ID: A

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28. Which linear relation is represented by the following graph?

A) y = −2x + 7 B) y = −2x + 3.5 C) y = 7x − 2 D) y = 2x − 7

29. Determine the simplified form of the expression (3xy)(2x).A) 6xy B) 5x2 y C) 6x2 y D) 1.5xy2

30. Order the rational numbers in descending order.

1 38 , −3 1

3 , 1 1516 , −1 10

11

A) −3 13 , −1 10

11 , 1 1516 , 1 3

8 B) 1 1516 , 1 3

8 , −1 1011 , −3 1

3 C) 1 38 ,−3 1

3 , −1 1011 , 1 15

16 D) 1 38 , 1 15

16 , −1 1011 , −3 1

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31. What is the area of the triangle shown below?

A) 3x B) 3x2 C) 6x2 D) 12x2

Name: ________________________ ID: A

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32. What is the measure of ∠AEB in the figure below?

A) 30° B) 60° C) 90° D) 120°

33. Simplify the following expression by grouping like terms. 5k − 4 − 2k 2 − 2k + k 3 − 3k 2 − 2k 3 + 2 + 3k 3 − 4k + 5 + k 2 A) 6k 3 − 6k 2 + 11k − 11 B) 2k 3 − 4k 2 − k + 3 C) −5k 2 − k − 1 D) k 3 − k 2 − k + 1

Name: ________________________ ID: A

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34. Which graph represents the equation y = −x + 6?

A) C)

B) D)

35. If the volume of the rectangular prism below is 36x3 cubic units, what is the missing dimension?

A) 3x B) 28x C) 3x2 D) 28x3

36. What is the opposite expression for −3a 2 + 5a − 6?A) 3a 2 − 5a + 6 B) −3a 2 − 5a − 6 C) 3a 2 + 5a − 6 D) 3a 2 + 5a + 6

37. What is the solution to the inequality 8 − 3x < 5?A) x > 1 B) x < 1 C) x < −1 D) x > −1

Name: ________________________ ID: A

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38. Combine the like terms in 2pq + 2p 2 q + 3p 2 q − 4pq − 3pq + 7 − 5. The answer isA) 2pq + 5p 2 q − 7pq + 2 B) 5pq 2 + 5pq + 2 C) 5p 2 q − 5pq − 2 D) 5p 2 q − 5pq + 2

39. What is the volume of this rectangular prism?

A) 24 B) −24x C) −24x2 D) 24x3

40. Evaluate 34 − 1

5 − 310 .

A) 15 B) 1

4 C) 310 D) 7

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41. Compare the surface area of Block B to that of Block C. Which statement is correct?

A) The surface area of Block B is equal to that of Block C B) The surface area of Block B is greater than that of Block C C) The surface area of Block C is greater than that of Block B D) The surface area of Blocks B and C cannot be determined

42. Subtract the following polynomials and combine like terms. (3m2 − 4mn + 5) − (m2 − 7mn − 2)A) 2m2 + 3mn + 3 B) 2m2 + 3mn + 7 C) 2m2 − 11mn + 3 D) 2m2 − 11mn + 7

43. Solve the following: 12 − 1.7 v = 4.15.A) v = –16.15 B) v = 2.89 C) v = 4.62 D) v = 9.5

44. When you combine the like terms in 3a 2 − 2a − 4a 2 − 3 + 5 − 3a, the result isA) 3a 2 − 3a + 2 B) −a 2 − 5a + 2 C) a 2 − 7a + 2 D) 7a 2 − 5a + 3

Name: ________________________ ID: A

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45. Which table of values represents a vertical line?

A) C)

B) D)

46. Simplify by combining like terms. (6w2 − 4w + 2) + (2w2 + 6w + 3) − (4w2 − w − 6) − (3w − 3w2 + 7)A) 7w2 − 2w + 4 B) w2 + 6w + 18 C) w2 + 6w + 4 D) 9w2 − 2w + 2

47. What equation is modelled below?

A) 3 + 7x = 16 B) 3x + 7 = 16 C) 3x + 2 = 3 D) 10x = 16

48. Which multiplication statement is represented by the area model below?

A) 3x 4x + 2 = 12x2 + 6x B) 3x 4x − 2 = 12x2 − 6x C) 3x 4x + 2 = 7x + 2 D) 3x 4x − 2 = 7x − 2

Name: ________________________ ID: A

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49. Which table of values represents the linear equation y = x?

A) C)

B) D)

50. Solve 4x = 3 + 2x.A) x = 1.5 B) x = 2 C) x = 3 D) x = 6

51. Solve the following: 5s + 4 = 22.A) s = 2.4 B) s = 3.6 C) s = 18 D) s = 22

52. Evaluate 49 + 1

6 × 23 .

A) 59 B) 11

18 C) 79 D) 5

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53. Solve 10.85a = 3.5.

A) a = 0.31 B) a = 0.323 C) a = 3.1 D) a = 37.975

54. Which diagram represents the power 43?

A) B) C) D)

55. Subtract the following polynomials. (7j 2 − 2j) − (−4j + 5)A) 7j 2 + 4j − 5 B) 7j 2 + 2j − 5 C) 7j 2 − 2j − 5 D) 7j 2 + 6j + 5

Name: ________________________ ID: A

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56. What rational number does the point B on the number line represent?

A) –3.2 B) –0.8 C) 0.8 D) 4.5

57. A theatre has 15 seats in the first row, 20 seats in the send row, 25 seats in the third row, and so on. Which graph represents this situation?

A) C)

B) D)

58. Express 72 × 76 as a single power.A) 72 B) 74 C) 78 D) 712

59. Simplify the following expression by grouping like terms. 8q − 2q 2 + 3q − 6 + 5q 2 − 4q + 4 + 3q 2 − 2 − 2q A) 10q 2 − 15q − 8 B) 3q 2 + 11q − 8 C) 10q 2 + 17q − 12 D) 6q 2 + 5q − 4

Name: ________________________ ID: A

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60. Determine a verbal representation of 3.4 ≤ r < 8.2.A) All numbers greater than or equal to 3.4 but less than 8.2. B) All numbers greater than or equal to 8.2 but less than 3.4. C) All numbers less than or equal to 3.4 but greater than 8.2. D) All numbers less than or equal to 8.2 but greater than 3.4.

61. Solve x1.8 ≥ −2.

A) x ≤ −3.6 B) x ≥ 3.6 C) x ≤ 3.6 D) x ≥ −3.6

62. Which of these numbers is a perfect square?A) 68 B) 92 C) 186 D) 225

63. Which number line represents the statement, “The puppy weighed less than 1.5 kg”?

A) B)

C) D)

64. A rectangle has an area of 18x2 m2 and a length of 3x m. What is the width of the rectangle?A) 6 B) 6x C) 54x D) 6x2

65. The degree of the term 3p 4q 3 r2 is A) 2 B) 3 C) 7 D) 9

66. Jory makes a flower garden as shown below. What is the area of this garden?

A) 4 units2 B) 27 units2 C) 44 units2 D) 324 units2

67. What is the result of 19 + 1

4 + 712?

A) 1718 B) 11

12 C) 89 D) 31

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68. Use the distributive property to expand 5.2x −3x + 2 .A) 15.6x2 − 10.4x B) 15.6x2 + 10.4x C) −15.6x2 + 10.4x D) −15.6x + 10.4

Name: ________________________ ID: A

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69. Determine the missing dimension of the rectangle.

A) x − 4 B) x + 4 C) x2 + 4 D) x2 − 4

70. Solve k−3 > 5.2.

A) k > 15.6 B) k < 15.6 C) k < −15.6 D) k > −15.6

71. If a colony of 1000 bacteria doubles in size every 2 h, what is the size of the colony after 6 h?A) 2000 B) 6000 C) 8000 D) 64 000

72. Solve t − 3.2 ≤ 5.6.A) t ≤ 2.4 B) t ≥ 8.8 C) t ≤ 8.8 D) t ≥ 2.4

73. The degree of the polynomial 5m4 + 2m3 − m2 + 3m + 7 is A) 2 B) 3 C) 4 D) 10

74. Expand the expression 34 x

8x + 4 using the distributive property.

A) 6x + 3 B) 8 34

x + 4 3

4 C) 6x2 + 3x D) 8 34

x2 + 4 3

4

x

75. Evaluate 57

53 .

A) 3125 B) 625 C) 125 D) 25

76. Which population would you use if you were asking: “Are Canadian voters supportive of the Prime Minister?”A) a sample from the voting-age population of Canada B) the entire population of Canada C) all the people who voted in the last federal election D) all adults between 21 and 65 years

77. Mike has taken four tests. His scores are 77%, 67%, 77%, and 97%. Mike has the choice of taking any measure of central tendency as his overall grade. Which of these measures will give Mike the highest overall grade?A) mode B) median C) mean D) they are all the same

Name: ________________________ ID: A

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CompletionComplete each statement.

78. The linear equation that represents this table of values is ________________________.

x y0 41 32 24 0

79. The division statement modelled by the algebra tiles shown below is _________________________.

80. 243 expressed as a power with base 3 is _________________________.

81. A comparison between the actual size of an object and the size of its diagram is the _________________________.

82. Brandon started to solve the equation below as follows:

3y(y − 2) = 9

3y2 − 6y = 9

Brandon used the _________________________.

83. Subtract the following polynomials. (2n + 5) − (−3n − 2)

84. The enlargement of an image is 3 times the size of the original. The value 3 represents the _________________________.

Name: ________________________ ID: A

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85. The base of the cylinder has an area of 7r square units. The height of the cylinder is _________________________.

86. The inequality symbol is reversed when you multiply or divide by a ___________________________ number.

87. Simplify the following by combining like terms.2b + 3 − 3b + 2 + 5b − 1

88. A figures that has all sides and all angles equal is a _________________________.

89. Any base raised to the exponent of zero equals _________________________.

90. 9 × 9 × 9 × 9 × 9 × 9 × 9 × 9 expressed as a power is _________________________.

91. The number line below represents the inequality _________________________.

92. When multiplying powers with the same base, keep the base the same and _________________________ the exponents.

93. Figures that have 3 or more equal corresponding angles and 3 or more proportional corresponding sides are _________________________.

