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

1

Final Exam Review

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

Choose the best answer.

____ 1. Pictographs are best for

a. comparing data across categories

b. comparing two sets of data across categories

c. comparing categories to the whole using percents

d. comparing data that can be easily counted and represented using symbols

____ 2. What type of graph could be used to show whether the player was progressing over time?

a. circle graph

b. double bar graph

c. line graph

d. pictograph

Name: ________________________ ID: A

2

____ 3. A normal deck of playing cards has 52 cards in four suits (clubs, diamonds, hearts, and spades) of 13 cards

each. Two of the suits are black and two of the suits are red. The ratio of black cards to red cards isa. 1:1 b. 1:2 c. 2:3 d. 2:4

____ 4. Eric is able to stop 85% of the shots on goal. If he faces 27 shots on goal, how many goals would likely be scored on him?

a. 3 b. 4 c. 9 d. 15

____ 5. Use the Pythagorean relationship to find the unknown area of the square.

a. 26 cm2 c. 104 cm2

b. 25 cm2 d. 2535 cm2

____ 6. Determine the missing side length.

a. 5 cm c. 7 cm

b. 6 cm d. 8 cm

____ 7. Which of the following whole numbers has a square root between 5 and 6?

a. 27 c. 44

b. 37 d. 56

Name: ________________________ ID: A

3

____ 8. What is the approximate side length of this square? Round your answer to the nearest tenth.

a. 12.2 cm c. 37.5 cm

b. 12.6 cm d. 75.5 cm

____ 9. The length of the hypotenuse, to the nearest metre, is

a. 15 m c. 17 m

b. 16 m d. 18 m

____ 10. The surface area of this triangular prism would be calculated as

a. 2(5 × 8) + 2(6 × 4)

b. 2(5 × 8

2) + 2(5 × 5) + (6 × 8)

c. 2(4 × 6

2) + 2(5 × 8) + (6 × 8)

d. 2(5 × 8) + 3(6 × 4)

Name: ________________________ ID: A

4

____ 11. Which object do these three views describe?

a. c.

b. d.

____ 12. What is the surface area of the two bases of a cylinder with a diameter of 6 cm and a height of 15 cm?

a. 282.6 cm2 b. 56.52 cm2 c. 28.26 cm2 d. 18.84 cm2

____ 13. What is the surface area of the 3-D object shown below?

a. 8 cm2 c. 32 cm2

b. 16 cm2 d. 40 cm2

Name: ________________________ ID: A

5

____ 14. In lowest terms, determine 20

27÷

5

9.

a.2

3b.

3

4c. 1

1

3d. 1

1

2

____ 15. As an improper fraction in lowest terms, what is 2

5×

2

3+

3

10

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃ ÷

8

15?

a.23

25b.

11

15c.

29

40d.

15

52

____ 16. Determine –5 × (–10) × (–2).

a. −100 c. 25

b. −50 d. 125

____ 17. A submarine dives at a rate of 16 m/min for eight minutes. How far does the submarine dive?

a. 2 m c. 128 m

b. −2 m d. −128 m

____ 18. Determine –8 – (– 6) × 3 – 5 × (–3).

a. 9 c. 25

b. −9 d. −25

____ 19. The height of a stack of recycling bins can be described as 12 cm plus 3 cm for each bin in the stack. Which of the following tables of values represents this description?

a. c.

b. d.

Name: ________________________ ID: A

6

____ 20. Julia made a mistake solving an equation. At what step did she make her mistake?

A 3 x − 5( ) = 21

B x − 5( ) =21

3

C x − 5( ) + 5 = 7 − 5

D x = −2

a. A c. C

b. B d. D

____ 21. When rolling a six-sided die and tossing a coin, the number of possible outcomes is

a. 6 b. 8 c. 12 d. 24

____ 22. An ice cream store offers 5 different flavours and 15 different toppings. How many combinations of one

flavour and one topping are possible?a. 15 b. 25 c. 75 d. 85

____ 23. The number of possible outcomes when randomly drawing from the cards shown below and flipping the coin is

a. 5 b. 6 c. 10 d. 20

____ 24. Which of the following shapes cannot be used to tile the plane?

a. regular hexagon c. irregular hexagon

b. isosceles triangle d. equilateral triangle

Name: ________________________ ID: A

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Short Answer

25. Carol delivers newspapers. Each week she earns $10, plus $0.25 per newspaper she delivers.

a) Complete the table of values showing Carol’s earnings.

Number of Papers Delivered, n Earnings, e ($)

0 10

16 14

32 18

48

64

80

b) Graph the ordered pairs.

c) Is it reasonable to have points on the graph between the plotted ones? Explain

26. Solve the equation. Verify your answer.2x + 3.5 = 11.5.

27. You roll a four-sided die numbered 2, 4, 6, and 8 and you spin a spinner with five equal sections numbered 6, 7, 8, 9, and 10.

a) List the sums of all the possible outcomes.

b) What is P(sum of 14)?

