Free Printable AP Calc AB Semester 1 Final Review

1.

Find the derivative. f(x) = 1/(3x²) + 4x³

a)

f'(x) = 6x³ + 12x²

b)

f'(x) = 6x + 12x²

c)

f'(x) = -2/(3x³) + 12x²

d)

f'(x) = -6/x² + 12x²

2.

If the position of a particle is represented by s(t) = -t² + 1, what is its instantaneous velocity at t = 1?

a)

Velocity = 0

b)

Velocity = 1

c)

Velocity = -1

d)

Velocity = -2

3.

If the position function for a particle is s(t) = -t² - t, what is the instantaneous velocity function for the particle?

a)

v(t) = -2

b)

v(t) = -2t - 1

c)

v(t) = t³

d)

v(t) = -t

4.

Find the derivative f(x) = (3x + 5)⁴

a)

f'(x) = 12(3x)³

b)

f'(x) = 12(3x + 5)³

c)

f'(x) = (3)⁴

d)

f'(x) = (3x + 5)³

5.

Find the second derivative of f(x) = x²+ e^x - cosx

a)

f"(x) = 2 + e^x + cosx

b)

f"(x) = 2x + e^x + cosx

c)

f"(x) = 2x + xe^x - cosx

d)

f"(x) = 2x + e^x + sinx

6.

Where does the function, f(x) = 2x³ - 9x²+ 12x -3 have relative max/min?

a)

Rel max x = -1, Rel min x = 2

b)

Rel min x = 1, Rel min x = 2

c)

Rel max x = 1, Rel min x = 2

d)

Rel max x = 2, Rel min x = 1

7.

Find the derivative f(x) = xe^x

a)

f'(x) = e^x

b)

f'(x) = xe^x + xe^x

c)

f'(x) = e^x - xe^x

d)

f'(x) = e^x + xe^x

8.

Find the derivative f(x) = tanxcosx

a)

f'(x) = sec²xcosx - tanxsinx

b)

f'(x) = sec²xcosx + tanxsinx

c)

f'(x) = sec²xsinx

d)

f'(x) = sec²xcosx - tanxcosx

9.

No Calc

a)

A

b)

B

c)

C

d)

D

10.

No Calc

a)

A

b)

B

c)

C

d)

E

11.

a)

A.

b)

B.

c)

C.

d)

D.

12.

a)

A.

b)

B.

c)

C.

d)

D.

13.

a)

A.

b)

B.

c)

C.

d)

D.

14.

Find the limit of the function as x approaches 2.

a)

1

b)

-1

c)

5

d)

DNE

15.

Find the limit of the function as x approaches 2⁺.

a)

1

b)

-1

c)

5

d)

DNE

16.

What is the limit?

a)

DNE

b)

Infinity

c)

6

d)

12

17.

What is the limit?

a)

DNE

b)

2/3

c)

1/4

d)

Infinity

18.

Find the derivative.

a)

x⁴cosx - 4x³sinx

b)

x⁴cosx + 4x³sinx

c)

4x³cosx

d)

-4x³cosx

19.

If a function has a derivative that is negative, what does that tell you?

a)

The function is increasing

b)

The function is decreasing

c)

The concavity of the function is up

d)

The concavity of the function is down

20.

a)

f '(x)

b)

0

c)

∞

d)

f(x)

21.

a)

Mean value theorem

b)

Rolle's theorem

c)

Intermediate Value Theorem

d)

Fundamental Theorem of Calculus

22.

a)

f '(x)⋅g(x) + f(x)⋅g'(x)

b)

f '(x)⋅g(x) - f(x)⋅g'(x)

c)

[f '(x)⋅g(x) + f(x)⋅g'(x)] / [g(x)]²

d)

[f '(x)⋅g(x) - f(x)⋅g'(x)] / [g(x)]²

23.

What is true about the following?

a)

A

b)

B

c)

C

d)

D

24.

f' is given, which could be f?

a)

A

b)

B

c)

C

25.

