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Foundations of Mathematics

and Pre-Calculus 10

Review Resource

PART A: MULTIPLE-CHOICE QUESTIONS

1. Which line has a positive slope and a negative x-intercept?

A. Graph A

B. Graph B

C. Graph C

D. Graph D

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Use this graph to answer Question 2

2. Which of the following equations describes the graph above?

I 𝑦 = −2

3𝑥 + 2

II 𝑦 + 6 = −3

2(𝑥 − 5)

III 3𝑥 + 2𝑦 − 27 = 0

A. I only

B. II only

C. I and III only

D. II and III only

3. What is the equation of the line passing through (−1, 10) and (2, −2)?

A. 𝑦 = −4𝑥 − 39

B. 𝑦 = −4𝑥 + 6

C. 𝑦 = 4𝑥 + 41

D. 𝑦 = −1

4𝑥 +

5

2

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4. Car A drives the 150km from Parksville to Victoria at an average speed of 100km/h. Car B drives

from Victoria to Parksville at an average speed of 75km/h. They pass each other and wave at some

point in the trip. Which of the following graphs best represents this passing point?

Graph A Graph B

Graph C Graph D

A. Graph A

B. Graph B

C. Graph C

D. Graph D

Dis

tan

ce f

rom

Vic

tori

a (

km)

25

50

75

10

0

1

25

15

0

1

75

0 1 2 3

Time (h)

Dis

tan

ce f

rom

Vic

tori

a (

km)

25

50

75

10

0

1

25

15

0

1

75

0 1 2 3

Time (h)

Dis

tan

ce f

rom

Vic

tori

a (

km)

25

50

75

10

0

1

25

15

0

1

75

0 1 2 3

Time (h)

Dis

tan

ce f

rom

Vic

tori

a (

km)

25

50

75

10

0

1

25

15

0

1

75

0 1 2 3

Time (h)

Car A Car B

Car A Car B

Car A Car B

Car A

Car B

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5. If 𝑓(𝑥) = 5𝑥 + 6, determine 𝑓(−3).

A. −9

B. −9

5

C. 3

D. 21

6. What is the Greatest Common Factor of 108, 56, and 40?

A. 4

B. 8

C. 28

D. 53

7. Which of the following is an irrational number?

A. √24

B. −√164

C. 2−4

D. (−0.4)2

8. What value is equal to 3√50

A. √150

B. 5√2

C. 15√2

D. 75√2

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9. Which situation is best represented by the following graph?

A. Dawn cycles for an hour and then stops for lunch for a second hour.

B. Dawn cycles for an hour and then walks her bicycle for a second hour.

C. Dawn walks for an hour and then gets on her bicycle and rides for a second hour.

D. Dawn cycles up a steep hill for an hour then cycles up a less steep hill for a second hour.

10. Which of the following describes the graph of 3𝑥 − 4𝑦 + 4 = 0?

A. I and II only

B. I and III only

C. II and III only

D. I, II, and III

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11. Which of these graphs represents a function?

Graph A Graph B

Graph C Graph D

A. Graph A

B. Graph B

C. Graph C

D. Graph D

12. Simplify: (−27𝑥)2

3

A. −27𝑥2

3

B. −18𝑥2

3

C. −9𝑥2

3

D. 9𝑥2

3

x

y

x

y

x

y

x

y

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13. A line segment has endpoints A(−7, 3) and B(8, −2). Determine the slope of AB.

A. 5

B. 3

C. 1

D. −1

3

Use the following graph to answer question 14.

14. Which of the following equations is represented by the line shown above?

A. 2𝑥 − 3𝑦 − 6 = 0

B. 2𝑥 − 3𝑦 − 2 = 0

C. 2𝑥 − 3𝑦 + 9 = 0

D. 3𝑥 − 2𝑦 − 4 = 0

15. The slope of a line segment joining 𝑀(−8, 3) and 𝑁(7, 𝑘) is 2

5. Determine the value of 𝑘.

(Hint: You can solve this algebraically, or you may find it easier to sketch a picture)

A. 6

5

B. 13

5

C. 9

D. 81

2

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16. A fitness club charges a fee to join as well as a monthly fee, as represented by the graph below

What is the cost to be a member for 6 months?

A. $270

B. $480

C. $540

D. $780

17. Determine an equation of the line passing through the point (−4, 3) and parallel to the line segment

joining A(5, −2) and B(3, 4).

A. 𝑦 = 3𝑥 + 15

B. 𝑦 = 3𝑥 − 9

C. 𝑦 = −3𝑥 + 15

D. 𝑦 = −3𝑥 − 9

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18. What is the slope of the staircase below?

A. 1

2

B. 2

3

C. 47

48

D. 63

95

6ft 4in

9ft 6in

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19. Which of the following describe the same linear function?

I

II 𝑥 − 2𝑦 + 6 = 0

III

IV 3 more than one half of a number

A. I and III only

B. I and IV only

C. II and III only

D. II and IV only

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20. Determine the range of the following graph.

A. −1 ≤ 𝑦 ≤ 3

B. −2 ≤ 𝑦 ≤ 4

C. 𝑦 ≤ −1 𝑜𝑟 𝑦 ≥ 3

D. All real numbers

21. Determine the 𝑦-intercept of the graph of 9𝑥 + 6𝑦 − 72 = 0

A. -72

B. 6

C. 8

D. 12

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22. Determine an equation of the following line:

A. 𝑦 = −4

5𝑥 + 4

B. 𝑦 = −4

5𝑥 + 5

C. 𝑦 = −5

4𝑥 + 4

D. 𝑦 = 4

5𝑥 + 4

23. The cost of a pizza varies with the number of toppings. The basic pizza costs $12.95 plus $1.25 for

each topping. What is the formula?

