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# Precalculus Practice Test

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## Precalculus Practice Test

#### Practice

1. What is the maximum or minimum functional value for f ( x ) = −( x − 5) 2 + 12?

(a) The maximum functional value is 12.

(b) The maximum functional value is 5.

(c) The minimum functional value is 12.

(d) The maximum functional value is 5.

2. Find an equation of the line containing the points (1, 9/2) and (−2, 6).

3. What is (are) the vertical asymptote(s) for the graph of

(a) x = 3

(b) x = −5

(c) x = 3 and x = −5

(d) There are no vertical asymptotes.

4. Find the product.

(d) The product does not exist.

5. cos 7π/6 =

6. What are the foci for the hyperbola

(a) (−1, −4) and (−1, 6)

(b) (−6, 1) and (4, 1)

(c) (−4, −1) and (6, −1)

(d) (1, −6) and (1, 4)

7. Find x + y for the system.

(a) 4

(b) 5

(c) 6

(d) 7

8. Find the fourth term of the arithmetic sequence whose 30th term is −180 and whose 45th term is −300.

(a) 20

(b) 28

(c) 35

(d) 46

9. If \$2000 is deposited into an account earning 9% annual interest, compounded monthly, what is it worth after 10 years?

(a) \$4902.71

(b) \$4734.73

(c) \$2155.17

(d) \$4870.38

10. For f ( x ) = 1 − x 2 and g ( x ) = 2 x + 5, what is f o g ( x )?

(a) −2 x 2 + 3

(c) −4 x 2 − 20 x − 24

(d) −2 x 3 − 5 x 2 + 2 x + 5

11. Evaluate f (2) for f ( x ) = 7.

(a) 2

(b) 7

(c) 14

(d) 2, 7

12. Find cos θ if sin θ = −4/5 and θ is in Quadrant IV.

(a) 3/5

(b) −3/5

(c) 9/25

(d) −9/25

13. What is the directrix for the parabola y 2 = 12( x −3)?

(a) y = −3

(b) y = 3

(c) x = 0

(d) x = 3

14. Are the lines 2 xy = 5 and 4 x − 8 y = 9 parallel, perpendicular, or neither?

(a) Parallel

(b) Perpendicular

(c) Neither

(d) Cannot be determined

15. 15. Find the second term of the arithmetic sequence whose fifth term is and whose tenth term is .

16. What is the domain for

(a) (−∞, −1) ∪ (−1, ∞)

(b) (−1, ∞)

(c) [−1, ∞)

(d) (−∞, ∞)

17. Find f o g (−2) for f ( x ) = x 2 + x and g ( x ) = 3 x + 9.

(a) 12

(b) 15

(c) 3

(d) 2

18. What is the vertex for y = 4 x 2 − 6 x + 5?

19. What is the inverse of

20. What is the fifth term of the sequence where a n = n 2 ?

(a) 10

(b) 15

(c) 20

(d) 25

21. What is an asymptote for the hyperbola

22. What is the phase shift for y = 3 sin(2 x − π/3)?

(a) −π/3

(b) π/3

(c) −π/6

(d) π/6

23. What is the period for y = 3 sin(2 x − π/3)?

(a) π

(b) π /4

(c) 4π

(d) π /2

24. Find 2 x + y for the system.

(a) 3 and 16

(b) 5 and 21

(c) 1 and 28

(d) 3 and 9

25. log 5 5 2 t =

(a) t

(b) 2 t

(c) 2

(d) 10 t

26. What is the horizontal asymptote for the graph of

(a) y = 0

(b)

(c) There is no horizontal asymptote.

27. Is the sequence arithmetic, geometric, or neither?

(a) Arithmetic

(b) Geometric

(c) Neither

(d) Cannot be determined

28. What is the inverse of

29. Write the product as a sum: sin 4 x sin x .

Problems 30-35 refer to the graph in Figure A. 14.