Where is the graph not differentiable?

a)

x = -2, -1, 0, 1

b)

x = -2, -1, 1

c)

x = -2, -1

d)

x = -1,

26.

A bug begins to crawl up a vertical wire at time t = 0. The velocity v of the bug at time t, 0 < t < 8, is given by the function whose graph is shown behind this text. At what value of t does the bug change direction?

a)

2

b)

4

c)

6.5

d)

7

27.

Find dy/dx

a)

A

b)

B

c)

C

d)

D

28.

a)

[-2,1]

b)

[-2,3]

c)

[3,5]

d)

[0,1.5] and [3,5]

29.

a)

1/2

b)

0

c)

Positive Infinity

d)

Negative Infinity

30.

What are the increasing intervals of the graph for f(x) = 2x⁴- 4x² + 1

a)

(-1,0)

b)

(0,1)

c)

(-∞,-1) and (0,1)

d)

(-1,0) and (1,∞)

31.

a)

(3x²-2) cos(x³-2x)

b)

-(3x²-2) cos(x³-2x)

c)

cos(2x²-2)

d)

sin(2x²-2)

32.

Which of the following best describes the continuity at x = 2?

a)

Continuous

b)

Removable Discontinuity

c)

Infinite Discontinuity

d)

Jump Discontinuity

e)

none of these

33.

\lim_{x\rightarrow-\frac{\pi}{2}}\frac{\cos^2x}{1+\sin x}

a)

2

b)

1/2

c)

0

d)

DNE

e)

none of these

34.

\lim_{x\rightarrow\infty}\frac{\left|x\right|}{3x}

a)

$\infty$

b)

1/3

c)

$-\infty$

d)

-1/3

e)

none of these

35.

\lim_{x\rightarrow4^-}\frac{\left|2x-8\right|}{x-4}

a)

1

b)

-2

c)

2

d)

-1

e)

none of these

36.

\lim_{x\rightarrow0^{ }}\frac{\left|2x\right|}{x}

a)

1

b)

-1

c)

0

d)

DNE

e)

none of these

37.

Which of the following is is a non-removable discontinuity for f(x)?

$f\left(x\right)\ =\frac{\left(x+1\right)^2\left(x+3\right)^3\left(x-2\right)^2}{\left(x+1\right)^3\left(x+3\right)^2\left(x-2\right)^2}$

a)

x = -1

b)

x = 2

c)

x = -3

d)

none of these

38.

Which of the following is a horizontal asymptote for f(x)?

$f\left(x\right)=\frac{2x^3-4x+1}{4x^2+2x-100}$

a)

y = 2

b)

y = 1/2

c)

y = -100

d)

no HA

e)

none of these

39.

$\lim_{x\rightarrow\infty}\frac{\pi x+\cos x}{x}$

a)

0

b)

$\pi$

c)

$\infty$

d)

DNE

e)

none of these

40.

$\lim_{x\rightarrow2}\frac{x^3-8}{x^2-4}$

a)

12

b)

3

c)

4.5

d)

DNE

e)

none of these

41.

Use the chart to find f'(3) for f(x) = g(x)/[2h(x)]

a)

(2π+3)/9

b)

-(3+2π)/9

c)

-(6+4π)/9

d)

-2(3+4π)/9

42.

Find the derivative of the given equation
f(x) = 7

a)

7

b)

0

c)

7x

d)

14

43.

Which if the following is not a correct notation for 'derivative?'

a)

f'(x)

b)

y'

c)

dy

d)

dy/dx

44.

Which represents the same function?

a)

b)

c)

d)

45.

What's the definition of derivative?

a)

Instantaneous rate of change

b)

Slope of tangent line

c)

46.

a)

A

b)

B

c)

C

d)

D

47.

a)

A

b)

B

c)

C

d)

D

48.

a)

A

b)

B

c)

D

d)

E

49.

