1. a Quadratic Function Has This Domain and Range

1. A quadratic function has this domain and range.

·  domain: {all real numbers}

·  range: {all real numbers greater than 1}

How many real zeroes does the function have?

a. at least 1 b. 0

c. exactly 2 d. exactly 1

2. The vertex of the quadratic function g(x) is located at (4,2). An x-intercept is located at (5,0). What is the y-intercept of g(x)?

a. (0,3) b. (0,-30)

c. (0,-4) d. (0,-14)

3. What is the vertex of the parabola:

y = x2 – 6x + 12?

a. (1, -2) b. (1,12)

c. (2,-3) d. (3,3)

4. Which of the following is the vertex form of :

y = 3x2 – 24x + 38?

a. y = (3x – 8)2 + 38 b. y = (3x – 12)2 - 10

c. y = 3(x – 6)2 - 38 d. y = 3(x – 4)2 - 10

5. To reflect a parabola over the x-axis, change:

a. the sign of the vertex

b. the sign of the y-intercept

c. the sign of the leading coefficient

d. the sign of the x-intercept(s)

6. The vertex of y = (x – 6)2 + 3 is:

a. (-6, 3) b. (6, 3)

c. (6, -3) d. (-6, -3)

7. The graph of y = -2(x + 1)2 + 4 will open:

a. up b. down

c. right d. left

8. Which type of graph would be the BEST representation for the data in the table?

a. a cubic with leading coefficient positive

b. a parabola with leading coefficient negative

c. a line with a positive slope

d. a parabola with leading coefficient positive

9. Which could be the graph of: y – 2 = ½(x + 3)2

a. b.

c. d.

10. A steady rate of change is represented by what type of function?

a. quadratic b. cubic

c. linear d. constant

11. If g(x) = - f(x), then the graph of g(x) will be

a. upside down

b. a reflection over the x-axis

c. a reflection over the y-axis

d. sideways

12. Use the graph below to determine for what x values is f(x) < 0

a. x < -2 b. -2 < x < 0

c. x < -2 or 1.5 < x < 5 d. x < 2

13. For the function y = 2x2 – 7, for which of these values of x does y = 1?

a. -1 b. -2

c. -3 d. -4

14. The inverse of f(x) = is:

a. –f(x) b. f(-x)

c. -f(-x) d. f(x)

15. Inverses of functions reflect over:

a. f(x) = x b. themselves

c. f(x) = -x d. f(x) = f-1(x)

16. The inverse of a quadratic function has a domain that is:

a. always negative b. always positive

c. restricted in some way d. all real numbers

17. Which system of equations is equivalent to the matrix equation:

a. x – 2y = 9 b. x + 4y = 12

-4x – 3y = 12 2x - 3y = 9

c. x – 4x = -9 d. x – 4y = -9

2y + 3y = 12 2x + 3y = 12

18. The inverse of the function f(x) = x2 – 10 is:

a. b.

c. d.

19. Solve: (x – 3)(x + 2) > 0

a. x > 3 b. x < -2

c. -2 < x < 3 d. x < -2 or x > 3

20. A graph representing exponential growth is always:

a. linear b. increasing

c. horizontal d. decreasing

21. Which expression is equivalent to:

a. b.

c. d.

22. A geometric sequence contains which of the following?

a. ratio b. difference

c. last term d. sum

23. The population in a city in 1990 was 213,426. The population increased at a rate of about 3.1% each year. What was the approximate population in the city in 2000?

a. 220,042 b. 298,602

c. 289,624 d. 155,770

24. You deposit $825 into an account that earns 7.95% interest compounded monthly. What is the balance in the account after 16 years?

a. $2931.26 b. $2805.54

c. $936.87 d. $2231.87

25. Negative exponents indicate:

a. fractions b. values of 0

c. negative numbers d. reciprocals

26. Given the following piecewise function, evaluate f(-3)

a. b.

c. d.