Fig. A.14

30. Is the graph in Figure A. 14 symmetric?

(a) Yes, with respect to the x -axis

(b) Yes, with respect to the y -axis

(c) Yes, with respect to the origin

(d) No

31. What is f (−4)?

(a) −2

(b) 0

(c) 2

(d) 4

32. What is the y -intercept?

(a) −2

(b) 0

(c) 2

(d) 4

33. Does the function have an inverse?

(a) Yes

(b) No

(c) Cannot be determined

34. What is the range?

(a) [−4, 4]

(b) [−2, 2]

(c) [−2, −4]

(d) [2, 4]

35. What is the increasing interval(s)?

(a) (−4, −2) ∪ (2, 4)

(b) (−4, 4)

(c) (2, 2)

(d) (−2, 2)

36. Is the function f ( x ) = x 2x + 2 even, odd, or neither?

(a) Even

(b) Odd

(c) Neither

(d) Cannot be determined without the graph

37. Are the points (−4, 2), (1, 3), (−1, 0), and (−2, 5) the vertices of a parallelogram?

(a) Yes

(b) No

(c) Cannot be determined

Fig. A.15

38. The solid graph in Figure A. 15 is the graph of f ( x ), and the dashed graph is the graph of a transformation. What is the transformation?

(a) f ( x + 1) + 3

(b) f ( x − 1) + 3

(c) 2 f ( x + 1)

(d) 2 f ( x − 1)

39. Find the sum.

−6 + (−2) + 2 + 6 + 10 + ... + 50

(a) 660

(b) 260

(c) 330

(d) Too many terms are missing to find the sum.

40. What is x + y for the system? Use a matrix method.

(a) 7

(b) 8

(c) 9

(d) 10

41. Are the angles 65° and −295° coterminal?

(a) Yes

(b) No

(c) Cannot be determined

42. Find .

Fig. A.16

43. The graph in Figure A. 16 is the graph of what function?

(a) f ( x ) = x 2 − 2 x − 1

(b) f ( x ) = x 2 + 2 x − 1

(c) f ( x ) = x 2 − 3 x − 1

(d) f ( x ) = x 2 + 3 x − 1

44. A biscuit recipe calls for 2/3 of a cup of milk for each cup of mix. Find an equation that gives the amount of milk in terms of the amount of mix.

(d) Cannot be determined

45. Rewrite m r = n as a logarithmic equation.

(a) log n r = m

(b) log m r = n

(c) log n m = r

(d) log m n = r

46. A museum offers group discounts for groups of 25 or more. For a group of 25, the ticket price is \$13.50. For each additional person attending, the price drops \$0.50. What group size maximizes the museum’s revenue?

(a) 26

(b) 27

(c) 28

(d) 29

47. The graph in Figure A. 17 is the graph of which function?

(a) P ( x ) = ( x + 3)( x − 1) 2 ( x + 1) = x 4 + 2 x 3 − 4 x 2 − 2 x + 3

(b) P ( x ) = −( x + 3)( x − 1) 2 ( x + 1) = − x 4 − 2 x 3 + 4 x 2 + 2 x − 3

(c) P ( x ) = ( x + 3)( x − 1)( x + 1) = x 3 + 3 x 2x − 3

(d) P ( x ) = −( x + 3)( x − 1)( x + 1) = − x 3 − 3 x 2 + x + 3

Fig. A.17

48. What is the determinant for

(a) 3

(b) 4

(c) 5

(d) 6

49. Find the domain for .

(a) (8, ∞)

(b) (−∞, 8) ∪ (8, ∞)

(c) (−∞, 8] ∪ [8, ∞)

(d) [8, ∞)

50. Are f ( x ) = 4 x 3 + 1 and inverses?

(a) Yes

(b) No

(c) Cannot be determined

51. Solve for x : log 5 (2 x − 7) = 1.

(a) x = 4

(b) x = 5

(c) x = 6

(d) x = 7

52. The graph in Figure A. 18 is the graph of which function?

Fig. A.18

53. According to the Rational Zero Theorem, which of the following is NOT a possible rational zero for f ( x ) = 6 x 4x 3 − 3 x 2 + x − 10?

