Free Printable PRECALCULUS -- AP EXAM REView

1.

a)

-16

b)

0

c)

16

d)

18

2.

a)

200

b)

400

c)

1600

d)

3200

3.

a)

0

b)

1/3

c)

7/6

d)

2

4.

a)

b)

c)

d)

5.

Which of the following best approximates the x-value at the inflection point for the polynomial y = f(x) graph above?

a)

x = -6.6

b)

x = -4

c)

x = -1.5

d)

x =3

6.

a)

b)

c)

d)

7.

a)

2

b)

4

c)

5

d)

6

8.

a)

2/3

b)

3/2

c)

2

d)

8

9.

a)

II only

b)

I and II only

c)

II and III only

d)

I, II, and III

10.

a)

b)

c)

d)

11.

a)

I only

b)

II only

c)

I and II only

d)

I, II, and III

12.

Ashley purchases a car and records its value over the next 4 years. Which of the following functions best models the value of the car t years after its purchase?

a)

b)

c)

d)

13.

a)

I only

b)

III only

c)

I and II only

d)

II and III only

14.

a)

b)

c)

d)

15.

Which of the following equations represents the graph above?

a)

b)

c)

d)

16.

a)

b)

c)

d)

17.

a)

b)

c)

d)

18.

If $f\left(x\right)=2x$ and $g\left(x\right)=2x^2-1$ find $f\left(g\left(x\right)\right)$

a)

$4x^2-1$

b)

$4x^2-2$

c)

$8x^2-1$

d)

$16x^2-1$

19.

What transformations have happened to f(x) = 2^x if the new equation is
g(x) = -2^(x+3) -6

a)

It stayed the same

b)

reflects, up 3, left 6

c)

reflects over y-axis, right 3, down 6

d)

reflects over x-axis, left 3, down 6

20.

Write the function for the following table:

a)

f(x)=1(3)^x

b)

$f(x)=3(3)^x$

c)

$f(x)=3x+3$

21.

Find the inverse of $f(x)=\frac{x-5}{3}$

a)

$f^{-1}(x)=\frac{3}{5}+x$

b)

$f^{-1}(x)=3x+5$

c)

$f^{-1}(x)=5x+3$

22.

Find the inverse of $f(x)=\frac{x-5}{3}$

a)

$f^{-1}(x)=\frac{3}{5}+x$

b)

$f^{-1}(x)=3x+5$

c)

$f^{-1}(x)=5x+3$

23.

Write the EXPLICIT rule for the arithmetic sequence

-10, -3, 4, 11,...

a)

a_n= 10n + 17

b)

a_n = 7n - 17

c)

a_n = -7n + 17

d)

a_n = 7n + 3

24.

The given graph models Mr. Passwater’s distance from his home over time. Time, in hours, is the independent variable and the distance from home, in miles, is the dependent variable. Which of the following verbal descriptions would be appropriate for the given graph?

a)

Mr. Passwater leaves school and drives toward his house at a constant rate. Then, he stops to eat at a restaurant for a period of time to eat dinner. After eating dinner, Mr. Passwater leaves and drives until he reaches his house, driving at a constant rate that is faster than the rate he was driving when he first left school.

b)

Mr. Passwater leaves school and drives toward his house, increasing his speed as he drives. Then, he drives at a constant rate for a period of time. Finally, he increases his speed again and drives until he reaches his home.

c)

Mr. Passwater leaves his house and drives at a constant rate to a nearby restaurant. After stopping for a period of time to eat lunch, Mr. Passwater drives back to his home at a constant rate that is faster than his rate when driving to the restaurant.

d)

Mr. Passwater leaves his house and drives to a restaurant at a constant rate. Then, he stops to eat at a restaurant for a period of time to eat breakfast. After eating breakfast, Mr. Passwater leaves and drives until he reaches his school, driving at a constant rate that is faster than the rate he was driving when he first left his house.

25.

At time t = 0, water begins pouring into an empty container at a constant rate. The water pours into the container until it is full. As the water begins to pour into the container at a constant rate, the depth of water in the container increases at an increasing rate for a period of time, and then the depth of water increases at a decreasing rate until the container is full. Which of the following containers would be appropriate for the given scenario?

a)

Container A

b)

Container B

c)

Container C

d)

Container D

26.

