Name: ______________________ Class: _________________ Date: _________ ID: A

1

MPM2D0 Exam Review

Multiple ChoiceIdentify the choice that best completes the statement or answers the question.

____ 1. Which of these ordered pairs is not a point on the graph of 2x + 4y = 24?

a. (–4, 8) c. (–1, 6)b. (–2, 7) d. (6, 3)

____ 2. Jill has $18 to buy tea biscuits and cookies at the school bake sale. Tea biscuits are 90¢ each and cookies are 45¢ each. Which equation describes Jill’s options?

a. 0.90x + 0.10y = 18 c. 0.90x – 0.45y = 18b. 0.90x + 0.45y = 18 d. 0.55x + 0.45y = 18

____ 3. Which ordered pair is a solution to the system of equations shown below?

x – y = 9y = 8x + 12

a. (3, 12) c. (–3, 12)b. (–3, –12) d. (3, –12)

____ 4. Identify the point of intersection for the graph shown below.

a. (0, 1) c. (1, 0)b. (–1, 4) d. (–4, 1)

____ 5. Isolate x in 0.4x – 0.4y = 2.4.

a. y + 6 c. –0.16y + 0.96b. 0.16y + 0.96 d. –y + 6

Name: ______________________ ID: A

2

____ 6. Add the equations in the given linear system. Select the new equation.

6x + y = –7x – 3y = 2

a. 5x + 4y = –9 c. 7x – 2y = –5b. 7x + 4y = 9 d. 5x + 2y = 5

____ 7. Solve the given system by using elimination.

x – y = 93x + 5y = –5

a. (–5, –4) c. (–4, 5)b. (4, 5) d. (5, –4)

____ 8. U(–6, 0) is one endpoint of UV. M(–0.5, 3) is the midpoint of UV. Determine the coordinates of endpoint V.

a. (6, –5) c. (–5, 6)b. (6, 5) d. (5, 6)

____ 9. Y(0, 5) is one endpoint of YZ. M(0, –1) is the midpoint of YZ. Determine the coordinates of endpoint Z.

a. (0, –7) c. (7, 0)b. (–7, 0) d. (0, 7)

____ 10. The graph shows a circle with its centre at (0, 0). Determine the radius of the circle.

a. 2 units c. 5 unitsb. 4 units d. 10 units

Name: ______________________ ID: A

3

____ 11. Which of these circles has the equation x2 + y2 = 64?

a. c.

b. d.

____ 12. Which point is on the circle with equation x2 + y2 = 85?

a. (–8, 6) c. (7, –7)b. (5, 4) d. (9, –2)

Name: ______________________ ID: A

4

____ 13. Calculate the slope of PS.

a. –4 c. 1b. –1 d. 4

____ 14. ABC has vertices at A(–4, 3), B(3, 2), and C(1, –2). Determine the coordinates of midpoint F.

a. (0, 5) c. (2, 0)

b. − 32

, 12

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃ d. − 1

2, 5

2

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

____ 15. Select the coordinates of the vertex for the quadratic relation y = −0.5x 2 + 5.

a. (0, 5) c. (1, 1)b. (2, 4) d. (–1, –2)

Name: ______________________ ID: A

5

____ 16. Select the maximum value for the quadratic relation.

a. (3, 2) c. (1, 1)b. (0, 5) d. (–1, –2)

Name: ______________________ ID: A

6

____ 17. Select the parabola that matches the quadratic relation y = –2x2 + x + 1.

a. c.

b. d.

____ 18. Determine the zeros of the quadratic relation y = 2x2 – 2x – 12.

a. (–3, 0) and (5, 0) c. (0.390, 0) and (4.277, 0)b. (–2, 0) and (3, 0) d. (–2.5, 0) and (2, 0)

____ 19. Determine the equation of the axis of symmetry for the quadratic relation y = –3x2 + 14x – 5.

a. x = –0.25 c. x = 2

b. x = 0.5 d. x = 73

____ 20. Use the distributive property to expand (x + 1)(x – 7). Then select the simplified expression.

a. x2 – 6x + 7 c. x2 + 6x + 7b. x2 + 6x – 7 d. x2 – 6x – 7

Name: ______________________ ID: A

7

____ 21. These data represent the path of a soccer ball as it flies through the air. Select the scatter plot that represents the data.

Horizontal Distance (m) 0.0 1.0 2.0 3.0 4.0Height (m) 2.7 4.3 5.0 4.3 2.7

a. c.

b. d.