Fig. A.19

54. The graph in Figure A. 19 is the graph of which inequality?

(a) x + y ≥ 2

(b) x + y > 2

(c) x + y ≤ 2

(d) x + y < 2

55. Find the quadratic function with vertex (−1, 3) with the point (2, −15) on its graph.

(a) f ( x ) = −18( x − 1) 2 + 3

(b) f ( x ) = 18( x − 1) 2 + 3

(c) f ( x ) = −2( x + 1) 2 + 3

(d) f ( x ) = 2( x + 1) 2 + 3

56. Rewrite as a single logarithm: ln x − 3 ln y − ln z .

Fig. A.20

57. The graph in Figure A.20 is the graph of which system?

58. The graph in Figure A.21 is the graph of which equation?

Fig. A.21

59. What is x + y + z for the system? Use a matrix method.

(a) 6

(b) 7

(c) 8

(d) 9

Fig. A.22

60. The graph in Figure A.22 is the graph of one period of which function?

(a) y = 3 sin( x − π/4)

(b) y = 3 sin( x + π/4)

(c) y = sin 3 ( x − π/4)

(d) y = sin 3( x + π/4)

61. Evaluate for f ( x ) = 2 x 2 − 1.

(a) 4 a + 2 h 2 − 2

(b) 4 a + 2 h 2 − 1

(c) 4 a + 2 h

(d) 4 a + 2 h 2

62. According to Descartes’ Rule of Signs, how many possible positive zeros are there for f ( x ) = 6 x 4x 3 − 3 x 2 + x − 10?

(a) 3 or 1

(b) 3

(c) 2 or 0

(d) 2

Fig. A.23

63. The graph in Figure A.23 is the graph of one period of which function?

(a) y = 2 sin( x − π/3)

(b) y = 2 sin( x + π/3)

(c) y = sin 2( x − π/3)

(d) y = sin 2( x + π/3)

64. The graph of 3 f ( x − 4) is the graph of f ( x )

(a) shifted to the right four units and vertically stretched.

(b) shifted to the left four units and vertically stretched.

(c) shifted to the right four units and vertically compressed.

(d) shifted to the left four units and vertically compressed.

Fig. A.24

65. Find the height of the triangle in Figure A.24.

66. Find all zeros for f ( x ) = 3 x 3 − 7 x 2 + 8 x − 2.

67. What are the intercepts for f ( x ) = − x 2 + x + 2?

(a) The x -intercepts are 1 and 2, and the y -intercept is 2.

(b) The x -intercepts are −1 and 2, and the y -intercept is 2.

(c) The x -intercepts are 1 and −2, and the y -intercept is −2.

(d) The x -intercepts are −1 and 2, and the y -intercept is −2.

68. cos(tan −1 1/5) =

69. What is the slant asymptote for the graph of

(a) y = x − 11

(b) y = x + 2

(c) y = x − 7

(d) y = x − 2

70. The population of a town grew from 2000 in the year 1980 to 10,000 in the year 2000. Assuming exponential growth, what is the town’s annual growth rate?

71. What is the quotient for

72. What is the quotient for (2 x 3x 2 + 2) ÷ ( x + 3)?

(a) 2 x 2 − 7 x − 21

(b) 2 x 2 + 5 x + 15

(c) 2 x 2 − 7 x + 23

(d) 2 x 2 − 7 x + 21

73. What are the vertices for the ellipse

(a) (−4, 0) and (4, 0)

(b) (0, −4) and (0, 4)

(c) (−5, 0) and (5, 0)

(d) (0, 5) and (0, −5)

74. A triangle has sides of length 8, 15, and 20. Which of the following is an approximate angle in this triangle?

(a) 48.3°

(b) 41.7°

(c) 50.6°

(d) 23.6°

75. Which one of the following statements is NOT true about the polynomial function f ( x ) = x 3 ( x − 4) 2 ( x + 1)?

(a) x = 0 is a zero of multiplicity 3.

(b) x = 4 is a zero of multiplicity 2.

(c) x = 1 is a zero of multiplicity 1.

(d) x = −1 is a zero of multiplicity 1.

#### Solutions

1. A

2. C

3. A

4. B

5. D

6. A

7. A

8. B

9. A

10. C

11. B

12. A

13. C

14. C

15. D

16. D

17. A

18. B

19. A

20. D

21. C

22. D

23. A

24. C

25. B

26. B

27. A

28. D

29. B

30. C

31. A

32. B

33. B

34. B

35. A

36. C

37. A

38. C

39. C

40. C

41. A

42. C

43. A

44. B

45. D

46. A

47. B

48. B

49. B

50. A

51. C

52. A

53. C

54. A

55. C

56. B

57. D

58. D

59. B

60. B

61. C

62. A

63. C

64. A

65. C

66. B

67. B

68. A

69. D

70. C

71. B

72. D

73. C

74. B

75. C

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