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Date: _______________________________
Mathematics 10 Option 2
Final Exam Multiple Choice and Numerical Response
Record your answers on the answer sheet provided.
A lot of the tools and equipment used in everyday life and in recreational activities were designed using
mathematical measurements and calculations. Apply your knowledge and skills of mathematics to solve
problems related to tools and equipment.
Use this information to answer #1.
Jack’s parents rented a Teardrop camper trailer for an affordable summer vacation. A model of the trailer has
the dimensions shown.
food
storage
2 cm
stove
refrigerator
double bed
water
4.5 cm
2.5 cm
1. If 1 cm = 24 in., what are the dimensions of the camper trailer?
A 60 ft by 108 ft by 48 ft
B 5 ft by 96 in. by 48 in.
C 5 ft by 9 ft by 4 ft
D 5 in. by 9 in. by 4 in.
Use this information to answer #2.
The dimensions of a different model of teardrop camper trailer
are 4 ft by 4 ft by 8 ft. To determine the approximate volume
of the trailer, Kristi divided the trailer into a triangular right
prism, a rectangular right prism, and a hemisphere.
d = 4 ft
4 ft
4 ft
3 ft
5 ft
2. If 1 ft3 ≈ 0.0283 m3, what is the approximate volume of the trailer, to the nearest cubic metre?
A 2 m3
B 3 m3
C 4 m3
D 5 m3
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Use this information to answer #3.
The manufacturer of a fuel-efficient car decides to promote the brand. The ad includes data about the fuel
consumption rating for this brand and one other brand.
Brand A: 66 mi/gal
Brand B: 4.8 L/100 km
Hint: 1 mi = 1.609 km.
3. If 1 gal ≈ 3.785 L, what is the approximate difference in the fuel consumption rating for the two vehicles?
A 3 L/100 km
B 1.2 L/100 km
C 0.1 mi/gal
D 10 mi/gal
Use this image to answer #4.
4. What is an appropriate referent for measuring the length of the car?
A a ball of string
B a paper clip
C a pencil
D a shoe lace
Use this information to answer #5.
Stella’s family purchases a trampoline with a safety net around the
outer edge. The net prevents users from bouncing over the edge.
d = 9 ft
5. The surface area of the safety net is 195 ft2. What is the approximate height of the net, to the nearest
tenth of a metre?
A 2m
B 2.4 m
C 3.5 m
D 5.2 m
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Use this information to answer #6–8.
Martin is building a shed to store his dirt bike. He decides to purchase
doors at a later date. The opening for the doors is in the centre of
the wall and measures 7.5 ft wide by 6 ft high.
18 in.
7 ft
6.5 ft
10 ft
6. What is the approximate amount of siding needed to build the shed, excluding the doors? Include the roof.
B 269 ft2
C 144 ft2
D 119 ft2
A 355 ft2
Numerical Response
7. What is the pitch of the roof, to the nearest hundredth? Note: The pitch refers to the slope of the roof.
Numerical Response
8. What angle does the roof form with the panel above the front wall, to the nearest degree?
Use this information to answer #9–10.
A surveyor collects data to determine the height of an office tower.
64°
7m
1.68 m
Numerical Response
9. What is the height of the building, to the nearest tenth of a metre?
10. Suppose that the surveyor moved 3 m farther back. He determined that the height of the building from his
new location was 15 m. What is the new angle of elevation?
A 29°
B 31°
C 53°
D 56°
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Use this information to answer #11.
Community volunteers have staked off an area in the park for a prairie garden.
26 m
10 m
x
32°
11. What is the length of x, to the nearest metre?
A 49 m
B 45 m
C 36 m
D 16 m
Use this information to answer #12–13.
The Pinto family took a road trip across Canada.
The graph shows one day during their trip.
d
Total Distance Travelled (km)
800
D
600
E
C
B
400
A
200
0
8:00
a.m.
10:00
12:00
p.m.
2:00
4:00
6:00
8:00 t
Time of Day
12. Which statement about segment C is correct?
A The car is at rest.
C The car travelled at its highest average speed.
B The car travelled 600 km.
D The car travelled at its lowest average speed.
13. Which statement about segment D is correct?
A The car is at rest and the slope of the line is 0.
B The car is at rest and the slope of the line is undefined.
C The car travelled 600 km and the slope of the line is 2.
D The car travelled 600 km in 2 h.
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Use this information to answer #14.
1
Jaspreet is 5 __2 ft tall and casts an 8-ft shadow. The pole supporting a basketball hoop is 12 ft high.