94. To simplify a power of a power, such as 32

3, keep the base the same and _________________________ the

exponents.

95. The quotient of 4.8t2 − 7.2t + 242.4 is _________________________.

96. The next value in the number pattern 24, 21, 18, 15, ... is ________________________.

97. The number line below represents the inequality _________________________.

98. Simplify the following by combining like terms.2w2 − 2w + 4 + 3w2 + 3w − 9

99. Theoretical probability is calculated as _________________________.

Name: ________________________ ID: A

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100. Simplify the following by combining like terms.−5 − 3p2 − 4p + 4 + 5p2 − 2p

101. The total area of the figure, in simplified form, is _________________________.

Matching

Identify the letter of the term that best matches the description, definition, or example given below. Each term may be used more than once or not at all.

A) algebraic expression D) polynomialB) distributive property E) termC) like terms F) variable

102. a number or a variable, or the product of numbers and variables 103. a quantity whose value can change or vary 104. a(x + y) = ax + ay 105. a mathematical phrase made up of numbers and variables, connected by addition or subtraction operators 106. terms that have identical variables

Match the correct term to each of the following descriptions. A term may be used more than once or not at all.

A) variable D) interpolateB) linear relation E) extrapolateC) linear equation F) coefficient

107. a relation that appears as a straight line when graphed 108. an equation whose graph is a straight line 109. to estimate a value between two given values 110. a symbol (usually a letter) in mathematical expressions and equations 111. to estimate a value beyond a set of given values

Name: ________________________ ID: A

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Identify the letter of the term that best matches the description or definition below. A term may be used more than once or not at all.

A) boundary point D) inequalityB) closed circle E) open circleC) graphical solution F) solution

112. a value or values that satisfy an inequality 113. shows the boundary point is included in the solution 114. a mathematical statement comparing expressions that may not be equal 115. shows the boundary point is not included in the solution 116. separates the values that are less than from the values that are greater than a specified value

Identify the letter of the inequality that best matches each number line shown. A solution may be used more than once or not at all.

A) x > −2 D) x > 3B) x ≤ −2 E) x ≤ 3C) x ≥ 3 F) x < 3

117.

118.

119.

120.

121.

Match each numerical solution to the appropriate expression. A solution may be used more than once or not at all..

A) –6.6 D) 2.53B) 1.4 E) 53.3C) 2.6 F) –8.4

122. 9.6 + 3.4 × 8.2 ÷ 2 123. −6.1 − 1.5 ÷ 3 124. 3.5 × −2.4

125. A rational number equivalent to 2 35

Name: ________________________ ID: A

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126. 1.96

Choose the term that best matches the description below. A term may be used more than once or not at all.

A) bias E) privacyB) cost F) time and timingC) cultural sensitivity G) use of languageD) ethics

127. The period during which the survey is conducted influences the responses. 128. Responses are not kept confidential or respondents do not have the right to refuse to answer. 129. Survey questions refer to an inappropriate topic or behaviour. 130. The expense of the survey is greater than the benefits obtained. 131. The wording of the question is not clear. 132. Survey questions show a preference or favour a specific answer.

Match the correct term to each of the following descriptions.A term may be used more than once or not at all.

A) base D) powerB) exponent E) standard formC) exponential form F) scientific notation

133. represents the number of times you multiply a number by itself 134. refers to an expression such as 52 or 24 135. used to represent 2 × 2 × 2 × 2 as 24

136. the number 5 in the expression 51

137. the number 2 in the expression 52

Match the correct term to each of the following definitions, descriptions, or explanations. A term may be used more than once or not at all.

A) arc E) inscribed angleB) bisector F) subtendedC) central angle G) tangentD) chord H) tangent-chord

138. an angle with the vertex and endpoints on the circle 139. an angle formed by two radii of a circle 140. a line that touches a circle at exactly one point 141. a portion of the circumference of a circle 142. a line segment with both endpoints on a circle

Name: ________________________ ID: A

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A) binomial D) polynomialB) monomial E) trinomialC) opposite expressions

143. the specific name for an expression with one term 144. an algebraic expression made up of terms connected by operations of addition and/or subtraction 145. two expressions that add to zero 146. the specific name for an expression with three terms

Identify the letter of the term that best matches the description or definition given below. Each term may be used more than once or not at all.

A) enlargement D) reductionB) proportion E) scale factorC) ratio

147. a decrease in the dimensions of an object by a constant factor 148. an increase in the dimensions of an object by a constant factor 149. a relationship that shows two ratios are equal 150. the constant factor by which all dimensions of an object are enlarged or reduced in a scale drawing

Identify the letter of the term that is equivalent to the expression below. Each term may be used more than once or not at all.

A) −4x D) 4x2

B) −4x − 8 E) 5x2 − 4xC) −6.2x2 F) 8x2 + 12x

151. 15x2 − 12x3

152. −8x2

2x 153. 4x 2x + 3

154. x + 2 −4x

x 155. 3.1x −2x


A) angle of rotation D) mirror lineB) centre of rotation E) order of rotationC) line of symmetry F) rotation symmetry

156. the number of times a shape or design fits onto itself in one turn 157. a figure may have one or more of these, or it may have none at all

Name: ________________________ ID: A

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158. the point about which the rotation of an object or design turns 159. the minimum number of degrees or fractions of a turn needed to turn a shape or design onto itself 160. occurs when a shape or design can be turned about its centre of rotation so that it fits onto its outline more than once

in a complete turn

Match the correct term to each of the following descriptions. A term may be used more than once or not at all..

A) square root D) non-perfect square B) rational number E) mixed number C) perfect square F) improper fraction

161. a rational number that cannot be expressed as the product of two equal rational factors 162. a factor that multiplies by itself to give that number

163. a fraction such as 113

164. a fraction such as 3 23

165. a number of the form ab , where a and b are integers and b ≠ 0

Choose the term that best matches the description below. A term may be used more than once or not at all.

A) convenience sample E) stratified sampleB) population F) systematic sampleC) random sample G) voluntary response sampleD) sample

166. a sample created by splitting the population into groups and randomly selecting a proportionate number of respondents from each group

167. a sample created by inviting the entire population to respond 168. any sample created where the selected individuals have an equal chance of being picked 169. a group of individuals selected from the population 170. a sample created by selecting respondents at set intervals from an ordered list of the entire population 171. a sample created by picking respondents who are easy to access


A) constant D) numerical coefficientB) distributive property E) termC) equation F) variable

172. a term that does not change 173. the number value in a term 174. a statement in which two mathematical expressions have the same value 175. a symbol in a mathematical expression 176. a number or variable, or the product of numbers and variables

Name: ________________________ ID: A

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Identify the letter of the term that is equivalent to the expression below. Each term may be used more than once or not at all.

A) 4x – 1 D) 36x2 – 12B) 4x2 E) 4x2 – xC) 12x – 12

177. 16x2 − 4x4x

178. 3x(12x – 4)

179. 24x3 − 6x2

6x

180. 12x3 − 3x2

3x2

181. (2x)(2x)

Match the correct term to each of the following definitions, descriptions, or explanations. A term may be used more than once or not at all.

A) central angle D) perpendicular bisectorB) chord E) point of tangencyC) inscribed angles F) tangent

182. an angle which has its vertex at the centre of a circle and its end points on the circumference of the circle 183. a line that passes through the midpoint of a line segment at 90° 184. the point where the tangent of a circle touches the circle 185. congruent angles that are subtended by the same arc and have their vertices on the circle 186. angles formed by two chords that share a common end point

Match the correct answer to the expression in each question. An answer may be used more than once or not at all.

A) 76 D) 140B) 43 E) 134C) 34 F) 9

187. 33 ÷ 33 ÷ 9

188. 36 ÷ 32

189. 77

7

190. 22

3

191. 6 + (43 × 2)

Name: ________________________ ID: A

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A) denominator E) opposite operationB) dividend F) productC) expression G) quotientD) numerator

192. the number of equal parts of a whole to be considered 193. the result of a division operation 194. can be referred to as an inverse operation 195. the result of a multiplication operation 196. a general term that can consist of numbers, variables, and operations 197. the number of equal parts into which the whole is divided


A) algebra D) termB) degree of a term E) variableC) expression

198. in 10p + 7, 10p is an example of this, so is 7 199. a branch of mathematics that uses symbols to represent unknown numbers or quantities 200. a symbol that represents an unknown number 201. the sum of the exponents on the variables in a single term

Short Answer

202. Use an algebra tile model to represent the polynomial 4x2 − 2x − 3.

203. Explain why experimental probability and theoretical probability are not always the same.

204. What is the difference between a sample and a population?

205. Jason made a drawing of his mountain bike. In the drawing, the diameter of the front wheel is 8 cm. The actual size of the front wheel is 60 cm. What scale factor did Jason use in his drawing?

206. Evaluate.a) 4 × (92 + 32 × 2) c) (73 – 33) ÷ 4 – (72 + 30)b) 54 – (83 – 25 × 3) d) 10 × (43 – 62) + 2 × (82 –42)

207. Evaluate.a) 1.69b) 3.61c) 0.09d) 0.36

Name: ________________________ ID: A

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208. Point C is the centre of the circle. a) What is the measure of ∠ADB? Explain your thinking.b) What is the length of chord AD? Justify your answer.

209. Simplify. Show the answer as an expression.

210. Determine the area of a square with each side length below.a) 7 cm c) 420 mm b) 13 m d) 2.5 km

211. Solve and show your work.

4(4.1c − 0.875) = 6(1.8c + 1.75)

212. Apply the distributive property to simplify 2x x − 4 − 3x x − 4 .

213. Given the side lengths below, calculate the volume of each cube.a) 8 cm c) 50 mmb) 14 m d) 0.6 km

Name: ________________________ ID: A

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214. Evaluate each expression. Write your answer in lowest terms.

a) 2 14 × 3 1

3 b) −1 34 + 2 1

6 c) 25 ÷ 1 1

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215. For the following figure, draw and label all lines of symmetry.

