Review Final #2 – Foundations of Math and Pre-Calculus 10 Name:

PART A: MULTIPLE-CHOICE QUESTIONS (calculator not permitted)

Value: 5 marks Suggested Time: 12 minutes Allowable Time: 17 minutes

INSTRUCTIONS: No calculator may be used for this part of the examination. For each question, select the best answer and record your choice on the blue Answer Sheet provided. Using an HB pencil, completely fill in the bubble that has the letter corresponding to your answer. You have a maximum of 17 minutes to work on this section.

1. Determine the equation of the line, in slope-intercept form that passes through (6, 5) and (-9, -5).

A. 7+= xy

B. 13

2+= xy

C. 42

3−= xy

D. 7+−= xy

2. The equation of AB is x – 2y + 4 = 0. AB intersects the y-axis at C. CD is perpendicular to AB. The equation of CD is:

A. x + 2y – 2 = 0

B. 2x + y – 2 = 0

C. 2x – y + 2 = 0

D. 2x + y – 4 = 0

0 x

y

A

C

B D

-10 -5 5 10

-10

-5

5

10

x

y

Use the following graph to answer question 3.

3. Which of the following equations describes the linear relation graphed above?

I.

51

3y x= − +

II.

( )5

4 33

y x+ = +

III.

5x – 3y – 3 = 0

A. II only

B. I and II only

C. I and III only

D. II and III only

Dis

tan

ce f

rom

Bik

e S

ho

p (

km

)

4. The graph below models a bicycle’s distance from a bike shop over time.

60

50 Q

40

30

P

20

10

0 1 2 3 4 5

Time (hours)

Calculate the average speed of the bike over the first five hours.

A. 5 km/h B. 11 km/h C. 12.5 km/h D. 20 km/h

5. The first equation of a linear system is –6x + 12y = –42. Choose a second equation to form a linear system

with no solution.

i) –6x + 12y = 126 ii) 18x – 36y = 126 iii) 18x + 12y = 126 iv) 18x + 36y = 0 A. Equation iv B. Equation ii C. Equation iii D. Equation i

This is the end of Part A (calculator not permitted).

If there is some time left, you have two options:

i) Make sure you have answered all the questions. You will not be able to go back to this section at the end of 17 minutes.

ii) You may proceed to the rest of the examination without the use of a calculator; there are many questions that do not require a calculator. Make sure you flag any questions you skip to remember to go back to them later.

Do not access your calculator until directed by the supervisor. At the end of the 17 minutes, the supervisor will give you permission to access your calculator.

PART B: MULTIPLE-CHOICE QUESTIONS (calculator permitted) Value: 29 marks Suggested Time: 55 minutes

INSTRUCTIONS: For each question, select the best answer and record your choice on the white

Answer Sheet provided. Using an HB pencil, completely fill in the bubble that has the letter corresponding to your answer.

6. Determine the slope of the graph 4x – 5y – 24 = 0.

A. 4

5−

B. 5

4−

C. 5

4

D. 4

5

7. Which of the following statements is false?

I. Two perpendicular lines have slopes that are reciprocals.

II. The product of the slopes of perpendicular lines is 1.

III. Vertical lines have an undefined slope.

IV. The x-intercept of y = -3x + 6 is 6.

A. I and II only B. I and IV only C. II, III and IV only D. I, II and IV only

8. If the slope of a ski hill is 3

1 and the coordinates of the bottom of the hill are (2, 5), what is the value of

y if the coordinates at the top of the hill are (8, y)?

A. 3

B. 7

C. 11

D. 23

9. Identify the line segment with m < 0, where m is slope.

10. The slope of an A-frame cottage is 5

2.

How high in meters is the peak of the cottage, given that the total width of the cottage is 20 m? A. 4 m B. 8 m C. 25 m D. 50 m

11. A line segment joins A(6, 2) and B(14, 12). What are the slope and y-intercept of the line perpendicular to AB and passing through the point (10, 7)?

12. Lines A and B are perpendicular and have the same x-intercept. The equation of line A is x + 2y – 6 =0. Determine the y-intercept of line B. A. –12 B. –6 C. 3 D. 6 13. A local drama production will make a profit of $200 if they sell 100 tickets. They will take a loss of

$120 if they only sell 60 tickets. Which linear relation represents their profit? A. y = 0.125x + 187.5 B. y = 0.5x + 150 C. y = 2x D. y = 8x – 600

14. Rewrite 2

53

y x= − + in general form.

A. 2

5 03

x y+ − =

B. 2x + 3y – 5 = 0 C. 2x + 3y – 15 = 0 D. 6x + 3y – 15 = 0

Slope y-intercept

A.

5

4−

-1

B.

5

4−

15

C.

4

5

5

D.

4

5

9

-5 5

-5

5

x

y

-5 5

-5

5

x

y

-10 -5 5 10

-10

-5

5

10

x

y

Use the following graphs to answer question 15.

15. Which of the following statements is true about the domain of the graphs shown above?

A. The domain of f(x) is greater. B. The domain of g(x) is greater. C. The domain of both graphs is equal. D. The relationship cannot be determined from the information given.

16. Which of the following statements about the graph is true?

A. The graph represents a relation. B. The graph represents a function. C. The graph is linear. D. The domain is all real numbers.

