Math10 Final Exam

For each multiple choice question, identify the correct letter. For each numerical response question, record your answer.

Use this information to answer #1.

A beginning skier practises by making turns around flags on a ski hill. The flags are spaced 2 m apart.

1. If there are 8 flags, what is the approximate distance that the skier travelled, to the nearest foot?

A 42 ft    B 46 ft    C 48 ft    D 52 ft

2. A trail map for a wall in the ski patrol of" ce is 8 2/1 ft long. If 7 in. of white border needs to be cut off, what is the " nal length of the trail map?

A 7′11″    B 7′5 ″    C 87 ″    D 84 ″

Use this information to answer #3.

A ski hill has a slope of 20/7.

3. What is the vertical distance, v ?

A 40 m    B 110 m    C 280 m    D 320 m

Use this information to answer #4.

A krumkake is a Norwegian cookie sold in ski resorts. It is baked in a krumkake iron and then rolled around a wooden cone. The cone has a diameter of 2 in. and a slant height of 6 in. The cookie covers only the lateral surface and not the circular base of the cone.

4. What is the minimum amount of cookie dough needed to cover the lateral surface of the cone, to the nearest square inch?

A 19 in.2    B 21 in.2    C 29 in.2    D 30 in.2

Use this information to answer #5.

At a winter sports event, one ice sculpture shaped like a hemisphere has a radius of 2.8 m.

5. What is the volume of the ice sculpture, to the nearest cubic metre?

A 46 m3    B 49 m3    C 92 m3    D 98 m3

Use this information to answer #6 to 8.

Freestyle. skiers train by skiing up a specially constructed ramp toward a jump. The ramp can be lengthened, creating two right triangles.

6. What is the height of the short ski ramp, x, to the nearest inch?

A 6 in.    B 9 in.    C 14 in.    D 16 in.

7. What is the measure of ∠θ, to the nearest degree?

A 30°    B 35°    C 55°    D 60°

Numerical Response

8. What is the length of the long ramp, y, to the nearest inch?

Use this information to answer #9.

Satellites transmit sports events around the world. When a satellite is h kilometres above Earth, the time, t, in minutes, that it takes to complete one orbit is given by the formula

9. How long would it take a satellite that is 28 km above Earth to orbit our planet twice? Express the answer to the nearest minute.

A 66 min    B 85 min    C 132 min    D 170 min

Use this information to answer #10. Circles are painted into the ice surface of a rink for a curling bonspiel.

10. Which algebraic expression represents the surface area of the shaded region?

A 4πr    C π(4r2 – 4)    B 4π(r – 1)    D π(4r2 – r + 40)

Use this information to answer #11 and 12.

The manager of a snack bar in the ski chalet used a table of values to determine how many people (p) need to buy each of two types of sausages for the costs (C) of the sausages to be equal.

Numerical Response

11. How many customers for sausages are needed for the costs to be the same?

12. Which system of equations representsthe table of values?

A C1 = 2/–1p – 4    B C1 = 2/–1p + 4

   C2 = 4/–3p – 5       C2 = 4/–3p + 5

C C1 = 2/1p – 4      D C1 = 2/1p + 4

    C2 = 4/3p – 5        C2 = 4/3p + 5

Use this information to answer #13 and 14.

The cross-country ski team stores ski waxes in a box.

13. What is the simpli" ed expression for the volume of the box?

A x(4x + 1)(3x + 2)

B 7x2 + 3x3

C (3x3 + 2x)(4x + 1)

D 12x3 + 11x2 + 2x

Numerical Response

14. If x = 20 cm, what is the volume of the box, to the nearest tenth of a cubic metre?

Use this information to answer #15.

Short track speed skaters train on an oval ice rink.