216. The scale diagram of a basketball court uses a scale of 1:280. The length of the court measures 10 cm in the diagram. What is the actual length of the court, in metres?

217. What is the difference between x > 3 and x ≥ 3? Show your answer graphically, then, explain your illustrations.

218. Tracy is walking near a motion detector.a) How far was Tracy from the sensor when she began walking?b) Was she walking toward or away from the motion sensor at the time?c) How long did it take her to reach the motion sensor?

Name: ________________________ ID: A

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219. Evaluate.a) 10 × 4 + 63 c) 82 ÷ 4 + 22

b) 5 × 25 – 62 × 2 d) 2 × 53 ÷ (35 – 52)

220. Describe a stratified sampling technique that could be used by the Student’s Council to determine students’ opinions on school safety.

Write your answer in the space provided.

221. Indicate where each number falls on the number line.

a) 0.75 b) − 13 c) 2 4

5 d) –3.5

222. A triangle has side lengths 2x + 1, 2x + 3, and 2x − 2. What values of x give the triangle a perimeter of 44 or more?

223. Evaluate each expression.a) 64 as a power of 2 c) 1296 as a power of 6b) 243 as a power of 3 d) 4096 as a power of 8

Problem

224. A map of a nature reserve shows the location of three look-out points. On the map, the distance between Point A and Point B is 4.5 cm and the distance between Point B and Point C is 6.0 cm. Each centimetre on the map represents 15 km of actual distance. Calculate the actual distance between Point A and Point C.

225. On a test, Laura completes the expression as shown. 43 × 35 = 128

a) Did Laura make a mistake? Justify your thinking.b) If Laura did make a mistake, complete the expression correctly.

Name: ________________________ ID: A

27

226. Kevin explained to Brad that 46 ÷ 42 = 43 .a) Was Kevin’s explanation correct or incorrect? Explain your thinking.b) Evaluate 46 ÷ 42 .

227. Write a simplified expression to describe the perimeter of the figure shown below.

228. Susan charges a flat rate of $20 per night of babysitting. She also charges an extra fee of $3 per hour for every hour she works past 8 p.m. If Susan received $32 for a night of babysitting, how late did she work?

229. The radius of a circle is 90 mm long and passes through the centre of a chord at a distance of 46 mm from the circumference of the circle. What is the length of the chord to the nearest hundredth? Show your thinking.

230. Determine the value of x.

a) 13 = x18 b) x

36 = 19 c) x

28 = 47

d) 15 = 7

x e) 3x = 15

55 f) 535 = x

7

Name: ________________________ ID: A

28

231. a) Reflect the figure over the y-axis. Label the coordinates of the image after the reflection.b) Is the design now symmetrical? Explain your thinking.

232. a) Write a simplified expression representing the perimeter of the figure.

b) If s = 12 m, what is the perimeter of the figure?

Name: ________________________ ID: A

29

233. Ms. Bondar gave her class a quiz worth 30 points. After marking the first 5 quizzes (shaded part of the table), she predicted that most students would not do well. The scores for all 30 students in the class are:

19 18 15 20 18 25 19 24 15 2027 24 22 20 19 13 28 22 24 3022 28 21 24 24 16 17 23 24 28

a) Based on Ms. Bondar’s sample, predict the average mark for the entire class. b) Why does Ms. Bondar’s sample lead her to a false prediction?

234. An observer stands 18.2 m from the door of a house, and 2.6 m from the street. The observer is 1.3 m tall. Calculate the height of the house.

235. A number of people at a public swimming pool are surveyed about raising local taxes to help fund a public swimming pool. a) Identify and explain the bias in this sample.b) Suggest how the bias could be removed.

236. Julia must keep her cell-phone bill below $65 per month. The basic charge is $25 and it costs her $3 per min for long-distance phone calls.a) What inequality can be used to determine how many long-distance minutes Julia can afford?b) How many minutes of long-distance phone calls can Julia make?

237. A rectangular swimming pool has a length that is four times its width. The pool covers an area of 144 m2. What are the dimensions of the pool?

Name: ________________________ ID: A

30

238. Whitney wants to repaint her bird feeder before she rehangs it in the yard. What is the surface area of the feeder? Express your answer to the nearest tenth of a square centimetre.

239. Circle Z has chord XY, which is subtended by inscribed angle ∠XWY and a central angle, ∠XZY. The inscribed angle measures 42°. a) What is the measure of ∠XZY? b) What is the measure of ∠XYZ?

Name: ________________________ ID: A

31

240. A can of waterproofing spray covers 8.1 m2. How many cans of waterproofing spray do you need in order to treat the exterior of walls of the tent, excluding the bottom?

241. A farmer wants to check his corn crop for signs of Ear Rot. Identify each of the following sampling methods the farmer could use.a) Assign a number to each stalk. Randomly select a starting stalk number and then inspect every tenth stalk after it.b) Sample 10% of the stalks closest to the road.c) Divide the crop into sections and randomly select 10% of the stalks in each section.

242. A rectangle’s length is 15 cm greater than its width, w.a) Draw the rectangle and label its dimensions.b) Write and simplify an expression for its perimeter.

243. A garden has the dimensions shown.

a) Determine an expression to represent the area of the garden.b) What is the area of the garden if x = 6 m?

Name: ________________________ ID: A

32

244. Apply a scale factor of 3 to the letter below. Draw your image on the grid provided.

245. A rectangle has a width of s + 2 and a length of 2s + 4. The perimeter of the rectangle is equal to 43.2 cm. What is the length of each side of the rectangle?

246. Calculate the perimeter of the triangle shown.

247. In the figure shown, what is the measure of ∠AFB? Justify your response.

Name: ________________________ ID: A

33

248. Replace each with >, <, or = to make each statement true.

a) 23 0.6 b) 14 0.25 c) 1.52 1 1

2

d) −34 0.75 e) −0.9 − 9

11 f) 0.954 0.946

249. Write an expression to represent this model. What is the opposite expression?

250. In the figure shown, what is the measure of ∠OPS?

ID: A

1

Final Exam ReviewAnswer Section

MULTIPLE CHOICE

1. ANS: C PTS: 1 DIF: Average OBJ: Section 5.3NAT: PR6 TOP: Adding and Subtracting Polynomials KEY: opposite | expression

2. ANS: A PTS: 1 DIF: Easy OBJ: Section 8.3NAT: PR3 TOP: Solving Equations: a(x + b) = c KEY: multi-step equation | division | subtraction | distributive property

3. ANS: D PTS: 1 DIF: Difficult OBJ: Section 2.1NAT: N3 TOP: Comparing and Ordering Rational Numbers KEY: rational numbers | ordering | decimal numbers | money | ascending

4. ANS: B PTS: 1 DIF: Easy OBJ: Section 1.3NAT: SS2 TOP: Surface Area KEY: faces | composite object

5. ANS: A PTS: 1 DIF: Average OBJ: Section 6.1NAT: PR1 TOP: Representing Patterns KEY: describe patterns

6. ANS: D PTS: 1 DIF: Average OBJ: Section 6.1NAT: PR1 TOP: Representing Patterns KEY: equation from description

7. ANS: A PTS: 1 DIF: Easy OBJ: Section 6.1NAT: PR1 TOP: Representing Patterns KEY: table of values

8. ANS: C PTS: 1 DIF: Easy OBJ: Section 6.1NAT: PR1 TOP: Representing Patterns KEY: describe patterns | extend patterns

9. ANS: D PTS: 1 DIF: Difficult OBJ: Section 6.3NAT: PR2 TOP: Graphing Linear Relations KEY: describe patterns | equation from figure

10. ANS: A PTS: 1 DIF: Easy OBJ: Section 6.1NAT: PR1 TOP: Representing Patterns KEY: describe patterns | table of values

11. ANS: B PTS: 1 DIF: Average OBJ: Section 6.1NAT: PR1 TOP: Representing Patterns KEY: describe patterns

12. ANS: A PTS: 1 DIF: Average OBJ: Section 6.1NAT: PR1 TOP: Representing Patterns KEY: substituting values | extend patterns

13. ANS: B PTS: 1 DIF: Average OBJ: Section 6.1NAT: PR1 TOP: Representing Patterns KEY: extend patterns

14. ANS: B PTS: 1 DIF: Easy OBJ: Section 2.4NAT: N5 TOP: Determining Square Roots of Rational NumbersKEY: rational numbers | perfect square

15. ANS: A PTS: 1 DIF: Average OBJ: Section 5.3NAT: PR6 TOP: Adding and Subtracting Polynomials KEY: polynomial | simplify | addition

16. ANS: D PTS: 1 DIF: Easy OBJ: Section 8.1NAT: PR3 TOP: Solving Equations: ax = b, x/a = b, a/x = b KEY: one-step equation | division

17. ANS: B PTS: 1 DIF: Easy OBJ: Section 2.4NAT: N5 TOP: Determining Square Roots of Rational NumbersKEY: rational numbers | perfect square | problem solving | area

ID: A

2

18. ANS: B PTS: 1 DIF: Average OBJ: Section 2.3NAT: N3 TOP: Problem Solving With Rational Numbers in Fraction FormKEY: rational numbers | fraction operations | problem solving

19. ANS: A PTS: 1 DIF: Difficult OBJ: Section 8.4NAT: PR3 TOP: Solving Equations: ax = b + cx, ax + b = cx + d, a(bx + c) = d(ex + f)KEY: multi-step equation | addition | multiplication | division

20. ANS: C PTS: 1 DIF: Average OBJ: Section 2.1NAT: N3 TOP: Comparing and Ordering Rational Numbers KEY: rational numbers | ordering | equivalent fractions | decimal numbers

21. ANS: B PTS: 1 DIF: Average OBJ: Section 7.3NAT: PR7 TOP: Dividing Polynomials by Monomials KEY: dividing a polynomial by a binomial | algebra tiles

22. ANS: D PTS: 1 DIF: Easy OBJ: Section 8.4NAT: PR3 TOP: Solving Equations: ax = b + cx, ax + b = cx + d, a(bx + c) = d(ex + f)KEY: multi-step equation | subtraction | addition | division

