Ms. Collins
Extra Credit Assignment
MPM2D 2011
1. Select the system or systems of equations that has (–2, 2) as a solution.
II –2x + y = 6
–x + y = 4
I 3x + y = 1
2x + 3y = –11
(a) I only
(b) II and III only
III x + y = 0
x–y=4
(c) II only
(d) I and III only
2. Marco saves dimes and quarters in a jar. Select the expression that shows the total
value in pennies, if d represents the number of dimes and q represents the number of
quarters.
(a) 2d + 5q
(b) 5(d + q)
(c) 5dq
(d) 10d + 25q
3. Clive is training to run the Starlight Marathon. To train, he runs and walks a total of
18 km. He runs 2 km more than twice as far as he walks. Select the system of
equations that can be solved to find the distance he walks, w, and the distance he runs,
r.
(a) w + r = 18
(b) w + r = 18
r = 2w – 2
r + 2w = 2
(c) w + r = 18 r = 2w + 2
(d) 2w + r = 16 r = 2w – 2
4. Draw the following lines and select the point whose ordered pair is a solution.
1
One line has a slope of 2 and the y-intercept is –1.
The other line has a slope of –1 and the y-intercept is 5.
(a) A
(b) B
(c) C
(d) D
5. Select the value of k that makes the graph of the following system of equations two
parallel lines.
y = 2kx + 6
4x + y = 2
a) –2
b) 0
c) 2
d) –4
6. Jim’s company manufactures skateboards. The production costs are given by C = 0.2x
+ 20, where x is the number of skateboards manufactured. The revenue is given by R
= 0.35x. How many skateboards must the company sell to break even?
a) 118 b) 125 c) 134 d) 146
7. Use the process of substitution and select the solution to this system of linear
equations.
y=1–x
2x + y = 4
a) (3, 2)
b) (2, 3)
c) (3, –2)
d) (–3, –2)
8. The perimeter of a rectangle is 120 cm. When the width is increased by 9 cm and the
length is decreased by 9 cm, the figure becomes a square. Select the dimensions of
the original rectangle.
a) 21 cm by 39 cm
c) 30 cm by 30 cm
b) 17 cm by 35 cm
d) 11 cm by 27 cm
9. At a bake sale, cakes sold for $7 each and pies sold for $9 each. The students sold a
total of 60 cakes and pies and made $478. How many cakes were sold?
a) 26 b) 34 c) 29 d) 31
10. Solve for x and y. (x and y are angle measures in degrees.)
a) x = 70 and y = 110
c) x = 110 and y = 70
b) x = 22 and y = 15
d) x = 15 and y = 22
11. What is the solution to the following system of linear equations?
–8a + 3b + 12 = 0
a) (–3, –12)
5a – 3b – 21= 0
b) (3, –4)
c) (3, 4)
d) (–3, 12)
2
12. What is the solution to the following system of linear equations?
3a + 5b = 1
a)
2
(3 ,
4
–3)
4a + 2b = 6
4
b) (–2, – 3 )
c) (2, –1)
d) (4,
1
–5
)
13. Select the formula for the distance, d, from the origin to any point (x, y).
a. d = x  y
c. d = x 2  y 2
b. d =
x2  y2
d. d = x2 + y2
14. Which of the following is the equation of a circle with centre at (0, 0) and radius r?
a. x2 – y2 = r2
c. x2 + r2 = y2
2
2
2
b. x + y = r
d. y2 – x2 = r2
15. What is the distance between points A(a, b) and B(c, d) on the coordinate plane?
a. (a – c)2 + (b – d)2
(a  c) 2  (b  d ) 2
c.
b.
(a  c) 2  (b  d ) 2
d.
(a + c)2 + (b + d)2
16. What are the coordinates of the midpoint of the line segment with end points A(a, b)
and B(c, d)?
a. (
ac bd
,
)
2
2
b. (a + c, b + d)
ac bd
,
)
2
2
ab cd
d. (
,
)
2
2
c. (
17. Which of the following statements is TRUE?
a. An equilateral triangle has
two equal sides.
b. An equilateral triangle has no
equal sides.
c. An equilateral triangle has
three equal sides.
d. An equilateral triangle has no
equal angles.
18. Which of the following statements is TRUE?
a. An isosceles triangle has two
equal sides.
b. An isosceles triangle has no
equal sides.
c. An isosceles triangle has
three equal sides.
d. An isosceles triangle has no
equal angles.
