Free Printable AP Calculus Review

1.

The graph of f has a relative extrema when f'

a)

changes sign

b)

equals zero

c)

goes from negative to positive

d)

goes from positive to negative

2.

Let $g\left(x\right)=\int_0^xf\left(t\right)dt$ , where the graph of f is shown above. On what interval(s) is g decreasing?

a)

[2,8]

b)

[0,5]

c)

[2,5]

d)

[-5,-2]U[0,5]

3.

If $w\left(x\right)=f\left(x\right)q\left(x\right)$ , then $w'\left(x\right)=$

a)

$f'\left(x\right)q'\left(x\right)$

b)

$f'\left(x\right)q'\left(x\right)+f\left(x\right)q\left(x\right)$

c)

$f'\left(q\left(x\right)\right)q'\left(x\right)$

d)

$f'\left(x\right)q\left(x\right)+f\left(x\right)q'\left(x\right)$

4.

For the function f, it is known that $\lim_{x\rightarrow-1^-}f'\left(x\right)=\lim_{x\rightarrow-1^+}f'\left(x\right)$ . Which of the following must be true?

I. f is continuous at x = -1

II. f is differentiable at x = -1

a)

Both I and II

b)

I only

c)

II only

d)

Neither I or II

5.

Evaluate $\lim_{x\rightarrow\frac{\pi}{4}}\frac{\cos x-\cos\left(\frac{\pi}{4}\right)}{x-\frac{\pi}{4}}$

a)

$-\frac{\sqrt{2}}{2}$

b)

DNE

c)

$0$

d)

$\frac{\sqrt{2}}{2}$

6.

$\frac{d}{dx}\left(\frac{1}{1-2x}\right)$ equals

a)

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

b)

$-2\ln\left|1-2x\right|$

c)

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

d)

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

7.

For a particle moving along the x-axis, the particle's speed equals 2 when

a)

$\left|v\left(t\right)\right|=2$

b)

$v\left(t\right)=2$

c)

$a\left(t\right)=2$

d)

$\left|a\left(t\right)\right|=2$

8.

If $f\left(x\right)=\int_4^x\left(\cos\left(2t\right)+3\right)dt$ , then $f'\left(x\right)=$

a)

$\frac{1}{2}\sin\left(2x\right)+3x$

b)

$\cos\left(2x\right)$

c)

$2\cos\left(2x\right)+3$

d)

$\cos\left(2x\right)+3$

9.

$\frac{d}{dx}\cos x=$

a)

$-\frac{1}{\sqrt{1-x^2}}$

b)

$\frac{1}{\sqrt{1-x^2}}$

c)

$-\sin x$

d)

$\sin x$

10.

The region R is the area enclosed by the functions $y=2x$ and $y=x^2$ . Which expression represents the area of R?

a)

$\int_0^2\left(x^2-2x\right)dx$

b)

$\int_0^2\left(2x-x^2\right)dx$

c)

$\int_0^4\left(2x-x^2\right)dx$

d)

$\int_0^4\left(x^2-2x\right)dx$

AP Calculus Review

Total questions: 10

Worksheet time: 14mins

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