Free Printable AP Calculus AB FINAL Review (Semester 2)

1.

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

2.

What are the conditions that satisfy the mean value theorem, and what does it mean?

a)

Continuous on the open and differentiable on the closed, and then there is at least 2 numbers c and d in the interval (a,b) (that is a < c < b) such that

b)

Discontinuous on the closed and differentiable on the open, then there is at least one number c in the interval (a,b) (that is a < c < b) such that f'(c)=(f(b)- f(a))/ (b-a)

c)

Continuous on the closed and differentiable on the open,and then there is at least one number c in the interval (a,b) (that is a < c < b) such that f'(c)=(f(b)- f(a))/ (b-a)

d)

Continuous on the open and differentiable on the open, and then there is no number c in the interval (a,b) (that is a < c < b) such that f'(c)=(f(b)- f(a))/ (b-a)

3.

Find the volume of a solid generated by the graph bounded by y=x² and the line y =9 when it is revolved around the x-axis

a)

456

b)

610.73

c)

194.4

d)

610.726

4.

A particle moves along the x-axis with velocity at time x>0 and the function is v(x)=x²+6x+3, is the speed of the particle increasing at x=4?

a)

No because both velocity and acceleration at x=4 is positive

b)

Yes because both velocity and acceleration at x=4 is positive

c)

No because both velocity and acceleration at x=4 is negative

d)

Yes because both velocity and acceleration at x=5 is positive

5.

Alec consumes beverages at a rate of r(x)=10+.2x²beverages per hour, how many beverages does Alec drink in the first 16 hours?

a)

25.068

b)

433.067

c)

5463.759

d)

Too many, Alec should seek medical attention

6.

What is the derivative of the function f(x)=∫₁^2x(6e^x)dx

a)

6e^2x

b)

12e^2x

c)

6e^2x-6e^x

d)

6e^2x

7.

What is the speed of the position function f(x)=-3x²-6x-6 at x=2

a)

-18

b)

18

c)

-6

d)

6

8.

Which of these is the definition of a derivative?

a)

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

b)

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

c)

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

d)

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

9.

Which of these sums up the Mean Value Theorem (MVT)?

a)

$f'\left(c\right)=\frac{f\left(b\right)-f\left(a\right)}{b-a}$

b)

$f\left(c\right)=\frac{f\left(b\right)-f\left(a\right)}{b-a}$

c)

$f\left(c\right)=\frac{f'\left(b\right)-f'\left(a\right)}{b-a}$

d)

$f'\left(c\right)=\frac{f'\left(b\right)-f'\left(a\right)}{b-a}$

10.

Volume using discs revolving around horizontal line.

a)

$\pi\int_{x=a}^{x=b}\left(top\ -bottom\right)^2dx\ \$

b)

$\pi\int_{x=a}^{x=b}\left(top\ -bottom\right)dx\ \$

c)

$\int_{x=a}^{x=b}\left(top\ -bottom\right)^2dx\ \$

d)

$\int_{x=a}^{x=b}\left(top\ -bottom\right)dx\ \$

11.

Volume using discs revolving around vertical line.

a)

$\pi\int_{y=a}^{y=b}\left(right\ -left\right)^2dy\ \$

b)

$\pi\int_{y=a}^{y=b}\left(right\ -left\right)dy\ \$

c)

$\int_{y=a}^{y=b}\left(right\ -left\right)^2dy\ \$

d)

$\int_{y=a}^{y=b}\left(right\ -left\right)dy\ \$

12.

Volume using washers revolving around horizontal line.

a)

$\pi\int_{x=a}^{x=b}R^2-r^2\ dx\ \$

b)

$\pi\int_{x=a}^{x=b}\left(R-r\right)^{2\ }dx\ \$

c)

$\int_{x=a}^{x=b}\left(R-r\right)^2dx\ \$

d)

$\int_{x=a}^{x=b}R^{2\ }-r^{2\ }dx\ \$

13.

Volume using washers revolving around vertical line.

a)

$\pi\int_{y=a}^{y=b}R^2-r^{2\ }dy\ \$

b)

$\pi\int_{y=a}^{y=b}\left(R-r\right)^2dy\ \$

c)

$\int_{y=a}^{y=b}\left(R-r\right)^2dy\ \$

d)

$\int_{y=a}^{y=b}R^2-r^{2\ }dy\ \$

14.

a)

A

b)

B

c)

C

d)

D

e)

E

15.

a)

sinx

b)

-sinx

c)

-cscx cotx

d)

sec²x

16.

Find the derivative.

a)

x⁴cosx - 4x³sinx

b)

x⁴cosx + 4x³sinx

c)

4x³cosx

d)

-4x³cosx

17.

Set up but do not solve an integral that will find the volume of the solid described.

a)

A

b)

B

c)

C

d)

D

e)

E

18.

a)

A

b)

B

c)

C

d)

D

19.

a)

A

b)

B

c)

C

d)

D

20.

Which equation below represents the slope field?

a)

dy/dx = x - 2

b)

dy/dx = 1/2x + 1

c)

dy/dx =1/2 y - 2

d)

dy/dx = y + 2

21.

dy/dx = 4x/y. Suppose y(0)=1
The particular solution is

a)

B

b)

C

c)

D

d)

E

22.

Consider the differential equation dy/dx = x + 2y for which g(x) is the solution. Which of the following statements is true if the particular solution contains (0,-1)

a)

g(x) is increasing and concave up

b)

g(x) is increasing and concave down

c)

g(x) is decreasing and concave up

d)

g(x) is decreasing and concave down

23.

Find the Particular Solution

a)

$y=2+e^{\left(\frac{x^2}{2}+x\right)}$

b)

$y=2e^{\left(\frac{x^2}{2}+x\right)}$

c)

$y=\ln\left|\frac{x^2}{2}+x+1\right|+2$

d)

$y=\ln\left|\frac{x^2}{2}+x+e^2\right|$

24.

Solve the following differential equations:
$\frac{\text{d}y}{\text{d}x}=e^x$

a)

$1=e^x+C$

b)

$y=\frac{e^x}{2}+C$

c)

$y=e^x+C$

d)

$0=e^x+C$

25.

Solve the following differential equations:
$\frac{\text{d}y}{\text{d}x}=3y$

a)

$y=Ce^{3x}$

b)

$y=3x+C$

c)

$\frac{y^2}{2}=3x+C$

d)

$\ln y=x+C$

AP Calculus AB FINAL Review (Semester 2)

Total questions: 25

Worksheet time: 27mins

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