Free Printable AP Calculus Review

1.

Use the graph of f(x) above to find $\lim_{x\rightarrow0}f\left(x\right)$

a)

-.05

b)

0

c)

1

d)

DNE

2.

People enter a line for Space Mountain at a rate modeled by $r\left(t\right)=3t^2+\left(t-4\right)^3$ where t is measured in minutes. At t=0 there are 15 people in line. Approximately how many people are in line after 5 minutes.

a)

85

b)

61

c)

76

d)

57

3.

Using the identity that $\frac{1}{x^2-5x+6}$ = $\frac{1}{x-3}-\frac{1}{x-2}$ evaluate $\int\frac{1}{x^2-5x+6}dx$

a)

$-\frac{1}{2}x^2-3x+c$

b)

$\ln\left|x-3\right|+\ln\left|x-2\right|+c$

c)

$\ln\left|x-3\right|-\ln\left|x-2\right|+c$

d)

$\frac{1}{\left(x-2\right)^3\left(x-3\right)^2}+c$

4.

Sarah watches her favorite tree grow every year. The height of the tree at time t is given by twice differentiable function shown in the table. What concept guarantees that there exists a value of t for $2\le t\le10$ such that H'(t)=1.75

a)

Intermediate Value Theorem

b)

Mean Value Theorem

c)

Fundamental Theorem of Calculus

d)

Alternating Series Test

5.

All of the following statements about the ratio test are true EXCEPT...

a)

The series $\sum_{ }^{ }a_n$ converges absolutely when $\lim_{n\rightarrow\infty}\left|\frac{a_{n+1}}{a_n}\right|>1$

b)

The ratio test is inconclusive when $\lim_{n\rightarrow0}\left|\frac{a_{n+1}}{a_n}\right|=1$

c)

The series $\sum_{ }^{ }a_n$ diverges when $\lim_{n\rightarrow\infty}\left|\frac{a_{n+1}}{a_n}\right|=\infty$

d)

The series $\sum_{ }^{ }a_n$ converges absolutely when $\lim_{n\rightarrow\infty}\left|\frac{a_{n+1}}{a_n}\right|<1$

6.

The region enclosed by the graph $f\left(x\right)=\frac{1}{2}x^4+x^3+2$ and the horizontal line y=3 is shown above. This region is the base of a solid where each cross section perpendicular to the x-axis is a square. Which of the following models the volume of the solid?

a)

$\int_{-2.19}^{.885}\left(3-\left(\frac{1}{2}x^4+x^3+2\right)\right)^2dx$

b)

$\int_0^{.885}\left(\frac{1}{2}x^4+x^3+2\right)^2dx$

c)

$\int_{-2.19}^{.885}\frac{1}{2}\left(\frac{1}{2}x^4+x^3+2\right)^2dx$

d)

$\int_{-2.19}^{.885}\frac{1}{2}\left(3-\left(\frac{1}{2}x^4+x^3+2\right)\right)dx$

7.

By the alternating series test, what two statements must be true for the series $\sum_{n=1}^{\infty}\left(-1\right)^nb_n$ to converge?

a)

$\lim_{n\rightarrow\infty}b_n=0$

b)

$\left\{\left(-1\right)^nb_n\right\}$ is a decreasing sequence

c)

$\left\{b_n\right\}$ is a decreasing sequence

d)

$\lim_{n\rightarrow\infty}b_n<1$

8.

Shay pulls her taquitos out of the oven at t=0. Their temperature at this time is 103°C and the temperature is greater than 82°C for all t>0. The temperature of the taquitos at time t is modeled by the function B that satisfies the differential equation $\frac{\text{d}B}{\text{d}y}=-\frac{3}{7}\left(B-82\right)$
Use an equation for the line tangent to the graph of B at t=0 to approximate the temperature of the taquitos at t=5.

a)

B(5)≈ 33°C

b)

B(5)≈ 21°C

c)

B(5)≈ 67°C

d)

B(5)≈ 58°C

9.

What method can be used to evaluate $\lim_{x\rightarrow6}\ \frac{x^2-36}{x-6}$ and what is the solution?

a)

Direct Substitution, DNE

b)

L'Hospital's Rule, 12

c)

Conjugation, 0

d)

Squeeze Theorem, 12

10.

All of the following conditions destroy differentiability EXCEPT...

a)

Discontinuities in the function

b)

Corners on the graph

c)

Horizontal Tangents

d)

Cusps on the graph

11.

Integrate $\int2\sin^2x\cos xdx$

a)

$2\sin x\cos x+c$

b)

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

c)

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

d)

$3\cos x+2\sin x+c$

12.

Freddy's snow-cone's paper cone has a height of 10cm and a diameter of 8cm. He notices the blue-raspberry ice leaking out of the cone onto his shirt at a rate of 2 cm³/min. Find the rate at which the ice level is changing when the height of the ice is at 5cm in the cup.

a)

$-\frac{1}{8\pi}$ cm/min

b)

$\frac{1}{8\pi}$ cm/min

c)

$-\frac{3\pi}{2}$ cm/min

d)

$\frac{3\pi}{4}$ cm/min

13.

Given $f"\left(x\right)=2\left(x-4\right)\left(x+2\right)^2$ which of the following is a point of inflection on the graph of y= f(x).

a)

x=2

b)

x=-2

c)

x=0

d)

x=4

14.

Which of the following is NOT an example of a series that can diverge by the nth test?

a)

$\sum_{k=1}^{\infty}\left(-1\right)^k$

b)

$\sum_{k=1}^{\infty}27\left(\frac{5}{4}\right)$

c)

$\sum_{k=1}^{\infty}\frac{1}{2^k}$

d)

$\sum_{k=1}^{\infty}x^2+4x$

15.

Does the series $\sum_{n=5}^{\infty}3\left(\frac{1}{4}\right)^{n-5}$ converge? If so, what is the sum?

a)

Diverges

b)

Converges, $\frac{4}{3}$

c)

Converges, $\frac{1}{4}$

d)

Converges, 4

16.

Jack and Jill are strawberry picking. The amount of strawberries in their basket is modeled by

f\left(t\right)=4\left(1.15\right)^t

where

f\left(t\right)

is in pounds and t is in minutes. Find the average value of strawberries in their basket over the first 20 minutes at the strawberry field rounded to the nearest whole number.

a)

22 strawberries

b)

440 strawberries

c)

36 strawberries

d)

6 strawberries

17.

A function f is modeled by the nth-degree Taylor polynomial for f about x=0. Given $f\left(0\right)=2,\ f'\left(0\right)=-1,\ f"\left(0\right)=\frac{1}{4}$ find $P_2\left(x\right)$

a)

$2-x+\frac{x^2}{4}$

b)

$-2+x-\frac{x^3}{4}$

c)

$2-x+\frac{x^3}{8}$

d)

$2-x+\frac{x^2}{8}$

18.

The function $r=4\cos3\theta$ has the graph of a

a)

Limacon

b)

Circle

c)

Rose Curve

d)

Lemniscate

19.

What is the arc length of the function $f\left(x\right)=\frac{1}{3}x^2$ over the interval $0\ge x\ge10$ ?

a)

22.176

b)

20.228

c)

35.653

d)

33.333

20.

What is the component form of a vector with a magnitude of 5 and a direction angle of 45°?

a)

$<5\sin45°,\ 5\cos45°>$

b)

$<5,45°>$

c)

$<5\cos45°,\ 5\sin45°>$

d)

$<45°,5>$

AP Calculus Review

Total questions: 20

Worksheet time: 56mins

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