15. What are the domain and the range of the oval?

A domain: x = – 4, 3; range: y = 4, –2

B domain: [– 4, 3]; range: [4, –2]

C domain: {x | – 4 ≤ x ≤ 3; x ∈R}; range {y | –2 ≤ y ≤ 4; y ∈R}

D domain: {– 4, 3}; range: {4, –2}

16. Which graph of a relation is not a function?

17. The general form. of a line is given as 3x + 6y + 12 = 0. What are the intercepts?

A The x-intercept is – 4. The y-intercept is –2.

B The x-intercept is –3. The y-intercept is –6.

C The x-intercept is 3. The y-intercept is 6.

D The x-intercept is 4. The y-intercept is 2.

Use this information to answer #18 and 19.

The factor tree shows the prime factorization of x.

18. What is the value of x3/1?

A 2    B 3    C 6   D 9

Numerical Response

19. What is the value of x?

20. Simplify, then evaluate [(4/3)-5 ÷ (4/3)3]-1.

A (4/3)8/1    B 4/3    C 16/9    D 10/1

Use this diagram to answer #21.

21. Which of the following square roots of perfect squares is represented by the shaded region?

A 2 B 5 C 7 D 9

Numerical Response

22. If p(x) = 2x3 + x2 – 5x + 3, what is the value of p(–2)?

Use this key to interpret the algebra tile models in #23.

The same tiles unshaded represent negative quantities.

23. Which model represents the product of (x + 4)(x +2)?

24. Given the linear equation y = 2x + 7, which of the following statements is correct?

A The linear function f (x) = 2x + 1 is parallel to y = 2x + 7.

B The line joining (–2, 3) and (0, 4) is parallel to y = 2x + 7.

C The slope of a line perpendicular to y = 2x + 7 is m = –2.

D The y-intercept of y = 2x + 7 is 2.

25. Amelie simpli" ed (x + a)(x + b), where a and b are > 0, to the form. x2 + mx + n. Which statement about m and n is true?

A m < 0 and n > 0

B m < 0 and n < 0

C m > 0 and n < 0

D m > 0 and n > 0

Use this number line to answer #26.

26. Which of the following correctly describes the number line?

A {n | –1 ≤ n ≤ 5, n ∈R}

B {n | –1 < n < 5, n ∈I}

C [–1, 5], n ∈I

D {–3, –2, –1, 0, 1, 2, 3, 4, 5}

Use this number line to answer #27.

27. Which of the following correctly describes the number line?

A – 6 < x < 4

B – 6 ≤ x < 4

C [– 6, 4]

D (– 6, 4)

28. What is √48 as an equivalent mixed radical?

A 4 √6    B 4 √3    C 4 3√3    D 2 √3

29. What is (3a2 ) 3 (4a3 ) 0 simplified?

A 9a6    B 27a6    C 36a8    D 108a9

30. Which ordered pair represents f (7) = –3?

A (–7, 3)    B (–3, 7)    C (3, 7)    D (7, –3)

31. What is the equation y = 7/x – 6 expressed in general form?

A x – 7y – 6 = 0

B x – 7y – 42 = 0

C 7x – y – 6 = 0

D 7x – 7y – 42 = 0

32. Which expression represents (4x – 5)2 expanded and simpli" ed?

A 16x2 + 25

B 16x2 – 25

C 16x2 + 40x + 25

D 16x2 – 40x + 25

Use this information to answer #33.

Melanie expanded and simplified (x – 2)(x2 + 4x + 4). Her work was as follows:

(x – 2)(x2 + 4x + 4)

= x (x2 + 4x + 4) – 1(x2 + 4x + 4) Step 1

= x3 + 4x2 + 4x – x2 + 4x + 4 Step 2

= x3 + 3x2 + 8x2 + 4 Step 3

= x3 + 11x2 + 4 Step 4

33. Melanie has errors in

A Step 1 and Step 2

B Step 1 and Step 4

C Step 1, Step 2, and Step 3

D Step 1, Step 3, and Step 4

34. Which set of numbers has rational numbers only?

A 2/–1 6.9 √25

B 2/1 –6  2/√3

C –3 4.17 4.121 314 15...