At time t = 0, water begins pouring into an empty container at a constant rate. The water pours into the container until it is full. As the water begins to pour into the container at a constant rate, the depth of water in the container increases at an increasing rate for a period of time, and then the depth of water increases at a decreasing rate until the container is full. Which of the following containers would be appropriate for the given scenario?

a)

Container A

b)

Container B

c)

Container C

d)

Container D

27.

At time t = 0, water begins pouring into an empty container at a constant rate. The water pours into the container until it is full. As the water begins to pour into the container at a constant rate, the depth of water in the container increases at an increasing rate for a period of time, and then the depth of water increases at a decreasing rate until the container is full. Which of the following containers would be appropriate for the given scenario?

a)

Container A

b)

Container B

c)

Container C

d)

Container D

28.

For his birthday, Mr. Passwater decides to go skydiving. As Mr. Passwater begins falling toward the ground below, the distance he falls increases at an increasing rate until he pulls his parachute. Once his parachute opens, the distance he falls increases at a decreasing rate until he safely lands on the ground. Which of the following graphs could depict this situation, where time, in seconds, is the independent variable and the total distance he has fallen, in feet, is the dependent variable?

a)

b)

c)

d)

29.

For his birthday, Mr. Passwater decides to go skydiving. As Mr. Passwater begins falling toward the ground below, the distance he falls increases at an increasing rate until he pulls his parachute. Once his parachute opens, the distance he falls increases at a decreasing rate until he safely lands on the ground. Which of the following graphs could depict this situation, where time, in seconds, is the independent variable and his distance from the ground, in feet, is the dependent variable?

a)

b)

c)

d)

30.

The figure shows a conical tank with water pouring into it. At t = 0, water begins to pour into the empty tank. The rate that water pours into the tank varies in such a way that the depth of the water inside the tank increases at a constant rate with respect to time. Which of the following graphs could depict this situation, where the depth of the water inside the tank, in feet, is the independent variable and the volume of water inside the tank, in cubic feet, is the dependent variable?

a)

b)

c)

d)

31.

Use the graph of f below for this problem. How many points of inflection does the graph of f have for 0 ≤ x ≤ 9?

a)

(A) 1

b)

(B) 2

c)

(C) 3

d)

(D) 4

32.

Use the graph of f below for this problem. How many points of inflection does the graph of f have for 0 ≤ x ≤ 9?

a)

(A) 1

b)

(B) 2

c)

(C) 3

d)

(D) 4

33.

Which of the following statements about the graph of f is correct for the interval 7 ≤ x < 9?

a)

(A) f is positive and increasing.

b)

(B) f is positive and decreasing.

c)

(C) f is negative and increasing.

d)

(D) f is negative and decreasing.

34.

Which of the following statements about the graph of f is correct for the interval 7 ≤ x < 9?

a)

(A) f is positive and increasing.

b)

(B) f is positive and decreasing.

c)

(C) f is negative and increasing.

d)

(D) f is negative and decreasing.

35.

Which of the following statements about the graph of f is correct for the interval 1 < x < 3?

a)

(A) f is increasing at an increasing rate.

b)

(B) f is increasing at a decreasing rate.

c)

(C) f is decreasing at an increasing rate.

d)

(D) f is decreasing at a decreasing rate.

36.

Which of the following statements about the graph of f is correct for the interval 0 < x < 1?

a)

(A) f is increasing and the graph of f is concave up.

b)

(B) f is increasing and the graph of f is concave down.

c)

(C) f is decreasing and the graph of f is concave up.

d)

(D) f is decreasing and the graph of f is concave down.

37.

Which of the following statements about the graph of f is correct for the interval 5 < x < 7?

a)

(A) The rate of change of f is positive and increasing.

b)

(B) The rate of change of f is positive and decreasing.

c)

(C) The rate of change of f is negative and increasing.

d)

(D) The rate of change of f is negative and decreasing.

38.

Use the graph of g below for this problem. How many points of inflection does the graph of g have?

a)

1

b)

2

c)

3

d)

4

39.