19. Which of the following CANNOT be determined by using only the formula for the
length of a line segment?
a. if a triangle is scalene
c. if a triangle is equilateral
b. if a triangle is isosceles
d. if a quadrilateral is a square
3
Ms. Collins
Extra Credit Assignment
20. Given ABC such that the slope of AB is
following is TRUE?
a. ABC is isosceles.
b. ABC is right-angled.
MPM2D 2011
4
3
and the slope of BC is  , which of the
3
4
c. AB is parallel to BC.
d. ABC is equilateral.
21. Given quadrilateral ABCD such that the lengths of all four sides are the same and the
slopes of opposite sides are equal, what type of quadrilateral is ABCD?
a. It is a rhombus.
c. It is a parallelogram.
b. It is a rectangle.
d. It is a square.
22. Suppose you are given the coordinates of the vertices of ABC. Which information
below will help you determine the equation of the altitude from A?
a. The length of AB and the
c. The midpoint of BC and the
slope of AC
coordinates of A
b. The negative reciprocal of the
d. The coordinates of A and the
slope of AB
negative reciprocal of the
slope of BC
23. Which formula can be used to verify statements about the lengths of line segments?
a.
b.
( x 2  x1 ) 2  ( y 2  y1 ) 2
x 2  x1
y 2  y1
c.
y 2  y1
x 2  x1
d. (
x1  x 2 y1  y 2
,
)
2
2
24. Which formula can be used to verify statements about the slopes of line segments?
a.
b.
( x 2  x1 ) 2  ( y 2  y1 ) 2
x 2  x1
y 2  y1
c.
y 2  y1
x 2  x1
d. (
x1  x 2 y1  y 2
,
)
2
2
25. Which formula can be used to find the midpoint of a line segment?
a.
b.
( x 2  x1 ) 2  ( y 2  y1 ) 2
x 2  x1
y 2  y1
c.
y 2  y1
x 2  x1
d. (
x1  x 2 y1  y 2
,
)
2
2
26. A parabola opens upward and passes through points (–4, 7) and (6, 7). How many xintercepts does this parabola have?
a. 0
c. 2
b. 1
d. There is not enough
information to tell.
27. Under what conditions will the parabola with equation y = 8(x – h)2 + k have two xintercepts?
a. h > 0
c. k > 0
b. h < 0
d. k < 0
28. What is the equation of the axis of symmetry for the relation y = (x + 3)2 – 8?
a. x = –8
c. x = 3
b. x = –3
d. x = 8
29. The graph of y = x2 is reflected in the x-axis, compressed vertically by a factor of 2,
and then, translated 2 units to the right and 11 units up. What is the equation of the
image parabola?
1
a. y = –2(x + 2)2 + 11
c. y  x  22  11
b. y   x  22  11
1
2
2
d. y = 2(x – 2)2 + 11
30. Which expression shows the relation y = 12 + 14x – 7x2 in partial factored form?
a. y = x(14 – 7x) + 12
c. y = –7x(x – 2) + 12
b. y = 7x(2 – x) + 12
d. all of the above
31. What value of b makes the expression x2 + bx + 4 a perfect square?
a. 0
c. 2
b. 1
d. 4
32. Suppose the expression 5x2 – 15x – 11 was written in the form a(x – h)2 + k. What is
the value of a?
a. a = –3
c. a = 5
b. a = 2.5
d. a = 1
33. What value of b makes the relation y = 3x2 + bx + 12 have only one zero?
a. –12
c. 9
b. –1
d. 16
34. What value of b makes the relation y = –2x2 + bx – 5 have two zeros?
a. –4
c. 5
b. 0
d. 7
35. What value of b makes the relation y = 6x2 + bx + 5 have no zeros?
a. 17
c. 4
b. 12
d. 11
36. Which expression will correctly solve a + bx + cx2 = 0 for x?
a.
 b  b 2  4ac
2a
c.
 b  b 2  4ac
2c
b.
b  b 2  4ac
2a
d.
 b  b 2  4ac
2b
5
Ms. Collins
Extra Credit Assignment
MPM2D 2011
37. A parabola has its vertex in the first quadrant and opens down. Select a possible value
for b2 – 4ac.
a. –4
c. 12
b. 0
d. There is not enough
information to tell
38. In ABC and PQR, A = P, B = Q, and C = R. Which of the following is
TRUE for the triangles?
a. ABC and PQR are
c. ABC and PQR are equal in
congruent.
area.
b. ABC and PQR are similar.
d. ABC and PQR are equal in
perimeter.
