Free Printable AP Calc Unit 2 Test Review

1.

Derivative means the same thing as

a)

slope of the tangent line

b)

slope of the normal line

c)

exponent

d)

potato

2.

The derivative of a function is its

a)

Slope

b)

Maximum/Minimum

c)

Instantaneous rate of change

d)

Common Denominator

3.

f'(x)=

a)

$\lim_{h\rightarrow0}\left(\frac{f\left(x+h\right)-f\left(x\right)}{h}\right)$

b)

$\lim_{x\rightarrow c}\left(\frac{f\left(x\right)-f\left(c\right)}{x-c}\right)$

c)

$\frac{\text{d}y}{\text{d}x}$

d)

an equation for the slope of the tangent line

4.

If

f\left(x\right)=x^2+2x

which of the following is the derivative of f(x)

a)

$\frac{\left(x+h\right)^2+2\left(x+h\right)\ -\left(x^2+2x\right)}{h}$

b)

$\frac{\left(x^2+2x+h\right)-\left(x^2+2x\right)}{h}$

c)

$\lim_{h\rightarrow0}\ \frac{\left(x^2+2x\ +h\right)-\left(x^2+2x\right)}{h}$

d)

$\lim_{h\rightarrow0}\ \frac{\left(x+h\right)^2+2\left(x+h\right)-x^2-2x}{h}$

5.

$\frac{d}{dx}\left(\frac{\sin x}{1+\cos x}\right)=$

a)

$\frac{\cos x}{-\sin x}$

b)

$\frac{-\sin^2x-\cos x+\cos^2x}{\left(1+\cos x\right)^2}$

c)

$\frac{1}{1+\cos x}$

d)

$\frac{-\cos^2x+\cos x+\sin^2x}{\left(1+\cos x\right)^2}$

6.

The function shown

a)

is continuous at x = 8

b)

is differentiable at x = 8

c)

has a limit that exists at x = 8

d)

exists at x = 8

7.

The function shown

a)

is continuous at x = 2

b)

is differentiable at x = 2

c)

has a limit that exists at x = 2

d)

exists at x = 2

8.

The function shown

a)

is continuous at x = 0

b)

is differentiable at x = 0

c)

has a limit that exists at x = 0

d)

exists at x = 0

9.

Which graph is the derivative of the top graph?

a)

A

b)

B

c)

C

d)

D

10.

f' is given, which could be f?

a)

A

b)

B

c)

C

11.

7

a)

A

b)

B

c)

C

d)

D

12.

The position of an object is given as a function of time by x = 3t² + 5t³- 2t
What is the acceleration of the object at time t = 2 s?

a)

64 m/s/s

b)

60 m/s/s

c)

66 m/s/s

d)

70 m/s/s

13.

Find the slope of the tangent line to f(x) = -3x²-6x at x = 1.

a)

m = 0

b)

f'(x) = -6x - 6

c)

f'(x) = 6x

d)

m = -12

14.

a)

sina

b)

-sina

c)

cosa

d)

-cosa

15.

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

16.

Use the definition of the derivative (aka the limit process) to find the derivative of y=x^2+9 (be ready to show work on the test).

a)

x^2

b)

2x+9

c)

2

d)

2x

17.

From 3 seconds to 11 seconds....

a)

Terrence is skating towards quickly

b)

Terrence is skating away quickly

c)

Terrence is not moving

d)

Terrence is skating towards slowly

18.

From 11 to 16 seconds....

a)

Terrence stopped to tie his shoe

b)

Terrence is skating quickly

c)

Terrence is skating slowly

d)

Terrence is at the top of a hill

19.

log(4x)

a)

log4-logx

b)

log4+logx

c)

4logx

d)

xlog4

20.

log(xy²)

a)

logx+2logy

b)

logx+logy²

c)

logx-2logy

d)

logx+logy+log2

21.

$\log\left(\frac{x}{y}\right)$

a)

logx+logy

b)

xlogy

c)

log(x-y)

d)

logx-logy

22.

When we "take the derivative" of a function what are we finding?

a)

What's a derivative?

b)

The rate at which our struggles in Calculus are increasing.

c)

The slope of the secant line

d)

The slope of the tangent line

23.

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

24.

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

25.

What is the derivative of ln(x)?

a)

xln(x)

b)

1/x

c)

e^x

d)

ln(x+1)

26.

The derivative of a function is its

a)

Slope

b)

Maximum/Minimum

c)

Instantaneous rate of change

d)

Common Denominator

27.

Given the following graph with tangent lines, at which

x-value is the derivative equal to zero?

a)

$x=-8$

b)

$x=-5$

c)

$x=-1.7$

d)

$x=1$

AP Calc Unit 2 Test Review

Total questions: 27

Worksheet time: 7hrs 45mins

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