Use the graph of g below for this problem. Which of the following statements about the graph of g is correct?

a)

On the interval 0 < x < 2, g is positive and increasing.

b)

On the interval 0 < x < 2, g is positive and decreasing.

c)

On the interval 0 < x < 2, g is negative and increasing.

d)

On the interval 0 < x < 2, g is negative and decreasing.

40.

Use the graph of g below for this problem. Which of the following statements about the graph of g is correct?

a)

On the interval 5 < x < 6, g is increasing at an increasing rate.

b)

On the interval 5 < x < 6, g is increasing at a decreasing rate.

c)

On the interval 5 < x < 6, g is decreasing at an increasing rate.

d)

On the interval 5 < x < 6, g is decreasing at a decreasing rate.

41.

Use the graph of g below for this problem. Which of the following statements about the graph of g is correct?

a)

On the interval 4 < x < 5, g is increasing and the graph of g is concave up.

b)

On the interval 4 < x < 5, g is increasing and the graph of g is concave down.

c)

On the interval 4 < x < 5, g is decreasing and the graph of g is concave up.

d)

On the interval 4 < x < 5, g is decreasing and the graph of g is concave down.

42.

Use the graph of g below for this problem. Which of the following statements about the graph of g is correct?

a)

On the interval 7 < x < 8, the rate of change of g is positive and increasing.

b)

On the interval 7 < x < 8, the rate of change of g is positive and decreasing.

c)

On the interval 7 < x < 8, the rate of change of g is negative and increasing.

d)

On the interval 7 < x < 8, the rate of change of g is negative and decreasing.

43.

The figure shows the graph of a function f for 0 ≤ x ≤ 5. Which of the following statements is true about the function f?

a)

f is increasing at an increasing rate.

b)

f is increasing at a decreasing rate.

c)

f is decreasing at an increasing rate.

d)

f is decreasing at a decreasing rate.

44.

The figure shows the graph of a function g for 0 ≤ x ≤ 5. Which of the following statements is true about the function g?

a)

g is increasing at an increasing rate.

b)

g is increasing at a decreasing rate.

c)

g is decreasing at an increasing rate.

d)

g is decreasing at a decreasing rate.

45.

The figure shows the graph of a function h for 0 ≤ x ≤ 5. Which of the following statements is true about the function h?

a)

h is increasing at an increasing rate.

b)

h is increasing at a decreasing rate.

c)

h is decreasing at an increasing rate.

d)

h is decreasing at a decreasing rate.

46.

The figure shows the graph of a function k for 0 ≤ x ≤ 5. Which of the following statements is true about the function k?

a)

k is increasing at an increasing rate.

b)

k is increasing at a decreasing rate.

c)

k is decreasing at an increasing rate.

d)

k is decreasing at a decreasing rate.

47.

The figure shows the graph of a function j for 0 ≤ x ≤ 5. Which of the following statements is true about the function j?

a)

The graph of j is increasing at an increasing rate.

b)

The graph of j is increasing at a decreasing rate.

c)

The graph of j is decreasing at an increasing rate.

d)

The graph of j is decreasing at a decreasing rate.

48.

The figure shows the graph of a function j for 0 ≤ x ≤ 5. Which of the following statements is true about the function j?

a)

The function j is increasing and the graph of j is concave up.

b)

The function j is increasing and the graph of j is concave down.

c)

The function j is decreasing and the graph of j is concave up.

d)

The function j is decreasing and the graph of j is concave down.

49.

The figure shows the graph of a function k for 0 ≤ x ≤ 5. Which of the following statements is true about the function k?

a)

The function k is increasing and the graph of k is concave up.

b)

The function k is increasing and the graph of k is concave down.

c)

The function k is decreasing and the graph of k is concave up.

d)

The function k is decreasing and the graph of k is concave down.

50.

The figure shows the graph of a function h for 0 ≤ x ≤ 5. Which of the following statements is true about the function h?

a)

The function h is increasing and the graph of h is concave up.

b)

The function h is increasing and the graph of h is concave down.

c)

The function h is decreasing and the graph of h is concave up.

d)

The function h is decreasing and the graph of h is concave down.

51.

The figure shows the graph of a function g for 0 ≤ x ≤ 5. Which of the following statements is true about the function g?

a)

The function g is increasing and the graph of g is concave up.

b)

The function g is increasing and the graph of g is concave down.

c)

The function g is decreasing and the graph of g is concave up.

d)

The function g is decreasing and the graph of g is concave down.