Name: ________________________ ID: A

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Problem

28. Craig took 20 minutes to swim 14 laps in the school swimming pool.

a) What is his unit rate per minute?

b) What is his unit rate per hour?

c) At this rate, how many laps can Craig swim in half an hour?

d) At this rate, how many laps can Craig swim in 3 h?

e) At this rate, how many laps can Craig swim in 2 h 20 min?

f) Why do you suppose Craig’s unit rate might decrease after a while?.

29. Use a number line to show how the following expression could be solved. Solve, and express your answer in

lowest terms.

6

7÷ 4 =

30. Model the following expression. Solve and express your answer in lowest terms.

3

8÷ 6 =

31. Local engineers have designed a new rectangular culvert that will be made of concrete. How much concrete will be required to build the culvert as illustrated below?

32. A circular swimming pool has a diameter of 8.6 m and it is filled to a height of 1.6 m. What is the volume of water in the pool? Express your answer to the nearest tenth of a cubic metre.

Name: ________________________ ID: A

9

33. The formula a + e = 85 is often used to determine when a police constable can retire.

a represents the constable’s age.e represents his or her number of years of employment.

a) Constable Patterson is 44 years old. He has been working for 21 years. Can he retire this year? Explain.

b) How many more years must Constable Patterson work?

ID: A

1

Final Exam ReviewAnswer Section

MULTIPLE CHOICE

1. ANS: D PTS: 1 DIF: Average OBJ: Section 1.1NAT: SP1 TOP: Advantages and Disadvantages of Different GraphsKEY: pictograph | advantages

2. ANS: C PTS: 1 DIF: Average OBJ: Section 1.3NAT: SP1 TOP: Critiquing Data Presentation KEY: line graph

3. ANS: A PTS: 1 DIF: Average OBJ: Section 2.1

NAT: N4 TOP: Two-Term and Three-Term Ratios KEY: ratio

4. ANS: B PTS: 1 DIF: Average OBJ: Section 2.3

NAT: N5 TOP: Proportional Reasoning KEY: probability | percent

5. ANS: A PTS: 1 DIF: Average OBJ: Section 3.2

NAT: M1 TOP: Exploring the Pythagorean Relationship KEY: Pythagorean relationship | Pythagorean triple

6. ANS: D PTS: 1 DIF: Average OBJ: Section 3.2

NAT: M1 TOP: Exploring the Pythagorean Relationship KEY: Pythagorean relationship | Pythagorean triple

7. ANS: A PTS: 1 DIF: Easy OBJ: Section 3.3

NAT: N2 TOP: Estimating Square Roots KEY: estimation | square root | benchmark

8. ANS: A PTS: 1 DIF: Average OBJ: Section 3.3

NAT: N2 TOP: Estimating Square Roots KEY: estimation | square root | benchmark

9. ANS: D PTS: 1 DIF: Easy OBJ: Section 3.4NAT: M1 TOP: Using the Pythagorean Relationship KEY: Pythagorean relationship | unknown hypotenuse

10. ANS: C PTS: 1 DIF: Difficult OBJ: Section 5.3NAT: SS3 TOP: Surface Area of a Prism KEY: surface area | triangular prism | calculate hypotenuse

11. ANS: A PTS: 1 DIF: Average OBJ: Section 5.1NAT: SS5 TOP: Views of Three-Dimensional Objects KEY: views | three-dimensional

12. ANS: B PTS: 1 DIF: Average OBJ: Section 5.4NAT: SS3 TOP: Surface Area of a Cylinder KEY: cylinder | surface area | base

13. ANS: D PTS: 1 DIF: Easy OBJ: Section 5.3NAT: SS3 TOP: Surface Area of a Prism KEY: rectangular prism | surface area

14. ANS: C PTS: 1 DIF: Average OBJ: Section 6.5NAT: N6 TOP: Dividing Fractions and Mixed Numbers KEY: division | fractions | lowest terms

15. ANS: C PTS: 1 DIF: Difficult OBJ: Section 6.6NAT: N6 TOP: Applying Fraction Operations KEY: order of operations | fractions | multiplication | division | lowest terms | improper fraction

16. ANS: A PTS: 1 DIF: Difficult OBJ: Section 8.2NAT: N7 TOP: Multiplying Integers KEY: multiplication | negative integers

17. ANS: D PTS: 1 DIF: Average OBJ: Section 8.2NAT: N7 TOP: Multiplying Integers KEY: multiplication | integers | problem

ID: A

2

18. ANS: C PTS: 1 DIF: Difficult OBJ: Section 8.5

NAT: N7 TOP: Applying Integer Operations KEY: order of operations

19. ANS: C PTS: 1 DIF: Average OBJ: Section 9.2

NAT: PR1 TOP: Patterns in a Table of Values KEY: create a table of values

20. ANS: C PTS: 1 DIF: Difficult OBJ: Section 10.4

NAT: PR2 TOP: Modelling and Solving Two-Step Equations: a(x + b) = cKEY: solve an equation | two-step equations | distributive property