A. C = 12.95t

B. C = 14.20t

C. C = 1.25t + 12.95

D. C = 12.95t + 1.25

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24.

Which equation represents a line with the same slope as line A and the same y-intercept as line B?

A. 4𝑥 − 𝑦 + 3 = 0

B. 3𝑥 + 2𝑦 − 2 = 0

C. 𝑥 − 4𝑦 + 12 = 0

D. 𝑥 + 4𝑦 − 12 = 0

25. The graph of 𝑦 = 4𝑥 + 𝑘 has an 𝑥-intercept of −20. Determine the value of 𝑘.

A. -20

B. -5

C. 16

D. 80

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26. Which of the following ordered pairs represents the solution to the following linear system?

𝑦 = 7𝑥 − 37 and 7𝑥 + 10𝑦 = 92

A. (5, 6)

B. (6, 5)

C. (−5, 6)

D. (−6, 5)

27. Solve the following system: 2𝑥 + 5𝑦 = 11

3𝑥 − 2𝑦 = 7

A. 3

B. (3, 1)

C. (1, 3)

D. 1

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28. Determine the number of solutions of the linear system:

𝑦 = −2𝑥 − 4

𝑦 = −2𝑥 + 3

A. No solutions

B. One solution

C. Two solutions

D. Infinite solutions

29. Order the following numbers from least to greatest

I √164

II −3√5

III 632

IV 1.602

A. I, II, III, IV

B. II, I, III, IV

C. II, IV, I, III

D. III, IV, I, II

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30. Simplify: (𝑥𝑎−1)3

(𝑥2𝑎)(𝑥)

A. 𝑥𝑎

B. 𝑥𝑎−2

C. 𝑥𝑎−3

D. 𝑥𝑎−4

31. Simplify: (3𝑥4𝑦

5𝑦−1)−2

A. −9𝑥8

25𝑦2

B. −3𝑦4

5𝑥8

C. 5

3𝑥8𝑦4

D. 25

9𝑥8𝑦4

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32. Write as an entire radical: 5√163

A. √803

B. √4003

C. √10203

D. √20003

33. What is the greatest common factor of 18𝑥2𝑦3, 30𝑥3𝑦, and 8𝑦4?

A. 2𝑦

B. 6𝑥𝑦3

C. 48𝑥3𝑦4

D. 360𝑥3𝑦4

34. This graph represents a 150-L hot-water tank being filled at a constant rate. Determine the rate of

change of the relation.

A. 3 L/min

B. 75 L/min

C. 0.33 L/min

D. 25

Time (min)

Vo

lum

e (

L)

Filling a Hot-Water Tank

(25, 75)

(50, 150)

0 10 20 30 40 50 t

25

50

75

100

125

150

175V

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35. Expand and simplify: (𝑥 + 5)(𝑥 − 4)(2𝑥 + 9)

A. 2𝑥3 − 180

B. 2𝑥3 + 9𝑥2 − 41𝑥 − 180

C. 2𝑥3 + 11𝑥2 − 31𝑥 − 180

D. 2𝑥3 + 11𝑥2 + 49𝑥 − 180

36. What value of k will make the following trinomial a perfect square?

𝑥2 + 8𝑥 + 𝑘

A. 4

B. 16

C. 32

D. 64

37. Factor the following: 6𝑥2 − 19𝑥 − 7.

A. (3𝑥 − 7)(2𝑥 + 1)

B. (3𝑥 − 1)(2𝑥 + 7)

C. (2𝑥 − 7)(3𝑥 + 1)

D. (2𝑥 − 1)(3𝑥 + 7)

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38. What factor is common to both of the following polynomials?

A. 2𝑥 − 1

B. 2𝑥 + 1

C. 4𝑥 − 1

D. 4𝑥 + 1

Use the following diagram to answer question 39.

39. Determine the area of the shaded region.

A. 7𝑥2 − 3𝑥 + 4

B. 7𝑥2 + 3𝑥 + 4

C. 7𝑥2 + 9𝑥 + 4

D. 7𝑥2 + 15𝑥 + 4

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40. The brace is 2.75 m long and must be anchored 1.5m from the base of the wall. What angle does the

brace make with the ground?

A. 27°

B. 33°

C. 57°

D. 61°

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41. In , UV = 8 m, , and . Determine the length of UT, to the nearest metre.

A. 9 m

B. 10 m

C. 11 m

D. 12 m

42. Bob is standing on a surveyors mark 25 m from the base of a building. He measures a 61° angle of

elevation to the top of the building. Bob is 1.8 m tall. How tall is the building to the nearest metre?

A. 23

B. 25

C. 45

D. 47

43. Calculate the length of YZ.

A. 16.06cm

B. 16.45cm

C. 19.61cm

D. 22.94cm

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PART B: Written Answer Questions

Use the following graph to answer question 44.

44. Determine the value of 𝑥 if 𝑓(𝑥) = −2

45. When (√𝑥34)(√𝑥108

) is written as a single power of x, what is the exponent?

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46. The point (6, 𝑦) is on a line that is perpendicular to the line 𝑦 = 2

3𝑥 + 4 , with a y-intercept of −2.

What is the value of 𝑦?

47. Carrie and Joel plan to sell pies at the county fair for $6 each. The ingredients used to make the pies

cost $3.75 per pie. They rent an oven for $54 to keep the pies hot throughout the day. How many pies

must Carrie and Joel sell in order to break even?

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48. Janelle and Mandeep are standing on opposite sides of a cell phone tower. Janelle is standing 105m

from the tower. Her angle of elevation to the tower is 23°. Mandeep’s angle of elevation to the top of

the tower is 36°. How far from the base of the tower is he standing? Answer to one decimal place.