52.

The figure shows the graph of a function f for 0 ≤ x ≤ 5. Which of the following statements is true about the function f?

a)

The function f is increasing and the graph of f is concave up.

b)

The function f is increasing and the graph of f is concave down.

c)

The function f is decreasing and the graph of f is concave up.

d)

The function f is decreasing and the graph of f is concave down.

53.

The figure shows the graph of a function r for 0 ≤ x ≤ 5. Which of the following statements is true about the function r?

a)

The rate of change of r is positive and increasing.

b)

The rate of change of r is positive and decreasing.

c)

The rate of change of r is negative and increasing.

d)

The rate of change of r is negative and decreasing.

54.

The figure shows the graph of a function p for 0 ≤ x ≤ 5. Which of the following statements is true about the function p?

a)

The rate of change of p is positive and increasing.

b)

The rate of change of p is positive and decreasing.

c)

The rate of change of p is negative and increasing.

d)

The rate of change of p is negative and decreasing.

55.

The figure shows the graph of a function p for 0 ≤ x ≤ 5. Which of the following statements is true about the function p?

a)

The rate of change of p is positive and increasing.

b)

The rate of change of p is positive and decreasing.

c)

The rate of change of p is negative and increasing.

d)

The rate of change of p is negative and decreasing.

56.

The figure shows the graph of a function m for 0 ≤ x ≤ 5. Which of the following statements is true about the function m?

a)

The rate of change of m is positive and increasing.

b)

The rate of change of m is positive and decreasing.

c)

The rate of change of m is negative and increasing.

d)

The rate of change of m is negative and decreasing.

57.

The figure shows the graph of a function j for 0 ≤ x ≤ 5. Which of the following statements is true about the function j?

a)

The rate of change of j is positive and increasing.

b)

The rate of change of j is positive and decreasing.

c)

The rate of change of j is negative and increasing.

d)

The rate of change of j is negative and decreasing.

58.

The figure shows the graph of a function k for 0 ≤ x ≤ 5. Which of the following statements is true about the function k?

a)

The rate of change of k is positive and increasing.

b)

The rate of change of k is positive and decreasing.

c)

The rate of change of k is negative and increasing.

d)

The rate of change of k is negative and decreasing.

59.

The figure shows the graph of a function h for 0 ≤ x ≤ 5. Which of the following statements is true about the function h?

a)

The rate of change of h is positive and increasing.

b)

The rate of change of h is positive and decreasing.

c)

The rate of change of h is negative and increasing.

d)

The rate of change of h is negative and decreasing.

60.

The figure shows the graph of a function g for 0 ≤ x ≤ 5. Which of the following statements is true about the function g?

a)

The rate of change of g is positive and increasing.

b)

The rate of change of g is positive and decreasing.

c)

The rate of change of g is negative and increasing.

d)

The rate of change of g is negative and decreasing.

61.

The figure shows the graph of a function f for 0 ≤ x ≤ 5. Which of the following statements is true about the function f?

a)

The rate of change of f is positive and increasing.

b)

The rate of change of f is positive and decreasing.

c)

The rate of change of f is negative and increasing.

d)

The rate of change of f is negative and decreasing.

62.

The figure shows the graph of a function r for 0 ≤ x ≤ 5. Which of the following statements is true about the function r?

a)

The graph of r is increasing at an increasing rate.

b)

The graph of r is increasing at a decreasing rate.

c)

The graph of r is decreasing at an increasing rate.

d)

The graph of r is decreasing at a decreasing rate.

63.

The figure shows the graph of a function p for 0 ≤ x ≤ 5. Which of the following statements is true about the function p?

a)

The graph of p is increasing at an increasing rate.

b)

The graph of p is increasing at a decreasing rate.

c)

The graph of p is decreasing at an increasing rate.

d)

The graph of p is decreasing at a decreasing rate.

64.

The figure shows the graph of a function m for 0 ≤ x ≤ 5. Which of the following statements is true about the function m?

a)

The graph of m is increasing at an increasing rate.

b)

The graph of m is increasing at a decreasing rate.

c)

The graph of m is decreasing at an increasing rate.

d)

The graph of m is decreasing at a decreasing rate.