D √11 3 √7 π

Use this information to answer #35 to 37.

Numerical Response

35. What is the length of side AD, to the nearest tenth?

Numerical Response

36. The exact length of side EB can be written in the form. x √y . What is the value of y ?

37. The ratio for cos ∠B is

A 42/√20    B 4/2    C 2/√3    D √12/4

38. A right pyramid fits exactly into a cube with edge length 5 cm. Suppose that the dimensions of the solids are doubled. By what factor would the volumes of the pyramid and the cube increase?

A 2    B 4    C 6    D 8

Use this information to answer #39 and 40.

Safe Transport has a fleet of delivery trucks. Two trucks leave the truck yard at the same time. Truck A travels north at 40 km/h and Truck B travels east at 60 km/h.

Numerical Response

39. How far apart are the two trucks after 1 h, to the nearest kilometre?

40. The shortest distance from a point to a line can be determined by drawing a perpendicular line. If the slope of the line shown is –2/3, what is the equation of the perpendicular line through the point at the truck yard?

A y = 3/–2x + 20    B y = 2/–3 x + 20

C y = 2/3x + 20   D y = x + 20

Use this information to answer #41.

The U Move company’s daily revenue can be represented by the function R(t) = 210t – 550, where t represents the number of trucks rented.

41. To ensure U Move earns daily revenue, what is the minimum number of trucks that must be rented?

A {t | t ≥ 3, t ∈I}

B {t | t > 3, t ∈R}

C {t | t ≤ 3, t ∈R}

D {t | t < 3, t ∈I}

Use this information to answer #42.

The owner of U Move decided to expand the truck yard. He purchased three smaller square " elds, each with area A, and two larger square " elds, each with area B.

42. Which simpli" ed radical represents length l ?

A 5 √AB

B 5 √A +B

C 3 √A + 2 √B

Use this information to answer #43 and 44.

U Move sends out a ! yer advertising cardboard boxes.

The dimensions of the storage compartment in a U Move truck are shown.

43. The correct order of the boxes from least to greatest volume is

A 1, 2, 3, 4

B 2, 1, 3, 4

C 4, 2, 1, 3

D 4, 3, 2, 1

44. If only one type of box is used to " ll the truck, which one will waste the least amount of space?

A Box 1

B Box 2

C Box 3

D Box 4

Use this information to answer #45.

A truck repair business uses a laser beam security system.

Numerical Response

45. What angle does the laser beam form. with the garage oor, to the nearest degree?

Written Response

You will need one sheet of grid paper.

Use this information to answer #46a) and b).

Marmot Basin ski resort in Jasper, Alberta, has the longest high-speed quad chair in the Canadian Rockies. The Canadian Rockies Express takes skiers up a vertical height of 600 m in 8 min.

Use this information to answer #46c).

Jim is on a ! at part of the ski hill looking up at the chairlift passing overhead.

46. a) Assume that the quad chair moves at a constant speed. What is the rate of change for height and time?

b) Sketch the shape of the graph representing the relationship between height and time.

c) How far apart are the chairs, to the nearest foot? Justify your answer mathematically

Use this graph to answer #47.

Kelly is driving home from a figure skating event. The graph represents changes in speed during the trip.

47. Describe a possible reason for the changes in speed at each stage.

Use this information to answer #48.

A company introduces a new product, B2, which it expects will sell well. The company plans to discontinue selling an older product, B1, over a short period of time. Assume that the daily sales of both products are constant. The situation can be represented using a system of linear equations.

B1: 3m + 2/3P = 6

B2: P = 3m – 1

In the equations, P represents pro" t, in thousands of dollars, and m represents the number of months of sales.

Use this information to answer #48e).

In his " rst attempts, the business manager records the following systems of equations to represent the two products.

