Free Printable Calculus AP Exam 5 for 5 Thursday Before

1.

If f is continuous on the interval [a,b] and differentiable on the interval (a,b), which of the following COULD be false?

a)

$f'\left(c\right)=\frac{f\left(b\right)-f\left(a\right)}{b-a}$ for some c such that a < c < b

b)

$f'\left(c\right)=0$ for some c such that a < c < b

c)

f has a minimum value on the interval [a,b]

d)

f has a maximum value on the interval [a,b]

e)

$\int_a^bf\left(x\right)dx$ exists.

2.

A tank is being filled with a liquid. The function V gives the volume of liquid in the tank, in liters, after t minutes.

What is the best interpretation for the following statement?

The value of the derivative of V at t=1 is equal to 2.

a)

After 1 minute, the tank was being filled at a rate of 2 liters.

b)

After 1 minute, the tank had 2 liters of liquid.

c)

After 1 minute, the tank was being filled at a rate of 2 liters per minute.

d)

During the first minute, the tank was being filled at a rate of 2 liters per minute.

3.

$\frac{d}{dx}\left(\int_0^{x^2}\sin\left(t^3\right)dt\right)=$

a)

$-\cos\left(x^6\right)$

b)

$\sin\left(x^3\right)$

c)

$\sin\left(x^6\right)$

d)

$2x\sin\left(x^3\right)$

e)

$2x\sin\left(x^6\right)$

4.

Which setup would find the volume of the solid formed by revolving the shaded region around the y axis?

a)

$\pi\int_0^2\ 4\ dy+\pi\int_2^4\left(4-\left(g\left(y\right)\right)^2\right)dy$

b)

$\pi\int_0^4\left(\left(2-g\left(y\right)\right)^2\right)dy$

c)

$\pi\int_0^24\ dy+\pi\int_2^4\left(\left(2-g\left(y\right)\right)^2\right)dy$

d)

$\pi\int_0^4\left(4-\left(g\left(y\right)\right)^2\right)dy$

5.

Let f be the function where the derivative is given by $f'\left(x\right)=x^2-\frac{8}{x}$ . On which of the following intervals is f decreasing?

a)

$\left(-\infty,-1\right]\ only$

b)

$\left(-\infty,0\right)$

c)

$\left[-1,0\right)\ only$

d)

$\left(0,2\right]$

e)

$\left[2,\infty\right)$

6.

What is the derivative of tanx?

a)

sec²x

b)

secxtanx

c)

-csc²x

d)

tan²x

7.

What is the derivative of secx?

a)

secx

b)

tan²x

c)

sec²x

d)

secxtanx

8.

What is the derivative?

a)

b)

c)

d)

Undefined

9.

a)

6

b)

2

c)

1

d)

0

10.

Use implicit differentiation to find y' for the following equation: 4x cos(y) = 1

a)

y' = cos(y) / x sin(y)

b)

y' = 4x sin(y)

c)

y' = cot(y)

d)

y' = 4 / sec(y)tan(y)

11.

The graph of $f'$ , the derivative of the function f, is shown above. Which of the following could be the graph of $f$

a)

b)

c)

d)

12.

A Particle moves on the x-axis. Given that $v\left(t\right)=-t^2+2t+5$ is the particle SPEEDING UP or SLOWING DOWN at t=4?

a)

Speeding Up

b)

Slowing Down

c)

Neither

Calculus AP Exam 5 for 5 Thursday Before

Total questions: 12

Worksheet time: 22mins

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