27. In the graph below, for what value of x is the function NOT defined?

a. infinity b. 3

c. 1 d. 0

28. A triangle has a height twice its base; its area is 64 square units. What is the size of the base?

a. 4 b. 8

c. 32 d. 2

29. The length of a rectangle is 4 inches more than twice its width. The area is 30 square inches. Find the dimensions (length and width).

a. 3 x 10 b. 5 x 14

c. 2 x 15 d. 5 x 6

30. The length of a rectangle is twice its width. The area is 32 square inches. Find the dimensions (length and width).

a. 8 x 16 b. 2 x 16

c. 4 x 8 d. 6 x 12

31. Logan works in a factory. Logan uses the formula y = x2 + x to determine how many impurities(y) are in a sample of water at any temperature (x) in degrees Celsius. For one sample of water, Logan found 20 impurities. Which are the possible temperatures for the sample of water?

a. 2 or -10 b. -5 or 4

c. -2 or 10 d. 5 or -4

32. What are the zeros of the function:

f(x) = x2 + 5x - 24?

a. 6, -4 b. -6, 4

c. -3, 8 d. 3, -8

33. What is the domain of the function below? (assume the function has “arrows” on each end)

a. x ≤ 4 b. x ≥ 4

c. all real numbers d. y ≤ 4

34. What is the range of the function in #33?

a. x ≤ 4 b. x ≥ 4

c. all real numbers d. y ≤ 4

35. What is the equation of the axis of symmetry of the graph of y = 3x2 + 12x - 2?

a. x = -2 b. x = 2

c. y = -2 d. y = 2

36. Find the roots of the function:

f(x) = x2 - 1

a. 1 b. 1, -1

c. I d. i, -i

37. On what interval is the function shown below increasing?

a. (-∞, -3) b. (3, ∞)

c. (2, ∞) d. (-∞, 2)

38. What is the interval of increase of the following function:

y = x2 + 3

a. x > 0 b. x < 0

c. x < 3 d. x > 3

39. Which of the following is the graph of

a.

b.

c.

d.

40. Solve:

a. no solution b. x = -4

c. x = 4 d. x = 0

41. Which of the following functions is always increasing?

a. b.

c. d.

42. What is the first step in solving the following equation:

a. square both sides

b. subtract four from both sides

c. subtract seven from both sides

d. taking the square root of both sides

43. An odd function contains the point (-1, -3). What other point is on the graph?

a. (1, 3) b. (-1, 3)

c. (1, -3) d. (-1, -3)

44. f(x) = x2 + 4 is

a. odd b. even

c. not symmetrical d. rotated 360 degrees

45. f(x) = -|x| has symmetry across

a. x-axis b. y-axis

c. origin d. y = 0

46. What is the value of ?

a. i b. 1

c. –i d. -1

47. Simplify: (4 – 7i)2

a. 33 – 56i b. -33 – 56i

c. -33 + 56i d. 33 + 56i

48. The complex conjugate of 3i + 2 is:

a. -3i b. 3i

c. 3i - 2 d. -3i - 2

49. The factored form of the expression

2x2 + 3x + 1 is:

a. (2x + 1)(x – 1) b. (2x – 1)(x – 1)

c. (2x – 2)(x - .5) d. (2x + 1)(x + 1)

50. Which is a factor of: x2 – 2x – 15?

a. (x – 3) b. (x – 15)

c. (x + 3) d. (x + 5)

51. Exponents change when polynomials are:

a. added b. subtracted

c. multiplied and divided d. divided

52. Simplify: 4x2 + x – 5 – (5x2 – 1)

a. -x2 + x – 6 b. 9x2 + x – 6

c. 9x2 + x – 4 d. -x2 + x – 4

53. A cardboard box has a length of x, width of 3x and height of x + 2. Which expression represents the volume of the box?

a. 3x3 + 2 b. 5x3 + 2

c. 3x3 + 6x2 d. 5x3 + 6x2

54. Which is equivalent to the following expression:

a. x - 2 b. x - 3

c. x + 2 d. x + 3

55. Which is equivalent to the following expression:

a. b.

c. d.