23. ANS: B PTS: 1 DIF: Average OBJ: Section 3.3NAT: N4 TOP: Order of Operations KEY: order of operations | problem solving | surface area

24. ANS: B PTS: 1 DIF: Easy OBJ: Section 7.2NAT: PR7 TOP: Multiplying Polynomials by Monomials KEY: multiplying a binomial by a monomial | distributive property | expand

25. ANS: C PTS: 1 DIF: Average OBJ: Section 2.2NAT: N3 | N4 TOP: Problem Solving With Rational Numbers in Decimal FormKEY: rational numbers | decimal numbers | order of operations | add | divide

26. ANS: B PTS: 1 DIF: Easy OBJ: Section 3.2NAT: N2 TOP: Exponent Laws KEY: zero exponent | exponent laws

27. ANS: C PTS: 1 DIF: Difficult OBJ: Section 1.3NAT: SS2 TOP: Surface Area KEY: surface area | composite object

28. ANS: A PTS: 1 DIF: Average OBJ: Section 6.3NAT: PR2 TOP: Graphing Linear Relations KEY: equation from graph

29. ANS: C PTS: 1 DIF: Average OBJ: Section 7.1NAT: PR7 TOP: Multiplying and Dividing Monomials KEY: multiplying monomials | simplify

30. ANS: B PTS: 1 DIF: Average OBJ: Section 2.1NAT: N3 TOP: Comparing and Ordering Rational Numbers KEY: rational numbers | ordering | mixed numbers | descending

31. ANS: C PTS: 1 DIF: Average OBJ: Section 7.1NAT: PR7 TOP: Multiplying and Dividing Monomials KEY: multiplying monomials | area model | area of a triangle

32. ANS: B PTS: 1 DIF: Average OBJ: Section 10.1NAT: SS1 TOP: Exploring Angles in a Circle KEY: central angle | inscribed angle

33. ANS: B PTS: 1 DIF: Difficult+ OBJ: Section 5.2NAT: PR5 TOP: Equivalent Expressions KEY: expression | simplify | like terms

34. ANS: C PTS: 1 DIF: Average OBJ: Section 6.3NAT: PR2 TOP: Graphing Linear Relations KEY: graph from equation

ID: A

3

35. ANS: A PTS: 1 DIF: Difficult+ OBJ: Section 7.1NAT: PR7 TOP: Multiplying and Dividing Monomials KEY: dividing monomials | volume

36. ANS: A PTS: 1 DIF: Average OBJ: Section 5.3NAT: PR6 TOP: Adding and Subtracting Polynomials KEY: opposite | expression

37. ANS: A PTS: 1 DIF: Average OBJ: Section 9.3NAT: PR4 TOP: Solving Multi-Step Inequalities KEY: solve multi-step inequality | division | subtraction | reverse the inequality symbol | multi-step inequality

38. ANS: D PTS: 1 DIF: Difficult OBJ: Section 5.2NAT: PR5 TOP: Equivalent Expressions KEY: like terms | simplify

39. ANS: D PTS: 1 DIF: Difficult+ OBJ: Section 7.1NAT: PR7 TOP: Multiplying and Dividing Monomials KEY: multiplying monomials | volume

40. ANS: B PTS: 1 DIF: Difficult OBJ: Section 2.3NAT: N3 | N4 TOP: Problem Solving With Rational Numbers in Fraction FormKEY: rational numbers | fractions | order of operations | subtract

41. ANS: A PTS: 1 DIF: Average OBJ: Section 1.3NAT: SS2 TOP: Surface Area KEY: surface area | faces | composite object

42. ANS: B PTS: 1 DIF: Average OBJ: Section 5.3NAT: PR6 TOP: Adding and Subtracting Polynomials KEY: polynomial | simplify | subtraction

43. ANS: C PTS: 1 DIF: Average OBJ: Section 8.2NAT: PR3 TOP: Solving Equations: ax + b = c, x/a + b = c KEY: multi-step equation | subtraction | division

44. ANS: B PTS: 1 DIF: Average OBJ: Section 5.2NAT: PR5 TOP: Equivalent Expressions KEY: like terms | simplify

45. ANS: B PTS: 1 DIF: Average OBJ: Section 6.3NAT: PR2 TOP: Graphing Linear Relations KEY: vertical line

46. ANS: A PTS: 1 DIF: Difficult+ OBJ: Section 5.3NAT: PR6 TOP: Adding and Subtracting Polynomials KEY: polynomial | simplify | like terms | addition

47. ANS: B PTS: 1 DIF: Easy OBJ: Section 8.2NAT: PR3 TOP: Solving Equations: ax + b = c, x/a + b = c KEY: multi-step equation | equation model

48. ANS: A PTS: 1 DIF: Easy OBJ: Section 7.2NAT: PR7 TOP: Multiplying Polynomials by Monomials KEY: multiplying a binomial by a monomial | area model

49. ANS: D PTS: 1 DIF: Easy OBJ: Section 6.3NAT: PR2 TOP: Graphing Linear Relations KEY: table of values from equation

50. ANS: A PTS: 1 DIF: Easy OBJ: Section 8.4NAT: PR3 TOP: Solving Equations: ax = b + cx, ax + b = cx + d, a(bx + c) = d(ex + f)KEY: multi-step equation | subtraction | division

51. ANS: B PTS: 1 DIF: Easy OBJ: Section 8.2NAT: PR3 TOP: Solving Equations: ax + b = c, x/a + b = c KEY: multi-step equation | subtraction | division

ID: A

4

52. ANS: A PTS: 1 DIF: Difficult OBJ: Section 2.3NAT: N3 | N4 TOP: Problem Solving With Rational Numbers in Fraction FormKEY: rational numbers | fraction operations | order of operations | add | multiply

53. ANS: C PTS: 1 DIF: Difficult OBJ: Section 8.1NAT: PR3 TOP: Solving Equations: ax = b, x/a = b, a/x = b KEY: multi-step equation | multiplication | division

54. ANS: B PTS: 1 DIF: Average OBJ: Section 3.1NAT: N1 TOP: Using Exponents to Describe Numbers KEY: represent powers | volume of a cube

55. ANS: B PTS: 1 DIF: Average OBJ: Section 5.3NAT: PR6 TOP: Adding and Subtracting Polynomials KEY: polynomial | simplify | subtraction

56. ANS: B PTS: 1 DIF: Easy OBJ: Section 2.1NAT: N3 TOP: Comparing and Ordering Rational Numbers KEY: rational numbers | decimal numbers | comparing

57. ANS: C PTS: 1 DIF: Difficult OBJ: Section 6.3NAT: PR2 TOP: Representing Patterns KEY: graph from description

58. ANS: C PTS: 1 DIF: Average OBJ: Section 3.2NAT: N2 TOP: Exponent Laws KEY: product of powers | exponent laws

59. ANS: D PTS: 1 DIF: Difficult OBJ: Section 5.2NAT: PR5 TOP: Equivalent Expressions KEY: expression | simplify | like terms

60. ANS: A PTS: 1 DIF: Difficult+ OBJ: Section 9.1NAT: PR4 TOP: Representing Inequalities KEY: double inequality | algebraic to verbal

61. ANS: D PTS: 1 DIF: Average OBJ: Section 9.2NAT: PR4 TOP: Solving Single-Step Inequalities KEY: solve single-step inequality | multiplication

62. ANS: D PTS: 1 DIF: Easy OBJ: Section 2.4NAT: N5 TOP: Determining Square Roots of Rational NumbersKEY: rational numbers | perfect square

63. ANS: C PTS: 1 DIF: Easy OBJ: Section 9.1NAT: PR4 TOP: Representing Inequalities KEY: less than | verbal to graphic

64. ANS: B PTS: 1 DIF: Average OBJ: Section 7.1NAT: PR7 TOP: Multiplying and Dividing Monomials KEY: dividing monomials | area model | area of a rectangle

65. ANS: D PTS: 1 DIF: Average OBJ: Section 5.1NAT: PR5 TOP: The Language of Mathematics KEY: term | degree

66. ANS: B PTS: 1 DIF: Easy OBJ: Section 3.3NAT: N4 TOP: Order of Operations KEY: order of operations | area

67. ANS: A PTS: 1 DIF: Difficult OBJ: Section 2.3NAT: N3 | N4 TOP: Problem Solving With Rational Numbers in Fraction FormKEY: rational numbers | fractions | order of operations | add

68. ANS: C PTS: 1 DIF: Average OBJ: Section 7.2NAT: PR7 TOP: Multiplying Polynomials by Monomials KEY: multiplying a binomial by a monomial | distributive property | expand

ID: A

5

69. ANS: B PTS: 1 DIF: Difficult+ OBJ: Section 7.1NAT: PR7 TOP: Multiplying and Dividing Monomials KEY: dividing binomials | area of a square

70. ANS: C PTS: 1 DIF: Average OBJ: Section 9.2NAT: PR4 TOP: Solving Single-Step Inequalities KEY: solve single-step inequality | multiplication | reverse the inequality symbol

71. ANS: C PTS: 1 DIF: Difficult OBJ: Section 3.4NAT: N1 TOP: Using Exponents to Solve Problems KEY: problem solving | population growth

72. ANS: C PTS: 1 DIF: Easy OBJ: Section 9.2NAT: PR4 TOP: Solving Single-Step Inequalities KEY: solve single-step inequality | addition

73. ANS: C PTS: 1 DIF: Average OBJ: Section 5.1NAT: PR5 TOP: The Language of Mathematics KEY: polynomial | degree

74. ANS: C PTS: 1 DIF: Difficult OBJ: Section 7.2NAT: PR7 TOP: Multiplying Polynomials by Monomials KEY: multiplying a binomial by a monomial | distributive property | expand

75. ANS: B PTS: 1 DIF: Average OBJ: Section 3.2NAT: N2 TOP: Exponent Laws KEY: quotient of powers | exponent laws

76. ANS: A PTS: 1 DIF: Difficult OBJ: Section 11.2NAT: SP2 TOP: Collecting Data KEY: identifying a population

77. ANS: C PTS: 1 DIF: Difficult OBJ: Section 11.3NAT: SP4 TOP: Probability in Society KEY: measures of central tendency

COMPLETION

78. ANS: y = −x + 4

PTS: 1 DIF: Average OBJ: Section 6.1 NAT: PR1TOP: Representing Patterns KEY: equation from table of values