17. If ( ) 2 1f x x= − + , which of the following expressions is equal to ( )1+xf ?

A. 2 1x− −

B. 2 1x− +

C. 2 2x− +

D. 22 1x x− − +

f(x)

-5 5

-5

5

x

y

g(x)

18. Determine the range of the following graph:

A. y = -3

B. y ≥ -3

C. y ≤ -3

D. All real numbers 19. Which of the following represent(s) a function?

A. I and II only B. I and III only C. II and III only D. I, II and III only

I.

(-6, 2), (-4, 1), (-2, 0), (0, -1), (2, -2), (4, -3)

II.

( ) 122++= xxxf

III.

y

x

20. Consider the following expressions: Evaluate f(-3) and put the expressions in order from least to greatest. A. B. C. D. 21. Jo wants to hold a spring dance. It costs $500 to rent the school’s gym and it will cost an additional $5

per person who attends. Which of the following statements are true?

A. II and IV only B. I and III only C. I, II and IV only D. I, III and IV only

I. ( ) 2 4 2f x x x= − −

II. ( )1

143

f x x= +

III. ( ) 23f x x x= +

IV. ( ) 7 5f x x= −

Least Greatest

I II III IV

I II IV III

II I III IV

II I IV III

I. The data representing this function is discrete.

II. The data representing this function is continuous.

III. The rate of change represents the cost per person who attends.

IV. The equation representing total cost is the linear function C = 5n + 500, where C is the total cost and n is the total number of people.

5 10 150

200

400

600

800

0t

V

22. Determine the range of the relation graphed below. A. (-8, 6] B. [-8, 6) C. (-7, 4] D. [-7, 4) 23. The graph represents how the volume of water, in ml, being drunk from a glass changes with time, in

seconds. What does the x-intercept represent in this situation? A. water capacity of the glass B. total volume of water in the glass C. total time until the glass is empty D. number of milliliters drunk from the glass

per second. 24. Which of the following linear systems could model the following situation: The perimeter of an

isosceles triangle is 36 cm. The base, b, of the triangle is 9 cm longer than each equal side, s. A. s + b = 36 B. 2s + b = 36 C. 2b + s = 36 D. 2s + b = 36 b – 9 = s b + 9 = s s + 9 = b s + 9 = b

-10 -5 5 10

-10

-5

5

10

x

y

25. Which of the following linear systems could model the following situation: The difference of two numbers, x and y, is 6. Twice the larger number is three more than triple the smaller number.

A. x – y = 6 B. x – y = 6 C. y – x = 6 D. y – x = 6 3x – 2y = 3 2x – 3y = 3 3x – 2y = 3 2x – 3y = 3 26. Use the graph to approximate the solution of the linear system:

y = –5x + 11

y = 5x – 11

-8 -6 -4 -2 2 4 6 8

-4

-2

2

4

x

y

A. (2.2, 0) B. (0, 2.2) C. (0.2, 2) D. (2, 0.2) 27. Solve the linear system:

x – y = 18

3 3 15

4 4 2x y+ = −

A. (–14, –14) B. (4, 4) C. (4, –14) D. (4, 18) 28. Which of the following linear systems is equivalent to the following system?

3

5 142

x y+ =

5 755

56 6

x y+ =

A. 10x + 3y = 1 B. 3x + 10y = 28 C. 10x + 3y = 28 D. 10x + 3y = 28 5x + 30y = 1 5x + 30y = 755 30x + 5y = 755 5x + 30y = 755

29. The solution of this linear system is (3, y). Determine the value of y.

1

3 52

x y− =

1 1

33 4

x y+ =

A. –8 B. –2 C. 2 D. 8 30. Solve the linear system: Frieda has a 30% silver alloy and a 80% silver alloy. Frieda wants to make 50

kg of an alloy that is 60% silver. How much of each alloy does she need? A. 30 kg of 30% silver alloy B. 20 kg of 30% silver alloy 20 kg of 80% silver alloy 30 kg of 80% silver alloy C. 78.8 kg of 30% silver alloy D. 20 kg of 30% silver alloy 28.8 kg of 80% silver alloy 70 kg of 80% silver alloy 31. Determine the number of solutions of the linear system:

5x + 7y = 76 –25x – 35y = –380

A. 2 solutions B. one solution C. infinite solutions D. no solution 32. Two lines in a linear system have the same slope, but different y-intercepts. How many solutions does

the linear system have? A. 2 solutions B. no solution C. infinite solutions D. one solution 33. For what value of k does the linear system below have infinite solutions?

2

163

x y+ =

2 32kx y+ =

A. 0 B. 2

3 C.

4

3 D. 32

PART C: NUMERICAL-RESPONSE QUESTIONS

(calculator permitted)

Value: 4 marks Suggested time: 8 minutes

34. The line 3x + 2y + 6 = 0 intersects the y-axis at P. Calculate the slope of the line joining P to Q(6, –2).

Answer to two decimal places.

Record your answer neatly on the Response Form. 35. Determine the y-value for the intersection of the following system:

7

348

x y+ = −

3 4 4x y− + = −

Record your answer neatly on the Response Form. 36. Bill and Sandy can paddle their canoe with a speed of 7 km/h without the current. They set off from

their camp, in their canoe, traveling with the current, and it takes them 20 minutes to reach an island. On the way back they are paddling against the current. After 24 minutes they stop for a rest and they are 1 km away from their camp. The speed of the current and the distance from their camp to the island are both unknown. Determine the speed of the current, in km/h.

Record your answer neatly on the Response Form.