65.

Over which of the following closed intervals is the average rate of change of f equal to 0? Use the graph of f below to answer.

a)

[0, 2]

b)

[2, 4]

c)

[2, 5]

d)

[2, 6]

66.

Over which of the following closed intervals is the average rate of change of f the least? Use the graph of f below to answer.

a)

[0, 4]

b)

[0, 8]

c)

[5, 8]

d)

[6, 8]

67.

What is the average rate of change of f over the closed interval from x = 2 to x = 6? Use the graph of f below to answer.

a)

-4/3

b)

-3/4

c)

-1/2

d)

1/2

68.

What is the average rate of change of f over the closed interval [4, 8]? Use the graph of f below to answer.

a)

-4

b)

-2

c)

-1

d)

1

69.

What is the average rate of change of f over the closed interval [3, 5]? Use the graph of f below to answer.

a)

1/2

b)

1

c)

3/2

d)

2

70.

Let k be the piecewise function defined by k(x) as given. Over the closed interval -4 <= x <= 2, the average rate of change of k is 2. What is the value of a?

a)

1/27

b)

1/13

c)

13

d)

27

71.

Let h be the piecewise function defined by h(x) as given. What is the average rate of change of h over the closed interval from x = 1 to x = 5?

a)

-13/4

b)

-3

c)

-1/3

d)

6

72.

Let g be the piecewise function defined by g(x) as given. What is the average rate of change of g over the closed interval [-2, 4]?

a)

-2

b)

1

c)

2

d)

7/3

73.

The table gives values for a continuous function h at selected values of x. What is the average rate of change of h over the closed interval [3, 9]?

a)

-2

b)

-1

c)

-1/2

d)

1/2

74.

The table gives values for a continuous function f at selected values of x. What is the average rate of change of f over the closed interval [0, 3]?

a)

1/2

b)

1

c)

2

d)

3

75.

The figure shows the graph of a function f in the xy-plane with four labeled points. It is known that a relative maximum of f occurs at D, and the only point of inflection of the graph of f is C. Of the following points, at which is the rate of change of f the greatest?

a)

A

b)

B

c)

C

d)

D

76.

The figure shows the graph of a function j in the xy-plane with four labeled points. It is known that a relative minimum of j occurs at D, and the only point of inflection of the graph of j is C. Of the following points, at which is the rate of change of j the least?

a)

A

b)

B

c)

C

d)

D

77.

The figure shows the graph of a function h in the xy-plane with four labeled points. It is known that a relative maximum of h occurs at C. For which of the following pairs of points is the average rate of change of h the least?

a)

A) between points A and C

b)

B) between points B and C

c)

C) between points B and D

d)

D) between points C and D

78.

The figure shows the graph of a function k in the xy-plane with three labeled points. It is known that a relative maximum of k occurs at B. Consider the rates of change of k at the three labeled points. Which of the following orders the rates of change of k in order from least to greatest?

a)

A) A, B, C

b)

B) B, A, C

c)

C) C, A, B

d)

D) C, B, A

79.

The figure shows the graph of a function k in the xy-plane with three labeled points. It is known that a relative maximum of k occurs at B. Consider the rates of change of k at the three labeled points. Which of the following orders the rates of change of k in order from least to greatest?

a)

A) A, B, C

b)

B) B, A, C

c)

C) C, A, B

d)

D) C, B, A

80.

Which of the following statements about the interval from E to F is true?

a)

The graph of g is concave up, because the rate of change of g is positive.

b)

The graph of g is concave up, because the rate of change of g is increasing.

c)

The graph of g is concave down, because the rate of change of g is negative.

d)

The graph of g is concave down, because the rate of change of g is decreasing.

81.

Which of the following statements about the interval from C to E is true?

a)

The graph of g is positive.

b)

The graph of g is increasing.

c)

The rate of change of g is positive.

d)

The rate of change of g is increasing.

82.

Which of the following statements about the interval from A to B is true?

a)

The function g is increasing at an increasing rate.

b)

The function g is increasing at a decreasing rate.

c)

The function g is decreasing at an increasing rate.

d)

The function g is decreasing at a decreasing rate.

83.