56. Simplify:

a. b.

c. d.

57. Given the hypotenuse of a 30°-60°-90° triangle is 16, what is the value of the short leg?

a. b. 16

c. d. 8

58. Given the long leg of a 30°-60°-90° triangle is, find the value of the hypotenuse.

a. b. 11

c. d. 22

59. The diagonal of a square is cm long. Find the length of a side of the square.

a. b. 12

c. 24 d. 6

60. Calculate the missing angle to the nearest degree.

a. 32 b. 52

c. 30 d. 38

61. Sam is trying to calculate the height of a tower. He is standing 95 meters from the base of a tower. The angle of elevation from Sam's position on the ground to the top of the tower is 35°. Calculate the height of the tower to the nearest tenth of a meter.

a. 66.5 meters b. 77.8 meters

c. 62.7 meters d. 54.5 meters

62. A 5'6" person walking down the street notices his shadow. If the angle of elevation from the tip of the shadow to the sun is 60°, what is the length of the shadow (round to 2 decimal places)?

a. 3.23 feet b. 11.00 feet

c. 3.18 feet d. 17.18 feet

63. A boat is spotted in the water with an angle of depression of 25° from the top of a lighthouse that is 89 feet tall. To the nearest foot, how far away is the boat from the base of the lighthouse?

a. 42 feet b. 37 feet

c. 211 feet d. 191 feet

64. Given a circle with a radius of 16 ft, and a central angle of 135°, find the length of the arc created by the angle.

a. 20 ft b. 10 ft

c. 12 ft d. 6 ft

65. Find the length of the minor arc:

a. 361 ft b. 150.4 ft

c. 15.8 ft d. 38 ft

66. Given circle B, what is the m?

a. 23°

b. 46°

c. 77°

d. 80°

67. In the given diagram, what is the m?

a. 32°

b. 114°

c. 46°

d. 100°

68. Given the diagram, find x.

a. 3

b. 4

c. 5

d. 6

69. In the circle below, if CE = 3, ED = 18, AE = 6, then EB = ?

a. 9

b. 1

c. 36

d. 3

70. In circle C, What is the measure of angle ACD?

a. 134°

b. 76°

c. 75°

d. 105°

71. If the radius of a sphere is doubled, by what factor does the surface area increase?

a. 8 b. 4

c. 16 d. 2

72. If the radius of a sphere is doubled, by what factor does the volume area increase?

a. 8 b. 4

c. 16 d. 2

73. A sphere has a volume of 322 cubic cm. What is the approximate diameter of the sphere?

a. 8.5 cm b. 5.1 cm

c. 4.3 cm d. 17.5 cm

74. Identify theradius of the circle:

(x-1)2 + (y-3)2 = 4

a. (1, 3) b. 16

c. 4 d. 2

75. Given the following properties, classify the polygon: two pair of parallel sides, diagonals are perpendicular bisectors, has four congruent sides, and the diagonals are perpendicular.

a. rectangle b. rhombus

c. parallelogram d. square

76. Which statement is true about all parallelograms?

a. The diagonals are perpendicular to each other.

b. The opposite angles are congruent.

c. The diagonals are congruent.

d. The area is the product of two adjacent sides.

77. If an exterior angle is 22.5 degrees, how many sides does the regular polygon have?

a. 16 b. 17

c. 18 d. 15

78. What is the measure of one interior angle in a regular pentagon?

a. 120° b. 540°

c. 90° d. 108°

79. In parallelogram ABCD, what is m?

a. 120°

b. 540°

c. 90°

d. 108°

80. What is the most specific name for the given figure?

a. rhombus

b. parallelogram

c. quadrilateral

d. kite