12 ft
5.5 ft
8 ft
y
14. How long is the shadow that the pole casts, to the nearest tenth of a foot?
A 8 ft
B 14.5 ft
C 17.5 ft
D 19 ft
Use this information to answer #15–16.
A carrying case for sports equipment has a surface area of 18 m2.
x
Numerical Response
15. What is the length of x, to the nearest tenth of a metre?
16. A proportionally smaller box has a volume of 16 m3. What is an exact value for the length of side x?
__
__
__
__
3
3
A 4 √2
B 3 √2
C 2 √2
D 2 √2
Use this information to answer #17.
A boat rental company uses the function A(n) = 20n - 400 to represent the revenue from rentals. In the
equation, A(n) represents the amount of money, in dollars, and n represents the number of rentals in a day.
Numerical Response
17. If the boat rental revenue is $6000, how many boats were rented?
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Use this information to answer #18–19.
Avi is making an open cardboard box. The bottom of the box has
dimensions 14 cm by 20 cm. The directions say to cut out the square
pieces marked x, as shown, and then fold up the sides to form the box.
20 cm
x
x
x
x
x
x
14 cm
x
x
18. Which expression for the volume of the box is correct?
A V = x(14)(20)
B V = x(14 - x)(20 - x)
C V = (14 - x)(20 - 2x)
D V = x(14 - 2x)(20 - 2x)
Numerical Response
19. If x is 6 cm, what is the volume of the box?
Use this information to answer #20–22.
The Malcolms are renting a farm house. Mr. Malcolm needs a
ladder that reaches the roof in order to rescue the family’s cat.
Wall
B
Wall A
23 ft
floor
20.7 ft
x
20. How far away is the foot of the ladder from the house, to the nearest foot?
A 1 ft
B 10 ft
C 15 ft
D 25 ft
21. Wall A is parallel to Wall B. What slope do these two walls have?
A undefined
B 1
C0
D -1
22. Which statement about the slopes of Wall B and the floor is correct?
A The product of the slope of Wall B and the floor is 1.
B The slope of Wall B is -1 and the slope of the floor is undefined.
C The slope of Wall B is undefined and the slope of the floor is 0.
D The slopes of Wall B and the floor are undefined.
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Use this information to answer #23.
The hot water heater in the farm house is shown.
d = 30 in.
6 ft
Numerical Response
23. What is the volume of the hot water heater, to the nearest tenth of a cubic foot?
24. The hot water heater can be drained at a constant rate of 1 ft3/min. The slope of the graph is
A 0
B negative
C positive
D undefined
Use this information to answer #25–26.
Chris decides to go biking on a trail.
d
Distance From Campsite (km)
50
40
30
20
10
0
11:00
a.m.
12:00
p.m.
1:00
2:00
3:00
4:00
5:00
6:00
7:00
8:00 t
Time of Day
25. When did Chris cover the greatest distance in the shortest time?
A from 7:00 p.m. to 8:00 p.m.
B from 3:30 p.m. to 5:00 p.m.
C from 2:00 p.m. to 2:30 p.m.
D from 11:00 a.m. to 12:00 p.m.
26. What is the domain of the graph?
A 0 ≤ x ≤ 2.5
B 0≤x≤5
C 0≤x≤7
D 0≤x≤8
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Use this information to answer #27.
Sprint skiers rely on markers to mark the path for a race. The markers, which
are shaped like right pyramids, are filled with sand and partially buried in the
snow. One marker is shown.
h = 12 in.
9 in.
6 in.
Numerical Response
27. To the nearest cubic inch, how much sand can the marker hold when filled?
Use this information to answer #28.
You order one scoop of chocolate ice cream. The exposed part of the scoop
of ice cream forms a perfect hemisphere.
r = 4.5 cm
15 cm
28. What is the exposed surface area of the scoop of ice cream and the cone, to the nearest square centimetre?
B 289 cm2
C 339 cm2
D 403 cm2
A 110 cm2
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Use this information to answer #29–30.
The graph shows the path of a soccer ball kicked into the air.
d
16
Height (m)
12
8
4
1
0
2
3
4
5
6
7
8
t
Time (s)
29. Which statement is true?
A The soccer ball reaches a minimum height at 8 s.
B The soccer ball reaches a minimum height at 4 s.
C The soccer ball reaches a maximum height at 5 s.
D The soccer ball reaches a maximum height at 4 s.