Find dy/dx if y = (cscx + 1)⁷

a)

-7(cscx + 1)⁶(cscxcotx)

b)

7(-cscxcotx)⁶

c)

7(cscx + 1)⁶(cscxcotx)

d)

-7(cscxcotx)⁶

50.

The displacement of a particle moving in a straight line is given by the equation of motion f(t) = t³ - 4t +3. Find the average velocity of the particle over the interval [0, 4].

a)

3

b)

12

c)

18

d)

24

51.

The interval in which $y=x^2e^{–x}$ is increasing is

a)

$\left(-2,\ 0\right)$

b)

$\left(-\infty,\ \infty\right)$

c)

$\left(2,\ \infty\right)$

d)

$\left(0,\ 2\right)$

52.

What is a vertical tangent?

a)

Has a positive slope.

b)

Has a negative slope.

c)

Has a slope of zero.

d)

Has an undefined slope.

53.

a)

-1/4

b)

1/4

c)

π/4

d)

-π

54.

a)

1/2

b)

-1/2

c)

0

d)

3/2

55.

a)

A

b)

B

c)

C

d)

D

56.

Let f be the function given by f(x) = x³. What are all values of c that satisfy the conclusion of the Mean Value Theorem on the closed interval [-1, 2]? (No calculator)

a)

0 only

b)

1 only

c)

√3 only

d)

-1 and 1

57.

Where is the point of inflection for the function $f\left(x\right)\ =\ x^{3\ }+6x^2$ ?

a)

$x=0$

b)

$x=-4$

c)

$x=-2$

d)

$x=4$

58.

The function f is twice differentiable with f(2) = 1, f'(2)=4, and f''(2)=3. What is the value of the approximation of f(1.9) using the line tangent to the graph of f at x = 2?

a)

0.4

b)

0.6

c)

0.7

d)

1.4

59.

Using this graph of f’(x), find the slope of the line tangent to f(x) at point c

a)

0

b)

1

c)

-1

d)

Not enough information

60.

a)

2x

b)

3

c)

6

d)

9

61.

The function shown is the graph of f '(x), the derivative of f(x). The domain is [-3,5]. On which interval is the graph of f(x) concave upward?

a)

(-1,1) & (3,5]

b)

[-3,-2) & (4,5]

c)

[-3,-1) & (1,3)

d)

(-2,1) & (1,4)

62.

A tank is in the form of an inverted cone having an altitude of 10 ft and a radius of 5 feet. Water is flowing into the tank at the rate of 1 ft³/min. How fast is the water level rising when the water is 3 ft deep?

a)

3.4 ft/min

b)

.14 ft/min

c)

1 ft/min

d)

1/2 ft/min

63.

If y=2x-8, what is the minimum value of the product xy?

a)

-16

b)

-8

c)

-4

d)

2

64.

Find the value for that makes f(x) continuous.

a)

0

b)

1

c)

1.5

d)

2

e)

No such value exists

65.

what is the average rate of change of the function f(x)=x²-6x+6 from 2 to 6?

a)

4

b)

2

c)

3

d)

23/4

66.

a)

Average Rate of Change

b)

Average Value of f

c)

Intermediate Value Theorem

d)

Rolle's Theorem

67.

a)

position

b)

velocity

c)

acceleration

d)

total distance

68.

a)

A

b)

B

c)

C

d)

D

e)

E

69.

a)

sin x

b)

-sin x

c)

cos x

d)

-cos x

70.

Find the derivative f(x) = x²/e^x

a)

f'(x) = (x²e^x - 2xe^x) / (e^x)²

b)

f'(x) = (2xe^x + x²e^x) / (e^x)²

c)

f'(x) = (2xe^x - x²e^x) / (e^x)²

d)

f'(x) = x²e^x + 2xe^x

AP Calc AB Semester 1 Final Review

Total questions: 70

Worksheet time: 4hrs 39mins

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