Free Printable AP Calculus AB

1.

What is the second derivative of f(x) = cos 4x?

a)

16 cos 4x

b)

-16 cos 4x

c)

16 sin 4x

d)

-16 sin 4x

2.

Find the limit.

a)

0

b)

8

c)

16

d)

Does Not Exist (DNE)

3.

Name the discontinuity at x=2.

(Click the image.)

a)

Infinite Discontinuity

b)

Removable Discontinuity

c)

Jump Discontinuity

d)

Continuous at x=2

4.

when is the function f(x)=x²+6x+9 increasing?

a)

(3,∞)

b)

(-∞,3)

c)

(-3,-∞)

d)

(-3,∞)

5.

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

6.

For a function g(x), g'(-2)=0 indicates that x=-2 is ________________.

a)

an inflection point

b)

a critical point

c)

a relative maximum

d)

a relative minimum

7.

For a function f(x), f''(4)=0 indicates that x=4 is _____________.

a)

an inflection point

b)

a critical point

c)

a relative maximum

d)

a relative minimum

8.

Given a function, f(x), if f'(x)>0 over a certain interval, then f(x) is __________ over that interval.

a)

increasing

b)

decreasing

c)

concave up

d)

concave down

9.

Integrate $\int_{ }\ \frac{x^2+3x-2}{x}\ \ dx$

a)

$\frac{x^2}{2}+3x-2\ln\left|x\right|+c$

b)

$\frac{x^2}{2}+x+c$

c)

$\frac{x^2}{2}+3x+c$

d)

$2x+3$

10.

Find $F'\left(x\right)$ given $F\left(x\right)=\int_0^{3x}\cos t\ dt$

a)

$\sin\ 3x$

b)

$-3\sin\ 3x$

c)

$\cos3x$

d)

$3\sin3x$

e)

$3\cos3x$

11.

Find the limit of the function as x approaches 2.

(Click the image.)

a)

1

b)

-1

c)

5

d)

DNE

12.

Find the slope of $y=3x^2-5$ at the point where $x=2$

a)

10

b)

11

c)

12

d)

13

13.

What is the derivative of tan(x)?

a)

tan(x)

b)

sec(x)

c)

tan²(x)

d)

sec²(x)

14.

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

15.

a)

Volume using Shells

b)

Volume using Disks

c)

Volume using Washers

d)

Volume using Cross Sections

16.

Find the mistake if possible. (Click the image.)

a)

The Diff EQ is solved correctly

b)

Step 1 is incorrect. The separation of variables wasn't done correctly.

c)

Step 2 is incorrect. They didn't integrate x² correctly.

d)

Step 3 is incorrect. They didn't take the reciprocal of x³/3+C correctly.

17.

Solve the Initial Value Problem

a)

$y=-\frac{1}{x}$

b)

$y=-x^2$

c)

$y=\frac{-1}{x+1}$

d)

$y=\frac{1}{x+1}$

18.

Which one should be used in the partial fraction decomposition of $\frac{x-11}{\left(x+3\right)^2\left(x-4\right)}?$

a)

$\frac{A}{\left(x+3\right)}+\frac{B}{\left(x+3\right)}+\frac{C}{\left(x-4\right)}$

b)

$\frac{A}{\left(x-4\right)}+\frac{Bx+C}{\left(x+3\right)^2}$

c)

$\frac{A}{\left(x+3\right)^2}+\frac{B}{\left(x-4\right)}$

d)

$\frac{A}{\left(x+3\right)}+\frac{B}{\left(x+3\right)^2}+\frac{C}{\left(x-4\right)}$

19.

What is the outer radius (R) needed to find the volume of the region revolving around $y=1$ ?

(Click the image.)

a)

$1-\left(-x^2+6\right)$

b)

$\left(-x^2+6\right)-1$

c)

$2-1$

d)

$1-2$

20.

Select the integral that would find the volume of the region revolving around the given axis.

(Click the image.)

a)

b)

c)

d)

AP Calculus AB

Total questions: 20

Worksheet time: 3600secs

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