Free Printable AP Calculus Review #2

1.

Selected values from the function f(x) are shown in the table. When a midpoint Riemann sum with two subintervals is used to complete $\int_2^{10}f\left(x\right)dx$ , the value is...

a)

24

b)

28

c)

36

d)

26

2.

$\frac{d}{dx}\left(\frac{1}{2x+5}\right)=?$

a)

$-\frac{2}{\left(2x+5\right)^2}$

b)

$\frac{2}{\left(2x+5\right)^2}$

c)

$\frac{1}{2}\ln\left|2x+5\right|$

d)

$2\ln\left|2x+5\right|$

3.

$\frac{dy}{dx}=e^{x+3}y^3$

What would be a step in solving the differential equation?

a)

$\int y^3dy=\int e^{x+3}dx$

b)

$\int\ \frac{1}{y^3}dy=\int\ e^{x+3}dx$

c)

$\int\ \frac{1}{y^3}dy=\int\ \frac{1}{e^{x+3}}dx$

d)

$\int\ y^3dy=\int\ \frac{1}{e^{x+3}}dx$

4.

Let $g\left(x\right)=\ \int_0^xf\left(t\right)dt$ , where the graph of f is shown. For what value(s) of x does g have an inflection point?

a)

-2, 0, 5

b)

-2 and 5 only

c)

-2, 2, and 8

d)

2 and 8 only

5.

$If\int_2^1f\left(x\right)dx=-3\ and\ \int_2^4f\left(x\right)dx=2.\ then\ \int_1^4f\left(x\right)dx=?$

a)

1

b)

-5

c)

-1

d)

5

6.

The graph of the function f is shown. At which of the following points is f'(x)<0 and f"(x)>0?

a)

c

b)

a

c)

b

d)

d

7.

Selected values from the function f(x) are shown in the table. When a left Riemann sum with two subintervals is used to approximate $\int_0^5f\left(x\right)dx$ , the value is...

a)

16

b)

21

c)

15

d)

11

8.

For a particle moving along the x-axis, x (1 )=5 and v (1)= 2. At time t = 1, it can be said that the particle is...

a)

Speeding up

b)

moving toward the origin

c)

moving away from the origin

d)

slowing down.

9.

Selected values of the twice differentiable function f and its derivative are shown in the table. What is the average value of f' from x = 2 to x = 8?

a)

16

b)

1/3

c)

2

d)

8/3

10.

$\frac{d}{dx}\left(e^{\frac{x}{5}}\right)=?$

a)

$-5e^{\frac{x}{5}}$

b)

$\frac{1}{5}e^{\frac{x}{5}}$

c)

$e^{\frac{x}{5}}$

d)

$5e^{\frac{x}{5}}$

AP Calculus Review #2

Total questions: 10

Worksheet time: 10mins

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