39. Which of the statements below is TRUE?
a. All congruent triangles are
similar.
b. All similar triangles are
congruent.
c. Similar triangles are never
congruent.
d. Congruent triangles are never
similar.
40. If ABC is similar to PQR, which proportion statement is TRUE?
a.
b.
AB PR

PQ AC
BC PQ

QR AB
c.
d.
AC QR

PR BC
AB AC

PQ PR
41. In this diagram, PQ is parallel to RT. Which statement below is TRUE?
a. POQ  ORT
b. POQ  TRO
c. POQ  ROT
d. POQ  TOR
42. In this diagram, PQ is parallel to BC. Which statement below is TRUE?
a.
b.
AQ
AB
=
QC
AP
AB
PQ
=
BC
AP
c.
d.
BC
AB
=
PQ
AP
AB
AQ
=
AC
AP
43. Find the length of x in this diagram.
a. 4 cm
b. 5 cm
c. 3 cm
d. 6 cm
44. In this diagram, PR is parallel to TU. Which statement below is TRUE?
a. PQR  TUS
b. PQR  SUT
c. PQR  UST
d. PQR  TSU
45. Which statement below is TRUE for this diagram?
a. ABC  DBA
b. ABC  BAD
c. ABC  ADB
d. ABC  ABD
7
46. The scale factor for the enlargement of ABC to PQC is 2.5. Find the perimeter of
PQC.
a. 12 cm
b. 30 cm
c. 24 cm
d. 15 cm
47. A 3.2 m ladder is leaning against a vertical wall with its foot 2.0 m away from the
wall. Another ladder 4.8 m long is leaning against the wall, parallel to the first ladder.
What distance is the foot of the second ladder from the wall?
a. 1.0 m
c. 4.8 m
b. 4.0 m
d. 3.0 m
48. Which ratio gives the value of sin A for ABC?
a.
b.
a
b
b
c
c.
d.
c
b
a
c
49. Find the slope of the straight line AB.
a. 25
b.
1
2
c. 0.47
d. cos 25
50. What is the value of tan A?
8
17
15
b.
8
a.
17
15
8
d.
15
c.
8
51. Find the measure of angle x.
a. 32
b. 0.53
c.
8
15

d. 1.875
52. If BM = MC and BC = 12 cm, then what is the length of x?
a. 9.3 cm
b. 7.8 cm
c. 3.9 cm
d. 18.7 cm
53. Find the length of x.
a. 14.3
b. 20.5
54. If
c. 17.5
d. 20
x
= tan 15, what is the value of x?
30
a. 8.04
b. 0.0089
c. 111.96
d. 8.66
55. Which of the following statements is TRUE?
a
c
a
b. cos A =
c
a. sin B =
c. tan B =
a
b
d. sin A = cos B
56. A ramp rises 2 cm for every 40 cm horizontal distance. What is the slope angle
correct to 1 decimal place?
a. 4
c. 2.9
b. 87
d. 3
9
57. In a play area, a slide has a slope angle of 40 and the horizontal distance of the slide
is 10 m. What is the height of the slide?
a. 6.4 m
c. 10 m
b. 7.7 m
d. 8.4 m
58. A ladder leaning against a wall makes a slope angle of 50. If the ladder reaches a
height of 5 m on the wall, what is the length of the ladder?
a. 42 m
c. 7.8 m
b. 10.6 m
d. 6.5 m
59. A crane has a length of 10 m and the slope angle of one end of the crane is 35. What
is the height of the crane?
a. 5.7m
c. 7.0 m
b. 8.2 m
d. 5.0 m
60. A helicopter uses a flashlight for searching. The distance from the helicopter to the
object is 60 m, and the angle of depression of the line of vision from the helicopter to
the object is 65. What is the horizontal distance from the helicopter to the object?
a. 54.4 m
c. 25.4 m
b. 128.7 m
d. 30.0 m
61. A ladder leaning against a wall reaches a height of 10 m up the wall and makes an
angle of 75 with the ground. What is the length of the ladder?
a. 10.4 m
c. 37.3 m
b. 38.6 m
d. 26 m
62. Select the TRUE statement.
a. Pairs of similar triangles have
equal angles and proportional
sides.
b. Pairs of similar triangles have
equal angles and equal sides.
c. Pairs of similar triangles have
equal sides and different
angles.
d. Pairs of similar triangles have
different sides and different
angles.