30. When is the soccer ball at rest?
A 0 s and 4 s
B 0 s and 5 s
C 0 s and 6 s
D 0 s and 8 s
Connections
Many of the concepts that you study in mathematics are related and can help you solve different kinds of
problems. Connect the concepts and skills you have learned to solve problems.
31. Which of the following is an irrational number?
___
A 4 -2
B (0.5)2
C √54
___
4
D √81
Use this information to answer #32.
Compare the following expressions.
-4 7
9
5 6
1
2
3
4 3 -3 17
4
5
32. Using the numerals 1 to 5, what is the correct order of the expressions from least to greatest value?
A 5, 1, 4, 2, 3
B 5, 1, 2, 4, 3
C 1, 5, 2, 4, 3
D 1, 5, 4, 2, 3
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33. Brent simplified (x + a)(x + b), where a < 0, b > 0, and a + b > 0, to the form x 2 + 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 the SI caliper to answer #34.
0
10
20
30
40
mm
0.1 mm
0
5
10
Numerical Response
34. What is the reading on the caliper, to the nearest tenth of a millimetre?
Numerical Response
35. If tan θ = 0.3512, what is the measure of θ, to the nearest tenth of a degree?
36. What is the greatest common factor of 4x5y 2, 12x 3y 2, and 6x 2y 4?
A 12x 5y 4
B 4x2y
C 3x2y 2
D 2x 2y 2
37. Which expression is a factor of x 2 - 9x - 36?
A x-3
B x-4
C x-6
D x - 12
__
√x5
__ , when simplified is
38. The expression, ___
3
√x2
8
__
5
A √x
__
B √x2
2
6
___
C √x11
__
D √x3
0
39. What is (4a3) (12a2) when simplified?
A 48a7
B 16a6
C 8a6
D 6a5
40. A line passes through (3, -2) and is perpendicular to the line segment going through (3, 2) and (-3, -4).
What is the equation of the line in slope-intercept form?
2
1
1
A y = -x - 5
B y = __3 x + __3
C y = -x + 1
D y = __2 x - 2
3
41. What is the equation y = __2 x + 7 written in general form?
-3
x-7+y=0
A ___
2
B 3x + 2y + 7 = 0
3
C __2 x - y + 7 = 0
D 3x - 2y + 14 = 0
42. What is the y-intercept of 3x - 4y = 7?
-7
A -4
B -3
C ___
4
4
D __7
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Use this diagram to answer #43.
y
II
I
x
0
III
IV
43. In which quadrant do the graphs of x = -4 and y = 3x + 2 intersect?
A quadrant I
B quadrant II
C quadrant III
D quadrant IV
Use this information to answer #44.
Maria was given the equation 2x + 4y = -8. She made the following conclusions:
1 The y-intercept is 2.
2 The range is all real numbers.
3 The line is parallel to y = ___
x.
2
-1
4 The equation of the line in slope-intercept form is y = ___
x + 2.
2
44. Which conclusions are correct?
A 1 and 4
B 1 and 3
-1
C 2 and 3
D 3 and 4
45. What is the slope of a line with a run of 6 and a rise of -15?
6
A __
15
2
B __5
-5
C ___
2
-15
D ____
1
46. If y = -3x + 7, what are the coordinates of the point on the line when x = -2?
A (-2, 13)
B (1, 13)
C (13, -2)
D (13, 1)
47. What is the value of m in the linear equation 2m - 3m(2m - 4) = -2m(3m - 8) + 2?
A 8
B 4
C -1
D -4
48. What is the equation E = mc2 expressed in terms of c?
A c=E-m
______
B c = √E - m
__
m
__
C c = √E
__
E
D c = √__
m
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Use this diagram to answer #49–51.
y
10 mm
z
50 mm
θ
80 mm
49. What is the length of z, to the nearest millimetre?
A 89 mm
B 94 mm
C 110 mm
D 130 mm
Numerical Response
50. The length of y, to the nearest millimetre is
51. What is the measure of angle θ, to the nearest degree?
A 32°
B 41°
C 56°
D 68°
Use this information to answer #52.
The path that a volleyball takes as it travels from one end of the court to the other end can be represented by
h(d) = -0.03d 2 + 0.3d, where h is height and d is the distance the ball travels.
52. Which ordered pair satisfies the function h(6) = 0.72?
A (0.72, 6)
B (0.72, 3)
C (6, 0.72)
D (3, 0.72)
Numerical Response
53. What is the edge length of a cube with surface area 54 cm2?
Use this diagram to answer #54.
A paperweight has the shape of a right pyramid with slant heights of 8.5 cm
and 9.5 cm.