Use the graph of f shown in the diagram to answer this question. On which intervals is f decreasing at an increasing rate?

a)

the interval from 4 to B

b)

the interval from B to C

c)

the interval from C to D

d)

the interval from D to E

84.

Use the graph of f shown in the diagram to answer this question. On which intervals is the rate of change of f positive?

a)

the interval from 4 to B only

b)

the intervals from 4 to B and from B to C

c)

the intervals from 4 to B and from D to E

d)

the intervals from C to D and from D to E

85.

Use the graph of f shown in the diagram to answer this question. On which intervals is f increasing and the graph of f concave down?

a)

the interval from A to B

b)

the interval from B to C

c)

the interval from C to D

d)

the interval from D to E

86.

Use the graph of f shown in the diagram to answer this question. On which intervals is the rate of change of f increasing?

a)

the interval from A to B only

b)

the interval from D to E only

c)

the intervals from A to B and from D to E

d)

the intervals from C to D and from D to E

87.

The graphs of the functions h, m, k, and g are shown above for 0 ≤ x ≤ 5. For which of the following are both the function and the rate of change of the function negative?

a)

(A) m only

b)

(B) h and m

c)

(C) k and m

d)

(D) g and m

88.

The graphs of the functions k, m, p, and g are shown above for 0 ≤ x ≤ 5. For which of the following functions is the rate of change negative?

a)

(A) m only

b)

(B) k and m only

c)

(C) k, m, and g

d)

(D) m, p, and g

89.

The graphs of the functions f, j, p, and r are shown above for 0 ≤ x ≤ 5. For which of the following functions is the rate of change increasing?

a)

(A) f only

b)

(B) f and r only

c)

(C) f, j, and r

d)

(D) f, p, and r

90.

The figure shows the graph of a function r for 0 ≤ x ≤ 5. Which of the following statements is true about the function r?

a)

The function r is increasing and the graph of r is concave up.

b)

The function r is increasing and the graph of r is concave down.

c)

The function r is decreasing and the graph of r is concave up.

d)

The function r is decreasing and the graph of r is concave down.

91.

The figure shows the graph of a function p for 0 ≤ x ≤ 5. Which of the following statements is true about the function p?

a)

The function p is increasing and the graph of p is concave up.

b)

The function p is increasing and the graph of p is concave down.

c)

The function p is decreasing and the graph of p is concave up.

d)

The function p is decreasing and the graph of p is concave down.

92.

The figure shows the graph of a function m for 0 ≤ x ≤ 5. Which of the following statements is true about the function m?

a)

The function m is increasing and the graph of m is concave up.

b)

The function m is increasing and the graph of m is concave down.

c)

The function m is decreasing and the graph of m is concave up.

d)

The function m is decreasing and the graph of m is concave down.

93.

The figure shows the graph of a function j for 0 ≤ x ≤ 5. Which of the following statements is true about the function j?

a)

The function j is increasing and the graph of j is concave up.

b)

The function j is increasing and the graph of j is concave down.

c)

The function j is decreasing and the graph of j is concave up.

d)

The function j is decreasing and the graph of j is concave down.

94.

The figure shows the graph of a function k for 0 ≤ x ≤ 5. Which of the following statements is true about the function k?

a)

The function k is increasing and the graph of k is concave up.

b)

The function k is increasing and the graph of k is concave down.

c)

The function k is decreasing and the graph of k is concave up.

d)

The function k is decreasing and the graph of k is concave down.

95.

The figure shows the graph of a function h for 0 ≤ x ≤ 5. Which of the following statements is true about the function h?

a)

The function h is increasing and the graph of h is concave up.

b)

The function h is increasing and the graph of h is concave down.

c)

The function h is decreasing and the graph of h is concave up.

d)

The function h is decreasing and the graph of h is concave down.

96.

The figure shows the graph of a function g for 0 ≤ x ≤ 5. Which of the following statements is true about the function g?

a)

The function g is increasing and the graph of g is concave up.

b)

The function g is increasing and the graph of g is concave down.

c)

The function g is decreasing and the graph of g is concave up.

d)

The function g is decreasing and the graph of g is concave down.

PRECALCULUS -- AP EXAM REView

Total questions: 96

Worksheet time: 2hrs 30mins

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