21. ANS: C PTS: 1 DIF: Easy OBJ: Section 11.2

NAT: SP2 TOP: Outcomes of Independent Events KEY: independent events | possible outcomes | dice | coin

22. ANS: C PTS: 1 DIF: Average OBJ: Section 11.2

NAT: SP2 TOP: Outcomes of Independent Events KEY: independent events | combinations

23. ANS: C PTS: 1 DIF: Easy OBJ: Section 11.2NAT: SP2 TOP: Outcomes of Independent Events KEY: possible outcomes | cards | coin

24. ANS: C PTS: 1 DIF: Easy OBJ: Section 12.1NAT: SS6 TOP: Exploring Tessellations With Regular and Irregular PolygonsKEY: tiling the plane

ID: A

3

SHORT ANSWER

25. ANS:

a)

Number of Papers Delivered, n Earnings, e ($)

0 10

16 14

32 18

48 22

64 26

80 30

b)

ID: A

4

c) Answers may vary. Example: Yes, because she may deliver a number of papers between the intervals on the x-axis.

PTS: 1 DIF: Average OBJ: Section 9.2 NAT: PR1TOP: Patterns in a Table of Values KEY: table of values | construct a graph | identify a pattern

26. ANS: x = 4Verify:

LS = 2(4) + 3.5

= 11.5

RS = 11.5LS = RS

PTS: 1 DIF: Difficult+ OBJ: Section 10.2 NAT: PR2TOP: Modelling and Solving Two-Step Equations: ax + b = c KEY: solve an equation | inspection | verify solution

27. ANS: Methods may vary. Example:

a) The possible sums are 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, and 18.

b)

Probability =favourable outcomes

possible outcomes

P(sum of 14) =3

20

The probability of getting a sum of 14 is 3

20, 15%, or 0.15.

PTS: 1 DIF: Average OBJ: Section 11.1 NAT: SP2TOP: Determining Probabilities Using Tree Diagrams and Tables KEY: sample space | dice | spinner

ID: A

5

PROBLEM

28. ANS:

a) 14 ÷ 20 = 0.7His unit rate is 0.7 laps/minute.

b) 60 × 0.7 = 42 His unit rate is 42 laps/hour.

c) 30 × 0.7 = 21 Craig can swim 21 laps in half an hour.

d) 3 × 42 = 126 Craig can swim 126 laps in three hours.

e) 2 × 42 + 20 × 0.7 = 98 Craig can swim 98 laps in 2 hours and 20 minutes.

f) Craig might get tired and start slowing down. This will decrease his unit rate.

PTS: 1 DIF: Average OBJ: Section 2.2 NAT: N5TOP: Rates KEY: rate | unit rate

29. ANS:

6

7÷ 4

=6

28

=3

14

PTS: 1 DIF: Difficult+ OBJ: Section 6.2 NAT: N6TOP: Dividing a Fraction by a Whole Number KEY: fractions | whole number | division | model

ID: A

6

30. ANS:

Models may vary. Example:

3

8÷ 6

=3

48

=1

16

PTS: 1 DIF: Difficult+ OBJ: Section 6.2 NAT: N6TOP: Dividing a Fraction by a Whole Number KEY: fractions | whole number | division | lowest terms | model

31. ANS: Determine the volume of the rectangular prism.

V = l × w × h

V = 2 × 2 × 10

V = 40

The volume of the rectangular prism is 40 m3.Determine the volume of the cylinder.

V = (π × r2) × h

V = (3.14 × 0.5 × 0.5) × 10

V = 7.85

The volume of the cylinder is 7.85 m3.

Volume of concrete required = volume of prism − volume of cylindrical space

V = 40 − 7.85

V = 32.15

The volume of concrete required for the culvert is 32.15 m3.

PTS: 1 DIF: Average OBJ: Section 7.4 NAT: SS4TOP: Solving Problems Involving Prisms and Cylinders KEY: right triangular prism | cylinder | volume

ID: A

7

32. ANS:

V = (π × r2) × h

V = (3.14 × 4.3 × 4.3) × 1.6

V = 92.89376

The volume of water in the pool is 92.9 m3.

PTS: 1 DIF: Average OBJ: Section 7.4 NAT: SS4TOP: Solving Problems Involving Prisms and Cylinders KEY: cylinder | depth

33. ANS:

a) 44 + 21 = 65, so Constable Patterson is not able to retire yet.

b) Solve the equation (44 + n) + (21 + n) = 85.Constable Patterson must work ten more years before he can retire.

PTS: 1 DIF: Difficult+ OBJ: Section 10.4 NAT: PR2TOP: Modelling and Solving Two-Step Equations: a(x + b) = c KEY: two-step equations | solve an equation