79. ANS: 6x2

−3x = −2x

PTS: 1 DIF: Average OBJ: Section 7.1 NAT: PR7TOP: Multiplying and Dividing Monomials KEY: dividing monomials | algebra tiles

80. ANS: 35

PTS: 1 DIF: Average OBJ: Section 3.1 NAT: N1TOP: Using Exponents to Describe Numbers KEY: exponential form

81. ANS: scale

PTS: 1 DIF: Average OBJ: Section 4.2 NAT: SS4TOP: Scale Diagrams KEY: scale | scale diagram

82. ANS: distributive property

PTS: 1 DIF: Average OBJ: Section 8.3 NAT: PR3TOP: Solving Equations: a(x + b) = c KEY: distributive property

ID: A

6

83. ANS: 5n + 7

PTS: 1 DIF: Average OBJ: Section 5.2 NAT: PR6TOP: Equivalent Expressions KEY: subtraction | polynomial

84. ANS: scale factor

PTS: 1 DIF: Average OBJ: Section 4.1 NAT: SS4TOP: Enlargements and Reductions KEY: enlargement | scale factor

85. ANS: 2r2 + 1

PTS: 1 DIF: Average OBJ: Section 7.3 NAT: PR7TOP: Dividing Polynomials by Monomials KEY: dividing a polynomial by a monomial | volume

86. ANS: negative

PTS: 1 DIF: Easy OBJ: Section 9.2 NAT: PR4TOP: Solving Single-Step Inequalities KEY: reverse the inequality symbol

87. ANS: 4b + 4

PTS: 1 DIF: Easy OBJ: Section 5.2 NAT: PR6TOP: Equivalent Expressions KEY: simplify | expression | like terms

88. ANS: regular polygon

PTS: 1 DIF: Average OBJ: Section 4.4 NAT: SS3TOP: Similar Polygons KEY: regular polygon

89. ANS: 1one

PTS: 1 DIF: Average OBJ: Section 3.2 NAT: N2TOP: Exponent Laws KEY: zero exponent

90. ANS: 98

PTS: 1 DIF: Easy OBJ: Section 3.1 NAT: N1TOP: Using Exponents to Describe Numbers KEY: exponential form | repeated multiplication

91. ANS: 0 ≤ x < 4 or x < 4 and x ≥ 0.

PTS: 1 DIF: Difficult OBJ: Section 9.1 NAT: PR4TOP: Representing Inequalities KEY: double inequality | number line | graphic to algebraic

92. ANS: add

PTS: 1 DIF: Easy OBJ: Section 3.2 NAT: N2TOP: Exponent Laws KEY: base | product of powers | exponent laws

ID: A

7

93. ANS: similar polygons

PTS: 1 DIF: Average OBJ: Section 4.4 NAT: SS3TOP: Similar Polygons KEY: corresponding angles | corresponding sides | similar polygons

94. ANS: multiply

PTS: 1 DIF: Easy OBJ: Section 3.2 NAT: N2TOP: Exponent Laws KEY: power of power | exponent laws

95. ANS: 2t2 − 3t + 10

PTS: 1 DIF: Difficult OBJ: Section 7.3 NAT: PR7TOP: Dividing Polynomials by Monomials KEY: dividing a polynomial by a monomial | simplify

96. ANS: 12

PTS: 1 DIF: Easy OBJ: Section 6.1 NAT: PR1TOP: Representing Patterns KEY: extend patterns

97. ANS: x ≥ −4

PTS: 1 DIF: Average OBJ: Section 9.1 NAT: PR4TOP: Representing Inequalities KEY: number line | represent graphically

98. ANS: 5w2 + w − 5

PTS: 1 DIF: Average OBJ: Section 5.2 NAT: PR6TOP: Equivalent Expressions KEY: simplify | expression | like terms

99. ANS: number of successful outcomes

number of possible outcomesnumber of successful outcomes/number of possible outcomes

PTS: 1 DIF: Average OBJ: Section 11.3 NAT: SP4TOP: Probability in Society KEY: theoretical probability

100. ANS: 2p 2 − 6p − 1

PTS: 1 DIF: Average OBJ: Section 5.2 NAT: PR6TOP: Equivalent Expressions KEY: simplify | expression | like terms

101. ANS: 2x2 + 5x

PTS: 1 DIF: Difficult OBJ: Section 7.2 NAT: PR7TOP: Multiplying Polynomials by Monomials KEY: multiplying a polynomial by a monomial | area model

ID: A

8

MATCHING

102. ANS: D PTS: 1 DIF: Easy OBJ: Section 7.1NAT: PR7 TOP: Multiplying and Dividing Monomials KEY: term | simplify

103. ANS: F PTS: 1 DIF: Easy OBJ: Section 7.1NAT: PR7 TOP: Multiplying and Dividing Monomials KEY: variable

104. ANS: B PTS: 1 DIF: Average OBJ: Section 7.2NAT: PR7 TOP: Multiplying Polynomials by Monomials KEY: distributive property

105. ANS: A PTS: 1 DIF: Average OBJ: Section 7.1NAT: PR7 TOP: Multiplying and Dividing Monomials KEY: expression

106. ANS: C PTS: 1 DIF: Easy OBJ: Section 7.1NAT: PR7 TOP: Multiplying and Dividing Monomials KEY: like terms

107. ANS: B PTS: 1 DIF: Easy OBJ: Section 6.1NAT: PR1 TOP: Representing Patterns KEY: linear relation

108. ANS: C PTS: 1 DIF: Easy OBJ: Section 6.1NAT: PR1 TOP: Representing Patterns KEY: linear equation

109. ANS: D PTS: 1 DIF: Average OBJ: Section 6.2NAT: PR2 TOP: Interpreting Graphs KEY: interpolation

110. ANS: A PTS: 1 DIF: Easy OBJ: Section 6.1NAT: PR1 TOP: Representing Patterns KEY: variable

111. ANS: E PTS: 1 DIF: Average OBJ: Section 6.2NAT: PR2 TOP: Interpreting Graphs KEY: extrapolation

112. ANS: F PTS: 1 DIF: Average OBJ: Section 9.2NAT: PR4 TOP: Solving Single-Step Inequalities KEY: solution

113. ANS: B PTS: 1 DIF: Average OBJ: Section 9.1NAT: PR4 TOP: Representing Inequalities KEY: boundary point | closed circle

114. ANS: D PTS: 1 DIF: Easy OBJ: Section 9.1NAT: PR4 TOP: Representing Inequalities KEY: inequality

115. ANS: E PTS: 1 DIF: Average OBJ: Section 9.1NAT: PR4 TOP: Representing Inequalities KEY: boundary point | open circle

116. ANS: A PTS: 1 DIF: Average OBJ: Section 9.1NAT: PR4 TOP: Representing Inequalities KEY: boundary point

117. ANS: D PTS: 1 DIF: Easy OBJ: Section 9.1NAT: PR4 TOP: Representing Inequalities KEY: open circle | number line | graphic to algebraic

118. ANS: B PTS: 1 DIF: Easy OBJ: Section 9.1NAT: PR4 TOP: Representing Inequalities KEY: closed circle | number line | graphic to algebraic

ID: A

9

119. ANS: C PTS: 1 DIF: Easy OBJ: Section 9.1NAT: PR4 TOP: Representing Inequalities KEY: closed circle | number line | graphic to algebraic

120. ANS: A PTS: 1 DIF: Easy OBJ: Section 9.1NAT: PR4 TOP: Representing Inequalities KEY: open circle | number line | graphic to algebraic

121. ANS: E PTS: 1 DIF: Easy OBJ: Section 9.1NAT: PR4 TOP: Representing Inequalities KEY: closed circle | number line | graphic to algebraic

122. ANS: E PTS: 1 DIF: Difficult OBJ: Section 2.2NAT: N3 TOP: Problem Solving With Rational Numbers in Decimal FormKEY: rational numbers | order of operations | add | divide | multiply

123. ANS: A PTS: 1 DIF: Average OBJ: Section 2.2NAT: N3 TOP: Problem Solving With Rational Numbers in Decimal FormKEY: rational numbers | order of operations | divide | subtract

124. ANS: F PTS: 1 DIF: Easy OBJ: Section 2.2NAT: N3 TOP: Problem Solving With Rational Numbers in Decimal FormKEY: rational numbers | decimal numbers | number operations | multiply

125. ANS: C PTS: 1 DIF: Easy OBJ: Section 2.1NAT: N3 TOP: Comparing and Ordering Rational Numbers KEY: rational numbers | decimal | mixed numbers

126. ANS: B PTS: 1 DIF: Easy OBJ: Section 2.4NAT: N6 TOP: Determining Square Roots of Rational NumbersKEY: square root | perfect square

127. ANS: F PTS: 1 DIF: Easy OBJ: Section 11.1NAT: SP1 TOP: Factors Affecting Data Collection KEY: timing

128. ANS: E PTS: 1 DIF: Easy OBJ: Section 11.1NAT: SP1 TOP: Factors Affecting Data Collection KEY: privacy

129. ANS: D PTS: 1 DIF: Average OBJ: Section 11.1NAT: SP1 TOP: Factors Affecting Data Collection KEY: ethics

130. ANS: B PTS: 1 DIF: Easy OBJ: Section 11.1NAT: SP1 TOP: Factors Affecting Data Collection KEY: cost

131. ANS: G PTS: 1 DIF: Average OBJ: Section 11.1NAT: SP1 TOP: Factors Affecting Data Collection KEY: language

132. ANS: A PTS: 1 DIF: Easy OBJ: Section 11.1NAT: SP1 TOP: Factors Affecting Data Collection KEY: bias

133. ANS: B PTS: 1 DIF: Easy OBJ: Section 3.1NAT: N1 TOP: Using Exponents to Describe Numbers KEY: exponent

134. ANS: D PTS: 1 DIF: Average OBJ: Section 3.1NAT: N1 TOP: Using Exponents to Describe Numbers KEY: power | exponential form