63. In ABC, A = 83 and B = 50.
a. a  b
b. b  a
c. c > b
d. a < c
64. In ABC, A = 87 and C = 43.
a. a2 + b2 = c2
b. a2 = b2 + c2
c. a + b > c
d. b + c < a
10
65. On a sunny day, Arim notices that the shadows of the basketball standard on his
driveway and a nearby building are clearly visible. The shadow of the basketball
standard is 2.6 m long, and the shadow of the building is 10.0 m. Knowing the height
of the basketball standard, 4.0 m, Arim can calculate the height of the building. How
tall is the building?
a. 2.5 m
c. 6.5 m
b. 26 m
d. 15.4 m
66. Select the FALSE statement about this diagram.
a.
b.
y
8
x
15
y3
8a
8
=
y 3
=
c.
d.
x
8
=
15
8a
3
a
=
8a
y 3
67. In this diagram, ABE = ACD. Which statement below is TRUE?
a. AEB  ACD
b. There is not enough
information to determine if
they are similar triangles.
c. EAB  DAC
d. BE = CD
68. WXZ contains a right angle at W, and the altitude from W meets XZ at Y. If WX is 5
cm and WY is 3 cm, what is the length of WZ?
a. 3.75 cm
c. 2.4 cm
b. 4 cm
d. 8.3 cm
11
69. Find the length of y.
a. 16 m
b. 9 m
c. 13 m
d. 5 m
70. If PRQ is similar to GHK, which statement below is TRUE?
a.
PQ
GK
=
HK
RQ
c.
HK
PR
=
GH
RQ
b.
PR
GK
=
PQ
GH
d.
PQ
GK
71. Select the statement that is TRUE.
a. Similar triangles have equal
angles, proportional sides.
b. Similar triangles have equal
angles and equal sides.
=
RQ
HK
c. Similar triangles have
proportional angles and equal
sides.
d. Similar triangles have some
angles equal.
72. Find the length of x.
a. 7.4 cm
b. 7.9 cm
c. 12.6 cm
d. 10.7 cm
73. Find the length of x.
a. 3.9 m
b. 2.3 m
c. 1.9 m
d. 4.8 m
12
74. Find the length of x.
a. 10.0 m
b. 8.1 m
c. 6.4 m
d. 9.9 m
75. Find the lengths of x and y.
a. x = 12.7 cm, y = 9.4 cm
b. x = 9.4 cm, y = 12.7 cm
c. x = 1.2 cm, y = 3.7 cm
d. x = 1.2 cm, y = 9.4 cm
76. Find the length of x.
a. 2.5 m
b) 5.0 m
c) 5.7 m
d) 4.4 m
77. An isosceles triangle has two sides of length 20 cm, and the contained angle is 50.
What is the length of the third side?
a. 20 cm
b) 16.9 cm
c) 45 cm
d) 23.7 cm
78. Solve ABC if A is 70, B is 50, and the contained side is 8 cm.
a. b = 8.7 cm, a = 7.1 cm, c = 8.0 cm, A = 70, B = 50, C = 60
b. a = 8.7 cm, c = 7.1 cm, b = 8.0 cm, A = 70, B = 50, C = 60
c. a = 8.7 cm, b = 7.1 cm, c = 8.0 cm, A = 70, B = 50, C = 60
d. c = 8.7 cm, b = 7.1 cm, a = 8.0 cm, A = 70, B = 50, C = 60
79. In ABC, A is 56, B is 64, and c is 6.0 cm. Find the length of side a.
a. a = 5.7 cm b) a = 6.3 cm c) a = 0.5 cm d) a = 0.96 cm
80. In ABC, A is 63, B is 26, and b is 16 cm. Find the length of side a.
a. a = 0.65 cm
b) a = 7.9 cm c) a = 32.5 cm d) a = 0.96 cm
13
81. Find the length of x.
a. 0.79 m
b) 0.82 m
c) 17.3 m
d) 37.0 m
82. Find the length of x.
a. 25.4 m
b. 23.7 m
c. 0.5 m
d. 17.0 m
83. Find the lengths of x and y.
a. x = 17.5 cm, y = 41.6 cm
b. x = 41.6 cm, y = 17.5 cm
c. x = 17.9 cm, y = 43.5 cm
d. x = 103 cm, y = 101 cm
84. An isosceles triangle has two sides of length 10 cm and the contained angle is 30.
Find the length of the third side.