____ 22. The data for Carla’s science experiment is best represented by the equation y = 7x2 + 12x – 5. Estimate the value of y when x = 2.8.

a. 47.12 c. 75.16b. 60.85 d. 83.48

____ 23. Evaluate the power (–2)4.

a. –16 c. 8b. –8 d. 16

Name: ______________________ ID: A

8

____ 24. Evaluate the power –50.

a. –5 c. 1b. –1 d. 5

____ 25. Evaluate the power 14

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃−2

.

a. 4 c. 30b. 16 d. 64

____ 26. Identify the greatest common factor of the terms x2y2 and xy.

a. x c. x2

b. xy d. y2

____ 27. Determine the missing factor in 36x2y4 = (–6xy3)().

a. 18xy2 c. 2xyb. –6xy d. 6xy

____ 28. Determine the greatest common factor in the expression 4x2 + 20x.

a. 2x c. 2x2

b. 4x d. 4x2

____ 29. The tiles in the model represent an algebraic expression. Identify its factors.

1 x –11 x –11 x –11 x –1

x x2 –x

x –1 a. (x + 1)(x – 4) c. (x – 1)(x + 4)b. (x – 3)(x + 4) d. (x + 1)(x + 4)

____ 30. Determine the missing factor in x2 + 9x + 18 = ()(x + 6).

a. (x – 2) c. (x – 4)b. (x + 1) d. (x + 3)

____ 31. Determine the missing factor in x2 + 6x – 16 = (x + 8)().

a. (x – 2) c. (x – 4)b. (x + 1) d. (x + 3)

Name: ______________________ ID: A

9

____ 32. Determine the missing value for 3x2 – x – 7 = (x + 1)(3x – 7).

a. 2 c. 6b. 4 d. 8

____ 33. Select the quadratic expression that is represented by the algebra tiles.

a. x2 + 16 c. x2 – 16b. 2x2 – 4 d. x2 – 4

____ 34. Determine the factors of the expression 9x2 + 42x + 49.

a. (3x + 7)2 c. (3x – 7)2

b. (9x – 6)(9x + 7) d. (3x – 7)(3x + 7)

____ 35. The thick, grey parabola is the graph of y = x 2 . What is the equation of the thin, black graph?

a. y = 2x 2 c. y = 3x 2

b. y = 0.5x 2 d. y = −2x 2

____ 36. The graph of y = x2 is transformed to y = 5x2. Determine the coordinates to which the original point (2, 4) is transformed.

a. (2, 20) c. (2, 4)b. (5, 25) d. (10, 20)

Name: ______________________ ID: A

10

____ 37. Which transformation would you apply to the graph of y = x2 to obtain the graph shown?

a. translate 2 units up c. translate 2 units rightb. translate 2 units left d. translate 2 units down

____ 38. Which graph matches the equation y = –4x2 + 1?

a. c.

b. d.

Name: ______________________ ID: A

11

____ 39. Which equation matches the graph shown?

a. y = (x + 2)2 – 5 c. y = 2(x – 3)2 – 1b. y = –x2 + 4 d. y = –0.4(x + 4)2 + 2

____ 40. Determine the equation of the axis of symmetry of a parabola that passes through points (–9, 3) and (–3, 3).

a. x = –6 c. x = 2b. x = –3 d. x = 5

____ 41. Determine which equation in vertex form is equivalent to y = (x – 5)(x + 1).

a. y = (x – 2)2 – 9 c. y = (x – 9)2 – 2b. y = (x + 2)2 – 9 d. y = (x + 9)2 – 2

____ 42. Complete the square for y = x2 + 18x – 10 to determine the coordinates of the vertex.

a. (9, 91) c. (–9, –91)b. (10, 18) d. (9, – 91)

____ 43. Solve the equation 6x2 – 150 = 0 by factoring.

a. x = –5 c. x = –5 and x = 5b. x = –10 and x = 15 d. x = 5

____ 44. Select the equation that has two real solutions.

a. –(x – 2)2 – 11 = 0 c. (2x – 3)2 = 0b. (x + 5)2 – 12 = 0 d. (x + 7)2 + 1 = 0

____ 45. For what value of k does the equation y = 3x2 + 9x + k have two real roots?

a. 5 c. 8b. 7 d. 12

Name: ______________________ ID: A

12

____ 46. A ball was kicked and its height, h, in metres, above the ground after time, t, in seconds, is represented by h = 0.5 + 16t – 2t2. What was the initial height of the ball?

a. 0.5 m c. 3.7 mb. 1.6 m d. 5.1 m

____ 47. Here is the graph of a model rocket being launched from a platform. What is the height of the platform? Height vs. Time