Trial 1

B1: 2/–3m = –3P + 4.5

B2: 2m – 4P = – 6

Trial 2

B1: 3m = 5/6P + 2

B2: 5/1P = 2/1m –3/2

48. a) Solve the system graphically. Label the lines as B1 and B2.

b) Verify your solution algebraically.

c) After how many months can product B1 be discontinued?

d) Explain the meaning of the y-intercept for B2.

e) The manager realizes that these systems of equations do not provide the needed solutions. Explain how many solutions each system has. Give a reason why the solutions cannot be applied to new product sales.

49. Simplify. Show your work.

50. Simplify. Show your work.

51. Evaluate.

52.Mason had $40 in his bank account when he started to save $15 each week.

a) Write an equation to represent the total amount, A dollars, he had in his account after w weeks.

b) After how many weeks did Mason have $355 in his account?

c) Suppose you graphed the equation you wrote in part a. What would the slope and the vertical intercept of the graph represent?

53.Write an equation for the line that passes through each pair of points. Describe your strategy.

i) G (– 3, – 7) and H(1, 5)                   ii) J(– 3, 3) and K(5, – 1)

54.Two families went on a traditional nuuchahnulth dugout canoe tour in Tofino harbour, B.C. One family paid $220 for 5 people. The other family paid $132 for 3 people.

a) Choose variables, then write an equation for the cost as a function of the number of people.

b) What is the cost per person? How can you determine this from the equation?

c) A third family paid $264. How many people went on the tour?

55. The total revenue from sales of ski jackets can be modelled by the expression Revenue R = 720 + 4x − 2x2 , where x represents the number of jackets sold above the minimum needed to break even. Revenue is also calculated as the product of the number of jackets sold and the price per jacket. Factor the given expression to determine the number sold and the price per jacket. The minimum price of a jacket is $18. Hint: As the price increases, the number sold decreases.

56.A square has an area of 9x2 + 30xy + 25y 2 square centimetres. What is the perimeter of the square?

57.Which sets of ordered pairs represent linear relations? Explain your answers.

a) {(1, 5), (5, 5), (9, 5), (13, 5)} b){(1, 2), (1, 4), (1, 6), (1, 8)} c){(– 2, – 3), (– 1, – 2), (2, 1), (4, – 3)}

58. A fire ranger is at the top of a 90-ft. observation tower. She observes smoke due east at an angle of depression of 5° and due west at an angle of depression of 4°. How far apart are the fires to the nearest foot? The diagram is not drawn to scale.

59. Carl is standing 10 km from town A and 10 km from town B. From where he stands, the angle between the two towns is 37o .A new hotel has just been built on the road connecting town A and town B, exactly halfway between the two towns. From where Carl is standing, he sees that the angle of elevation to the top of the hotel is 1o . Determine the height of the hotel to one decimal place. Include a diagram with your solution.

60. Drew θ = 260° in standard position. What is its reference angle?

61. Given cosθ = − 7/4, in quadrant 3, what is the exact value of tanθ?

62. Let (−8,1) be a point on the terminal arm of δ, 0 ° ≤ δ < 360° .

a) State sinδ, as an exact value.

b) Determine δ.

63. Kelly observes the top of a hill at an angle of elevation of 40° . He then walks 100m closer and observes the summit at an angle of elevation of 50° . Determine the height of the hill.

64. Jill is in a hot air balloon 350m above the ground. She notes that the angle of depression to a distant home is 25° . From this same home, Jack sees Jill’s balloon and a cloud, directly above Jill. He measures the angle of elevation to the cloud at 42° . How long would it take for Jill to reach the cloud if she is ascending at 2 m/s?

65. Given an arithmetic sequence with S5 = 130 and t7 = 14, algebraically determine d.

66. Evaluate 59 + 78 + 97 + ⋯ + 1617

67. For a given arithmetic series, the sum of the first 50 terms is 200 and the sum of the next 50 terms is 2700.Determine the first term.