ID: A

10

135. ANS: C PTS: 1 DIF: Easy OBJ: Section 3.1NAT: N1 TOP: Using Exponents to Describe Numbers KEY: exponential form | repeated multiplication

136. ANS: A PTS: 1 DIF: Easy OBJ: Section 3.1NAT: N1 TOP: Using Exponents to Describe Numbers KEY: base | exponential form

137. ANS: B PTS: 1 DIF: Easy OBJ: Section 3.1NAT: N1 TOP: Using Exponents to Describe Numbers KEY: exponential form

138. ANS: E PTS: 1 DIF: Average OBJ: Section 10.1NAT: SS1 TOP: Exploring Angles in a Circle KEY: inscribed angle

139. ANS: C PTS: 1 DIF: Average OBJ: Section 10.1NAT: SS1 TOP: Exploring Angles in a Circle KEY: central angle

140. ANS: G PTS: 1 DIF: Easy OBJ: Section 10.1NAT: SS1 TOP: Exploring Angles in a Circle KEY: angle

141. ANS: A PTS: 1 DIF: Easy OBJ: Section 10.1NAT: SS1 TOP: Exploring Angles in a Circle KEY: arc

142. ANS: D PTS: 1 DIF: Easy OBJ: Section 10.1NAT: SS1 TOP: Exploring Angles in a Circle KEY: chord

143. ANS: B PTS: 1 DIF: Easy OBJ: Section 5.1NAT: PR5 TOP: The Language of Mathematics KEY: monomial | expression

144. ANS: D PTS: 1 DIF: Average OBJ: Section 5.1NAT: PR5 TOP: The Language of Mathematics KEY: expression | term | addition | subtraction | polynomial

145. ANS: C PTS: 1 DIF: Average OBJ: Section 5.3NAT: PR6 TOP: Adding and Subtracting Polynomials KEY: opposite | expression

146. ANS: E PTS: 1 DIF: Easy OBJ: Section 5.1NAT: PR5 TOP: The Language of Mathematics KEY: trinomial | expression

147. ANS: D PTS: 1 DIF: Average OBJ: Section 4.1NAT: SS4 TOP: Enlargements and Reductions KEY: reduction | scale factor

148. ANS: A PTS: 1 DIF: Average OBJ: Section 4.1NAT: SS4 TOP: Enlargements and Reductions KEY: enlargement | scale factor

149. ANS: B PTS: 1 DIF: Average OBJ: Section 4.2NAT: SS4 TOP: Scale Diagrams KEY: proportion | ratio

150. ANS: E PTS: 1 DIF: Average OBJ: Section 4.1NAT: SS4 TOP: Enlargements and Reductions KEY: scale factor | scale diagram

151. ANS: E PTS: 1 DIF: Average OBJ: Section 7.3NAT: PR7 TOP: Dividing Polynomials by Monomials KEY: dividing a polynomial by a monomial

152. ANS: A PTS: 1 DIF: Easy OBJ: Section 7.1NAT: PR7 TOP: Multiplying and Dividing Monomials KEY: dividing monomials

ID: A

11

153. ANS: F PTS: 1 DIF: Average OBJ: Section 7.2NAT: PR7 TOP: Multiplying Polynomials by Monomials KEY: multiplying a binomial by a monomial | distributive property

154. ANS: B PTS: 1 DIF: Difficult OBJ: Section 7.2 | Section 7.3NAT: PR7 TOP: Multiplying Polynomials by Monomials | Dividing Polynomials by MonomialsKEY: multiplying a polynomial by a monomial | dividing a polynomial by a monomial | distributive property

155. ANS: C PTS: 1 DIF: Average OBJ: Section 7.1NAT: PR7 TOP: Multiplying Polynomials by Monomials KEY: multiplying monomials

156. ANS: E PTS: 1 DIF: Average OBJ: Section 1.2NAT: SS5 TOP: Rotation Symmetry and Transformations KEY: rotation symmetry | order of rotation

157. ANS: C PTS: 1 DIF: Average OBJ: Section 1.1NAT: SS5 TOP: Line Symmetry KEY: symmetry | line of symmetry

158. ANS: B PTS: 1 DIF: Easy OBJ: Section 1.2NAT: SS5 TOP: Rotation Symmetry and Transformations KEY: rotation symmetry | centre of rotation

159. ANS: A PTS: 1 DIF: Average OBJ: Section 1.2NAT: SS5 TOP: Rotation Symmetry and Transformations KEY: rotation symmetry | angle of rotation

160. ANS: F PTS: 1 DIF: Easy OBJ: Section 1.2NAT: SS5 TOP: Rotation Symmetry and Transformations KEY: symmetry | rotation symmetry

161. ANS: D PTS: 1 DIF: Easy OBJ: Section 2.4NAT: N6 TOP: Determining Square Roots of Rational NumbersKEY: non-perfect square | definition

162. ANS: A PTS: 1 DIF: Average OBJ: Section 2.4NAT: N5 TOP: Determining Square Roots of Rational NumbersKEY: square root | definition

163. ANS: F PTS: 1 DIF: Easy OBJ: Section 2.3NAT: N3 TOP: Problem Solving With Rational Numbers in Fraction FormKEY: improper fraction

164. ANS: E PTS: 1 DIF: Easy OBJ: Section 2.3NAT: N3 TOP: Problem Solving With Rational Numbers in Fraction FormKEY: mixed number

165. ANS: B PTS: 1 DIF: Easy OBJ: Section 2.1NAT: N3 TOP: Problem Solving With Rational Numbers in Decimal FormKEY: rational numbers | definition

166. ANS: E PTS: 1 DIF: Average OBJ: Section 11.2NAT: SP2 TOP: Collecting Data KEY: stratified sample

167. ANS: G PTS: 1 DIF: Average OBJ: Section 11.2NAT: SP2 TOP: Collecting Data KEY: voluntary response sample

168. ANS: C PTS: 1 DIF: Easy OBJ: Section 11.2NAT: SP2 TOP: Collecting Data KEY: random sample

ID: A

12

169. ANS: D PTS: 1 DIF: Easy OBJ: Section 11.2NAT: SP2 TOP: Collecting Data KEY: sample

170. ANS: F PTS: 1 DIF: Average OBJ: Section 11.2NAT: SP2 TOP: Collecting Data KEY: systematic sample

171. ANS: A PTS: 1 DIF: Easy OBJ: Section 11.2NAT: SP2 TOP: Collecting Data KEY: convenience sample

172. ANS: A PTS: 1 DIF: Average OBJ: Section 8.1NAT: PR3 TOP: Solving Equations: ax = b, x/a = b, a/x = b KEY: constant | term

173. ANS: D PTS: 1 DIF: Average OBJ: Section 8.1NAT: PR3 TOP: Solving Equations: ax = b, x/a = b, a/x = b KEY: term | number

174. ANS: C PTS: 1 DIF: Easy OBJ: Section 8.1NAT: PR3 TOP: Solving Equations: ax = b, x/a = b, a/x = b KEY: equation | expression

175. ANS: F PTS: 1 DIF: Easy OBJ: Section 8.1NAT: PR3 TOP: Solving Equations: ax = b, x/a = b, a/x = b KEY: variable | symbol | expression

176. ANS: E PTS: 1 DIF: Average OBJ: Section 8.1NAT: PR3 TOP: Solving Equations: ax = b, x/a = b, a/x = b KEY: expression | product | number | variable

177. ANS: A PTS: 1 DIF: Easy OBJ: Section 7.3NAT: PR7 TOP: Dividing Polynomials by Monomials KEY: dividing a polynomial by a monomial

178. ANS: D PTS: 1 DIF: Easy OBJ: Section 7.2NAT: PR7 TOP: Multiplying Polynomials by Monomials KEY: multiplying a binomial by a monomial | distributive property

179. ANS: E PTS: 1 DIF: Easy OBJ: Section 7.3NAT: PR7 TOP: Dividing Polynomials by Monomials KEY: dividing a polynomial by a monomial

180. ANS: A PTS: 1 DIF: Easy OBJ: Section 7.3NAT: PR7 TOP: Dividing Polynomials by Monomials KEY: dividing a polynomial by a monomial

181. ANS: B PTS: 1 DIF: Easy OBJ: Section 7.1NAT: PR7 TOP: Multiplying Polynomials by Monomials KEY: multiplying monomials

182. ANS: A PTS: 1 DIF: Average OBJ: Section 10.1NAT: SS1 TOP: Exploring Angles in a Circle KEY: central angle

183. ANS: D PTS: 1 DIF: Average OBJ: Section 10.2NAT: SS1 TOP: Exploring Chord Properties KEY: perpendicular bisector

184. ANS: E PTS: 1 DIF: Easy OBJ: Section 10.3NAT: SS1 TOP: Tangents to a Circle KEY: point of tangency

185. ANS: C PTS: 1 DIF: Average OBJ: Section 10.1NAT: SS1 TOP: Exploring Angles in a Circle KEY: inscribed angle

ID: A

13

186. ANS: C PTS: 1 DIF: Average OBJ: Section 10.1NAT: SS1 TOP: Exploring Angles in a Circle KEY: inscribed angle | chord

187. ANS: F PTS: 1 DIF: Average OBJ: Section 3.3NAT: N4 TOP: Order of Operations KEY: order of operations

188. ANS: C PTS: 1 DIF: Easy OBJ: Section 3.2NAT: N2 TOP: Exponent Laws KEY: quotient of powers | exponent laws

189. ANS: A PTS: 1 DIF: Easy OBJ: Section 3.2NAT: N2 TOP: Exponent Laws KEY: quotient of powers | exponent laws

190. ANS: B PTS: 1 DIF: Average OBJ: Section 3.2NAT: N2 TOP: Exponent Laws KEY: power of power | exponent laws

191. ANS: E PTS: 1 DIF: Easy OBJ: Section 3.3NAT: N4 TOP: Order of Operations KEY: order of operations

192. ANS: D PTS: 1 DIF: Easy OBJ: Section 8.1NAT: PR3 TOP: Solving Equations: ax = b, x/a = b, a/x = b KEY: fraction | numerator