Time (s)

a. about 16 m c. about 23 mb. about 21 m d. about 27 m

____ 48. Determine the value of x.

a. 30° c. 60°b. 45° d. 90°

Name: ______________________ ID: A

13

____ 49. For the triangle, which side is the hypotenuse?

a. AB c. ACb. BC d. none of the above

____ 50. Which side is adjacent to ∠D?

a. DE c. DFb. EF d. none of the above

____ 51. Determine the value of θ, to the nearest degree.

a. 21° c. 65°b. 43° d. 82°

____ 52. Determine the value of θ, to the nearest degree.

a. 19° c. 41°b. 36° d. 84°

Name: ______________________ ID: A

14

____ 53. Reena needs to drill an oil well. How far below the ground must she drill?

a. about 2360 m c. about 2730 mb. about 2580 m d. about 2910 m

____ 54. A kite makes an angle of 39° with the horizontal from where the string was released. If 18 m of string was released, determine the height of the kite.

a. about 11 m c. about 18 mb. about 15 m d. about 23 m

____ 55. Solve, to one decimal place, for the unknown side length in wsin 35°

= 4.0sin 75°

.

a. 0.9 c. 4.1b. 2.4 d. 5.6

____ 56. Solve, to one decimal place, for the unknown angle measure in 12.0sin Y

= 15.8sin 72°

.

a. 16.7° c. 46.2°b. 21.8° d. 70.4°

____ 57. Solve for the length of side s in s2 = 42 + 72 – 2(4)(7) cos 80°.

a. about 1.3 c. about 7.4b. about 4.6 d. about 10.2

Name: ______________________ ID: A

15

____ 58. Determine the length of side r.

a. about 2.7 m c. about 8.3 mb. about 5.8 m d. about 14.6 m

____ 59. Determine the length of side h.

a. about 6.3 m c. about 9.3 mb. about 8.6 m d. about 13.7 m

____ 60. Solve for the unknown side length in ssin 65°

= 7.4sin 45°

.

a. about 3.2 c. about 7.1b. about 4.6 d. about 9.5

Short Answer

61. Greg is offered a new job that earns $900/week plus 4.5% commission. Use variables for the situation, and write an equation.

62. Kevin sells cars and earns $250/week plus 5% commission. Write an equation for this situation.

63. Solve the given linear system by graphing.

x – y = –5y = 3x + 1

Name: ______________________ ID: A

16

64. Isolate x in 14

x + y = 3.

65. To eliminate x from the given linear system, by what numbers would you multiply equations (1) and (2)?

5x – y = 1 (1)2x + 2y = –2 (2)

66. Is the line segment with endpoints (3, 5) and (1, 5) vertical, horizontal, or diagonal?

67. A curve of good fit is represented by the equation y = x2 – 5x + 11. Use the equation to estimate the value of y when x = –2.8.

68. Determine the missing factor for 3x2 – 15x – 72 = ()(3x + 9).

69. Identify what transformation(s) must be applied to the graph of y = x2 to create a graph of y = 2x2. Then state the image of point (3, 9).

70. Write the equation of a parabola that has a vertex at (1, –5), opens upward, and is narrower than y = x2.

71. Determine the equation of a quadratic relation in vertex form if the vertex is at (–3, 5) and it passes through (–2, 2).

72. Determine the equation of a quadratic relation in vertex form if the vertex is at (–3, –3) and it passes through (0, 8).

73. Determine the equation of a quadratic relation in vertex form if the vertex is at (6, 0) and it passes through (8, 8).

74. Solve 3x2 + 20x + 12 = 0 by factoring.

75. Simplify and then solve the equation x(x + 2) = 8.

76. Replace each symbol to complete the square.

y = x2 + 12x + 5y = x2 + 12x + – + 5 y = (x2 + 12x + ) – + 5y = (x + )2 –

77. Use the discriminant to determine the number of real solutions that the equation –4x2 + 3x + 1 = 0 has.

78. State the number of times that the relation y = –5(x + 7)2 – 2 passes through the x-axis.

Name: ______________________ ID: A

17

79. Determine whether the vertex of the parabola y = 3x2 – 5x + 7 lies above, below, or on the x-axis.

80. What ratio can be used to determine the scale factor of the two triangles?

81. Fred, who is 2.1 m tall, is walking away from a hydro pole that is 4.5 m tall. Draw a diagram that can be used to calculate the length of Fred’s shadow when he is 1.1 m from the hydro pole.

82. Determine the measure of θ, in cos θ = 35

, to one decimal place.

83. Determine the measure of θ, in sin θ = 79

, to one decimal place.

84. Solve for the unknown side length in ssin 39°

= 9.5sin 64°

.

Round your answer to one decimal place.

85. Determine the length of side b to one decimal place.

Name: ______________________ ID: A

18

86. Determine the length of side d to one decimal place.

87. Determine the length of side t to one decimal place.