a. 25 cm
b) 5.2 cm
c) 4.3 cm
d) 18.8 cm
85. Solve ABC, if A is 75, B is 50 and the contained side is 8.0 cm.
a. a = 7.5 cm, b = 9.4 cm, c = 8.0 cm, A = 75, B = 50, C = 55
b. a = 12 cm, b = 7.5 cm, c = 8.0 cm, A = 75, B = 50, C = 55
c. a = 6.8 cm, b = 8.5 cm, c = 8.0 cm, A = 75, B = 50, C = 55
d. a = 9.4 cm, b = 7.5 cm, c = 8.0 cm, A = 75, B = 50, C = 55
86. If, in ABC, A = 57, b = 5.0 cm, and c = 8.0 cm, find the length of side a.
a. 45.4 cm b) 6.7 cm
c) 9.4 cm
d) 11.5 cm
14
87. Find the measure of angle .
a. 13
b) 43
c) 137
d) 47
88. Find the measure of angle .
a. 72
b) 31
c) 58
d) 70
89. Find the measure of angle .
a. 68
b) 158
c) 43
d) 22
90. If, in ABC, B = 54, a = 12.0 cm, and c = 9.0 cm, find the length of side b.
a. 7.1 cm
b) 18.8 cm
c) 9.9 cm
d) 15 cm
91. If, in ABC, A = 62, b = 20 m, and c = 18 m, find the length of side a.
a. 19.6 m
b) 32.6 m
c) 9.4 m
d) 26.9 m
92. In ABC, for which set of data could the cosine law be used to solve for b?
a. B = 54, a = 10 cm, c = 23 cm
b. A = 45, C = 56, b = 15 m
c. a = 35 cm, c = 18 cm
d. A = 47, B = 72
93. Solve ABC if A = 58, b = 10.0 cm, and c = 14.0 cm.
a. B = 90, C = 32, a = 9.8 cm
b. B = 86.5, C = 35.5, a = 17.2 cm
c. B = 44.5, C = .5, a = 12.2 cm
d. B = 77.5, C = 44.5, a = 12.2 cm
15
94. The creek beside the school has gone over its banks because of massive rainfall.
Members of the math class were able to place stakes and take the following
measurements: BC = 15 m, CE = 5 m, CD = 4 m, ACB = 35. What is the width of
the flooded creek?
a. 2.9 m
b. 10.8 m
c. 12 m
d. 24 m
95. The route for a bike race starts at Albertville and is a 19 km straight line to
Barkerfield, followed by a 15 km straight line to Clifton. If the final leg is a 23 km
straight line from Clifton back to Albertville, what angle does the cyclists have to turn
at Barkerfield?
a. 41
c. 55
b. 40
d. 84
96. Find the measure of angle .
a. 52
b. 49
c. 41
d. 89
97. Find the unknown measures in ABC, if A = 48, b = 15 cm, and c = 18 cm.
a. B = 40, C = 92 , a = 23 cm
b. B = 29, C = 103, a = 23 cm
c. B = 54.5, C = 77.5, a = 13.7 cm
d. B = 77.5, C = 54.5, a = 13.7 cm
16
98. Which of the following is TRUE for solving a triangle?
a. Solving a triangle means finding the length of an unknown side.
b. Solving a triangle means finding the measure of an unknown angle.
c. Solving a triangle means determining the measures of all three sides and all
three angles.
d. Solving a triangle means determining the measures of the indicated
unknowns.
99. Which of the following is a TRUE statement for XYZ?
a. x2 = y2 + z2 – 2xy cos X
b. x2 = y2 + z2 – 2zy cos X
c. x2 = y2 + z2 – 2yz sin X
d. y2 = x2 + z2 – 2xz cos X
100. Mohammed has been driving his ATV for 3.2 km on a bearing of 54. He uses his
compass to take a new bearing of 205 and continues for 4.6 km. In order to return
directly to his starting point, what distance and in which direction should Mohammed
travel?
a. 2.4 km at 302
c. 2.4 km at 32
d. 5.6 km at 3
b. 2.4 km at 58
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