193. ANS: G PTS: 1 DIF: Average OBJ: Section 8.1NAT: PR3 TOP: Solving Equations: ax = b, x/a = b, a/x = b KEY: quotient | division

194. ANS: E PTS: 1 DIF: Average OBJ: Section 8.1NAT: PR3 TOP: Solving Equations: ax = b, x/a = b, a/x = b KEY: opposite expression | inverse operation

195. ANS: F PTS: 1 DIF: Average OBJ: Section 8.1NAT: PR3 TOP: Solving Equations: ax = b, x/a = b, a/x = b KEY: multiplication | product

196. ANS: C PTS: 1 DIF: Easy OBJ: Section 8.3NAT: PR3 TOP: Solving Equations: a(x + b) = c KEY: expression | variable | operation

197. ANS: A PTS: 1 DIF: Easy OBJ: Section 8.1NAT: PR3 TOP: Solving Equations: ax = b, x/a = b, a/x = b KEY: fraction | denominator

198. ANS: D PTS: 1 DIF: Average OBJ: Section 5.1NAT: PR5 TOP: The Language of Mathematics KEY: term | expression | variable

199. ANS: A PTS: 1 DIF: Easy OBJ: Section 5.1NAT: PR5 TOP: The Language of Mathematics KEY: algebra | symbol

200. ANS: E PTS: 1 DIF: Easy OBJ: Section 5.1NAT: PR5 TOP: The Language of Mathematics KEY: variable | symbol

201. ANS: B PTS: 1 DIF: Average OBJ: Section 5.1NAT: PR5 TOP: The Language of Mathematics KEY: degree | term

ID: A

14

SHORT ANSWER

202. ANS:

PTS: 1 DIF: Easy OBJ: Section 5.2 NAT: PR6TOP: Equivalent Expressions KEY: model | polynomial

203. ANS: Example: Theoretical probability is calculated as the number of successful outcomes divided by the number of possible outcomes. The theoretical probability of an event does not change.Experimental probability is calculated as a ratio of the number of successful trials divided by the total number of trials. The number of successful trials is based on the results of an experiment, and can change each time you repeat the experiment.

PTS: 1 DIF: Difficult OBJ: Section 11.3 NAT: SP4TOP: Probability in Society KEY: theoretical probability | experimental probability

204. ANS: Example: The population is the entire group about which you are gathering information. A sample is a small group that represents the entire population.

PTS: 1 DIF: Easy OBJ: Section 11.2 NAT: SP2TOP: Collecting Data KEY: population | sample

205. ANS: Scale factor: 8 cm ÷ 60 cm = 0.13.The scale factor used to create Jason’s drawing is 0.13.

PTS: 1 DIF: Easy OBJ: Section 4.1 NAT: SS4TOP: Enlargements and Reductions KEY: scale factor | reduction

206. ANS: a) 396 c) 0b) 209 d) 376

PTS: 1 DIF: Average OBJ: Section 3.3 NAT: N4TOP: Order of Operations KEY: order of operations

207. ANS: a) 1.3b) 1.9c) 0.3d) 0.6

PTS: 1 DIF: Easy OBJ: Section 2.4 NAT: N5TOP: Determining Square Roots of Rational Numbers KEY: rational numbers | perfect square | square root

ID: A

15

208. ANS: a) AB is the diameter of the circle. Since it is a straight line, the central angle of the circle is 180°. ∠ADB will be half of that, or 90°.

b) Triangle ADB is a right triangle. AB is the hypotenuse. 152 = 92 + DA2

225 = 81 + DA2

DA2 = 225 – 81 DA2 = 144 DA = 144 DA = 12Chord AD is 12 cm long.

PTS: 1 DIF: Easy OBJ: Section 10.1 NAT: SS1TOP: Exploring Angles in a Circle KEY: Pythagorean relationship | diameter | central angle

209. ANS: p 2 − p + 3

PTS: 1 DIF: Average OBJ: Section 5.3 NAT: PR6TOP: Adding and Subtracting Polynomials KEY: expression | simplify | model

210. ANS: a) 49 cm2 c) 176 400 mm2

b) 169 m2 d) 6.25 km2

PTS: 1 DIF: Average OBJ: Section 3.4 NAT: N1TOP: Using Exponents to Solve Problems KEY: area of a square | problem solving

211. ANS: 4(4.1c − 0.875) = 6(1.8c + 1.75)

16.4c − 3.5 = 10.8c + 10.5

16.4c − 10.8c = 10.5 + 3.5

5.6c = 14.0

c = 2.5

PTS: 1 DIF: Difficult OBJ: Section 8.4 NAT: PR3TOP: Solving Equations: ax = b + cx, ax + b = cx + d, a(bx + c) = d(ex + f)KEY: multi-step equation | distributive property | addition | subtraction | division

212. ANS: −x2 + 4x

PTS: 1 DIF: Average OBJ: Section 7.2 NAT: PR7TOP: Multiplying Polynomials by Monomials KEY: multiplying a binomial by a monomial | like terms

ID: A

16

213. ANS: a) 512 cm3 c) 125 000 mm3

b) 2744 m3 d) 0.216 km3

PTS: 1 DIF: Average OBJ: Section 3.4 NAT: N1TOP: Using Exponents to Solve Problems KEY: volume of a cube | problem solving

214. ANS:

a) 2 14 × 3 1

3 = 94 × 10

3

= 152

= 7 12

b) −1 34 + 2 1

6 = −74 + 13

6

= −2112 + 26

12

= 512

c) 25 ÷ 1 1

15 = 25 ÷ 16

15

= 25 × 15

16

= 38

PTS: 1 DIF: Average OBJ: Section 2.3 NAT: N3TOP: Problem Solving With Rational Numbers in Fraction Form KEY: mixed numbers | fraction operations | lowest terms | positive and negative integers | multiply | add | divide

ID: A

17

215. ANS:

PTS: 4 DIF: Difficult OBJ: Section 1.1 NAT: SS5TOP: Line Symmetry KEY: symmetry | oblique line of symmetry | horizontal line of symmetry | vertical line of symmetry

216. ANS: 1

280 = 10x

x = 2800 cm

1 m = 100 cm

2800 cm = 28 mThe length of the actual basketball court is 28 m.

PTS: 1 DIF: Difficult+ OBJ: Section 4.2 NAT: SS4TOP: Scale Diagrams KEY: scale factor

ID: A

18

217. ANS: Example:The open circle here indicates that the solution includes all values greater than 3, but does not include 3.

The closed circle here indicates that the solution includes 3 as well as all values greater than 3.

PTS: 1 DIF: Average OBJ: Section 9.1 NAT: PR4TOP: Representing Inequalities KEY: boundary point | number line | algebraic to graphic

218. ANS: a) She was 5 m from the sensor when she began walking.

b) She was walking toward the motion sensor.

c) It took her 10 s to reach the motion sensor.

PTS: 1 DIF: Difficult OBJ: Section 6.2 NAT: PR2TOP: Interpreting Graphs KEY: interpreting graphs

219. ANS: a) 256 c) 20b) 88 d) 25

PTS: 1 DIF: Average OBJ: Section 3.3 NAT: N4TOP: Order of Operations KEY: order of operations

220. ANS: Example: A stratified sample can be created by dividing the school into grades and randomly selecting the corresponding proportion of people from each grade.

PTS: 1 DIF: Average OBJ: Section 11.2 NAT: SP2TOP: Collecting Data KEY: stratified sample

221. ANS:

PTS: 4 DIF: Average OBJ: Section 2.1 NAT: N3TOP: Comparing and Ordering Rational Numbers KEY: rational numbers | ordering | decimal numbers | fractions | mixed numbers

ID: A

19

222. ANS: 2x + 1 + 2x + 3 + 2x − 2 ≥ 44

6x + 2 ≥ 44

6x ≥ 42

x ≥ 7The value of x can be greater than or equal to 7.

PTS: 1 DIF: Difficult OBJ: Section 9.3 NAT: PR4TOP: Solving Multi-Step Inequalities KEY: multi-step inequality | perimeter | problem solving

223. ANS: a) 26 c) 64

b) 35 d) 84

PTS: 1 DIF: Average OBJ: Section 3.1 NAT: N1TOP: Using Exponents to Describe Numbers KEY: represent powers | exponential form

PROBLEM

224. ANS:

Distance between Point A and Point C on the map = AB2 + BC2

= 4.52 + 6.02

= 20.25 + 36

= 56.25

= 7.5Scale of the map = 1 cm:75 kmDistance on map × 15 = actual distance

7.5 × 15 = 112.5 kmThe actual distance between Point A and Point C is 112.5 km.

PTS: 1 DIF: Difficult OBJ: Section 4.3 NAT: SS4TOP: Similar Triangles KEY: similar triangles | problem solving

225. ANS: a) Yes, Laura made a mistake. Example: She multiplied the bases and added the exponents. For questions such as this, you need to calculate the number that each power represents, then, multiply those two numbers.

b) 43 × 35 = 64 × 243

= 15 552The correct answer is 15 552.

PTS: 1 DIF: Average OBJ: Section 3.2 NAT: N2TOP: Exponent Laws KEY: evaluate powers | exponent laws

ID: A

20

226. ANS: a) Kevin’s explanation was incorrect. When dividing powers, the exponents should be subtracted. Kevin divided the exponent.

b) 46 ÷ 42 = 4(6 − 2)

= 44

= 256The correct answer is 256.

PTS: 1 DIF: Average OBJ: Section 3.2 NAT: N2TOP: Exponent Laws KEY: quotient of powers | exponent laws

227. ANS: w + 2w + w − 1 + 2w − 8 + 2w + 6 = w + 2w + w + 2w + 2w − 1 − 8 + 6

= 8w − 3The perimeter is 8w − 3.

PTS: 1 DIF: Average OBJ: Section 5.3 NAT: PR6TOP: Adding and Subtracting Polynomials KEY: expression | simplify | perimeter

228. ANS: Let h represent the number of hours past 8 p.m. that Susan worked.

32 = 20 + 3h

32 − 20 = 3h

12 = 3h

4 = h4 hours past 8 p.m. is 12 a.m.Susan worked until midnight.