9.5 cm
8.5 cm
9 cm
10 cm
54. What is the surface area of the paperweight, to the nearest tenth of a square centimetre?
B 260.5 cm2
C 261.5 cm2
D 297 cm2
A 170.5 cm2
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Use this graph to answer #55.
The graph shows a set of line segments.
y
A
B
C
D
0
x
E
F
55. Which line segments have a positive slope?
A line segments A and B
B line segments A, B, and D
C line segments A, C, and F
D line segments D and F
56. Given that 4x - By - 3 = 0 passes through point (2, 1), what is the value of B?
A -8
B -5
C5
D 8
Use this information to answer #57–58.
The prime factorization of a number, x, is 3 × 3 × 2 × 2 × 2 × 2 × 5 × 5 × 3 × 2 × 2 × 5.
Numerical Response
57. What is the cube root of x?
Numerical Response
2
__
58. What is the value of x3?
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Use this graph to answer #59–60.
The graph shows a linear system.
y
8
6
4
2
-6
-4
-2
0
2
4
x
-2
59. Which point is the solution to the linear system?
A (-5, 0)
B (1, 5)
C (3, 0)
D (5, 1)
60. Which linear system does the graph represent?
A y = -x + 4 and y = -2x + 7
B y = -x + 4 and y = 2x + 4
C y = x + 4 and y = 2x + 4
D y = x + 4 and y = -2x + 7
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Mathematics 10 Option 2
Final Exam Written Response
Write your response in the space provided. Present your response in a well-organized way,
using complete sentences and correct units.
Use this information to answer #1a)–c).
The Johnsons are building a children’s play structure in their backyard.
l
14.7 ft
10 ft
5 ft
7 ft
65°
x
climbing
ramp
1. a) Assume that the play structure is drawn to proportion. Determine the length of l.
b) What is the length of x, to the nearest tenth of a foot? to the nearest inch?
c) How long is the climbing ramp, to the nearest inch? to the nearest hundredth of a metre?
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Use this information to answer #1d)–e).
The house on the play structure has three sides
closed in, each with an identical window.
3 ft
2 ft
1 ft
3 ft
4 ft
open
area
1 ft
3 ft
d) Determine the amount of stain needed to treat the exterior of the house, including the roof. Show
your work.
e) If 1 can of stain covers 45 ft 2, how many cans of stain are needed?
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Use this information to answer #2a).
A water fountain that looks like a sailboat is installed on a
playground. The hull and the mast fill with water and then water
sprays down the surface of the boat into a basin.
mast
hull
2. a) Assume the scale is 1 cm = 30 cm. If the diagram were 9 cm in height, what would be the height
of the fountain, to the nearest tenth of a metre?
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Use this information to answer #2b–d).
Each component of the water fountain is shown. The base of the water fountain is shaped like a right prism.
d = 20 cm
2.7 m
Sail A
1.9 m
1.8 m
Sail B
mast
15 cm
0.75 m
0.8 m
d=2m
15 cm
hull
0.5 m
1m
1.2 m
base
b) Determine the volume of water that the mast and the hull can hold, to the nearest tenth of a cubic
metre. Show your work.
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c) What is the volume of each sail? Express each answer to the nearest hundredth of a cubic metre.
Show your work.
d) Determine the amount of stainless steel used to make the top and the sides of the base, to the nearest
tenth of a square metre. Show your work.
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Use this information to answer #3.
Cam and David exchanged solutions with those of another group. They were asked to check the work,
correct any errors, and explain the error and correct solution. Write the response that Cam and David should
develop for each problem.
3. a) Problem: What reading is shown on the caliper?
0
10
20
30
40
mm
0.1 mm
0
5
10
Solution: The reading on the caliper is 1.74 mm.
b) Problem: Determine the area of a park with dimensions 36 ft by 89 ft.
Solution: The park has an area of 1068 yd2.
c) Problem: On a car trip, the Lee family travelled 200 mi in 3 h. What is this distance in kilometres
per hour?
Solution: This distance is approximately 108 km/h.
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d) Problem: What is the value of x?
60 cm
49°
47°
x
Solution:
60
60
sin 49° = __
x
sin 47° = __
x
60
______
60
______
sin 49°
=x
sin 47°
x = 80
80 + 82 = 162
The value of x is 162 cm.
=x
x = 82
e) Problem: Solve the system of linear equations graphically.
–4x – y – 5 = 0
x–y–2=0
Solution:
y
6
-4x - y - 5 = 0
4
2
-4
-2
0
-2
2
4
6
x
x-y-2=0
-4
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