PTS: 1 DIF: Difficult OBJ: Section 8.2 NAT: PR3TOP: Solving Equations: ax + b = c, x/a + b = c KEY: multi-step equation | subtraction | division | money | problem solving

ID: A

21

229. ANS: OQ = 90 − 46

= 44 mm

MQ = 902 − 442

= 8100 − 1936

= 6164

= 78.511146 mmChord MN = 2 × 78.511146

= 157.02229. . . mmChord MN has a length of 157.02 mm.

PTS: 1 DIF: Difficult OBJ: Section 10.2 NAT: SS1TOP: Exploring Chord Properties KEY: Pythagorean relationship | perpendicular bisector | chord

230. ANS: a) x = 6 b) x = 4 c) x = 16d) x = 35 e) x = 11 f) x = 1

PTS: 5 DIF: Easy OBJ: Section 2.1 NAT: N3TOP: Comparing and Ordering Rational Numbers KEY: rational numbers | equivalent fractions | comparing

231. ANS: a)

b) Example: Yes, the design is now symmetrical. It has vertical line symmetry along the y-axis.

PTS: 5 DIF: Difficult OBJ: Section 1.1 NAT: SS5TOP: Line Symmetry KEY: symmetry | reflection | line of reflection | draw shape with symmetry

ID: A

22

232. ANS: a) s + s + s − 7 + s − 7 = 4s − 14The perimeter is 4s − 14.

b) 4s − 14 = 4(12) − 14

= 48 − 14

= 34The perimeter is 34 m.

PTS: 1 DIF: Easy OBJ: Section 5.2 | Section 5.3NAT: PR6 TOP: Equivalent Expressions | Adding and Subtracting PolynomialsKEY: perimeter | expression | simplify

233. ANS: a) To predict the average mark, Ms. Bondar could use the measures of central tendency.Mean:

Mean = 19 + 18 + 15 + 20 + 185

= 18Median: The median is 18.Mode: The mode is 18.

b) Example: Ms. Bondar assumed that the sample consisting of the first five papers wasrepresentative of the entire class. This is false. The mean score in the sample is 18, while themean score of the population is approximately 22. The mode in the sample is 18, while themode of the population is 24. Ms. Bondar may have considered too few scores in making herprediction. The sample does not represent the population.

PTS: 1 DIF: Average OBJ: Section 11.2 | Section 11.3NAT: SP2 | SP4 TOP: Collecting Data | Probability in Society KEY: measures of central tendency | false prediction | problem solving

234. ANS: Height of house

Height of observer = distance from street to housedistance from street to observer

h1.3 = 18.2 + 2.6

2.6

h = 10.4 mThe height of the house is 10.4 m.

PTS: 1 DIF: Average OBJ: Section 4.3 NAT: SS4TOP: Similar Triangles KEY: similar triangles | problem solving

ID: A

23

235. ANS: Example:a) The sample is biased because only people at the swimming pool are surveyed. The population consists of all tax-payers, including those who may not use the swimming pool. People who do not use the swimming pool may feel differently about funding it.

b) The bias could be removed by randomly surveying selected local taxpayers instead.

PTS: 1 DIF: Easy OBJ: Section 11.2 NAT: SP2TOP: Factors Affecting Data Collection KEY: bias

236. ANS: a) Let t represent the amount of time, in minutes, for a long-distance phone call.25 + 3t < 65

b) 25 + 3t < 65

3t < 40

t < 13. 3Julia can make up to 13 min of long-distance calls.

PTS: 1 DIF: Average OBJ: Section 9.1 NAT: PR4TOP: Representing Inequalities KEY: represent algebraically | money | problem solving

237. ANS: Example:Let the width of the pool be represented by w. Let the length of the pool be represented by 4w.Area = length × width

144 = 4w × w

144 = 4w2

1444 = w2

36 = w2

6 = wThe width of the pool is 6 m and the length is 24 m.

PTS: 1 DIF: Difficult OBJ: Section 2.4 NAT: N5TOP: Determining Square Roots of Rational Numbers KEY: rational numbers | square root | area

ID: A

24

238. ANS: Surface area of top cylinder: 2π2.52 + 2π2.5 9

= 39.25 + 141.3

= 180.55 cm2

Surface area of bottom cylinder: 2π42 + 2π4 1.5

= 50.24 + 37.68

= 87.92 cm2

Surface area of join: 2π2.52

= 39.25 cm2

Total surface area: surface area of top + surface area of bottom − surface area of join

= 180.25 + 87.92 − 39.25

= 228.92 cm2

The total surface area of Whitney’s bird feeder is 228.9 cm2.

PTS: 5 DIF: Difficult+ OBJ: Section 1.3 NAT: SS2TOP: Surface Area KEY: surface area | faces | area of face | cylinder

239. ANS: a) An inscribed angle is half of the central angle. ∠XZY = 2 ∠XWY

= 2(42)

= 84°

∠XZY is 84°.b) Angles in a triangle add to 180°. ∠XYZ = ∠ZXY.

∠XYZ = 180 − ∠XZY2

= 180 − 842

= 48°∠XYZ is 48°.

PTS: 1 DIF: Easy OBJ: Section 10.1 NAT: SS1TOP: Exploring Angles in a Circle KEY: chord | central angle | inscribed angle

ID: A

25

240. ANS:

Slant length of tent = (1.8)2 + (2.4)2

= 3.24 + 5.76

= 9

= 3 mSurface area of slanted faces: 2 × 3.0 × 4.5 = 27 m2

Surface area of front and back triangular faces: 2 × 12 × 3.6 × 2.4 = 8.64 m2

Total surface area of walls of the tent 27.0 + 8.64 = 35.64 m2

Each can of waterproofing spray covers 7.4 m2. The amount of spray needed to cover the walls = 35.64 ÷ 8.1 = 4.4 cans.You need five cans of waterproofing spray must be purchased to treat all of the exterior walls of the tent.

PTS: 5 DIF: Difficult OBJ: Section 1.3 NAT: SS2TOP: Surface Area KEY: surface area | faces | area of face

241. ANS: a) This is a systematic sample.

b) This is a convenience sample.

c) This is a stratified sample.

PTS: 1 DIF: Average OBJ: Section 11.2 NAT: SP2TOP: Collecting Data KEY: convenience sample | stratified sample | systematic sample

242. ANS: Example: a)

b) (w + 15) + w + (w + 15) + w = 4w + 30The perimeter is 4w + 30.

PTS: 1 DIF: Average OBJ: Section 5.2 NAT: PR6TOP: Equivalent Expressions KEY: expression | term | perimeter

ID: A

26

243. ANS: a) A = 3x x + 2 − x x + 1

A = 3x2 + 6x − x2 − x

A = 2x2 + 5xAn expression for the area of the garden is 2x2 + 5x.

b) A = 2x2 + 5x

A = 2 6 2 + 5 6

A = 72 + 30

A = 102The area of the garden is 102 m2.

PTS: 1 DIF: Difficult OBJ: Section 7.2 NAT: PR7TOP: Multiplying Polynomials by Monomials KEY: multiplying a polynomial by a monomial | area model

244. ANS:

PTS: 1 DIF: Average OBJ: Section 4.2 NAT: SS4TOP: Scale Diagrams KEY: scale factor | enlargement | draw an enlargement

ID: A

27

245. ANS: Perimeter = 2(length) + 2(width)

43.2 = 2(2s + 4) + 2(s + 2)

43.2 = 4s + 8 + 2s + 4

43.2 = 6s + 12

31.2 = 6s

5.2 = sWidth = s + 2

= 5.2 + 2

= 7.2Length = 2s + 4

= 2(5.2) + 4

= 10.4 + 4

= 14.4The length of the rectangle is 14.4 cm and the width is 7.2 cm.

PTS: 1 DIF: Difficult+ OBJ: Section 8.3 NAT: PR3TOP: Solving Equations: a(x + b) = c KEY: multi-step equation | subtraction | division | perimeter

246. ANS: P = 5x2 − 2x + 4x2 + 4x + 5x2 + 6x

P = 14x2 + 8xThe perimeter is 14x2 + 8x.

PTS: 1 DIF: Easy OBJ: Section 5.3 NAT: PR5TOP: Adding and Subtracting Polynomials KEY: polynomial | subtraction | perimeter

ID: A

28

247. ANS: Since CE is a radius bisecting chord AB, ∠ADC equals 90°. The other angles, ∠ACD and ∠DAC, form an isosceles triangle with angles adding to 180°.∠ACD = ∠DAC

= 180° − 90°2

= 45°90 + 2x = 180

2x = 90

x = 45

∠ACD = 45°

∠DBC = 45°

∠ACB = 90°∠AFB is an inscribed angle subtended by the same chord as central angle ∠ACB. ∠AFB is half the size of ∠ACB. ∠AFB equals 45°.∠AFB measures 45°.

PTS: 1 DIF: Average OBJ: Section 10.2 NAT: SS1TOP: Exploring Chord Properties KEY: chord | perpendicular bisector | inscribed angle | central angle

248. ANS:

a) 23 > 0.6 b) 14 = 0.25 c) 1.52 > 1 1

2

d) −34 < 0.75 e) −0.9 < − 9

11 f) 0.954 > 0.946

PTS: 1 DIF: Easy OBJ: Section 2.1 NAT: N3TOP: Comparing and Ordering Rational Numbers KEY: comparing | fractions | decimal numbers

249. ANS: (3x2 − 2x + 4) and (−3x2 + 2x − 4)

PTS: 1 DIF: Average OBJ: Section 5.2 NAT: PR6TOP: Equivalent Expressions KEY: model | expression

ID: A

29

250. ANS: ∠OPQ = 90°∠POQ = 180° – (90° + 56°) = 34°

∠PSQ =∠POQ

2

= 342

= 17°Since OPS is an isosceles triangle, ∠OSP = ∠OPS, so ∠OPS is 17°.∠OPS is 17°.

PTS: 1 DIF: Average OBJ: Section 10.3 NAT: SS1TOP: Tangents to a Circle KEY: tangent | point of tangency | central angle | inscribed angle

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