ap calculus summer assignment - east river hs...the next page is where your summer assignment...

AP Calculus Summer Assignment

Welcome to AP Calculus! I’m excited to start our Calculus journey together next school year! To

prepare for the class, I have attached several general questions from Algebra 2 and Pre-Calculus that

you should know how to complete. I have had several students ask what else they should look at over

the summer to help prepare them for AP Calculus. Below are some topics that can be found on khan

academy that would be helpful.

1) Unit Circle – have memorized including radians

2) Equations of lines including parallel and perpendicular lines

3) Inverses

4) Expanding and Condensing Logarithms

5) Composite Functions

6) How to use a graphing Calculator including finding intersections, zeros, minimums and

maximums.

7) Limits

When school begins we will start with content right away. The second day of school you will have a unit

circle quiz, and the first Friday will be a review quiz. Our first topic in AP Calculus is limits and continuity.

Be ready to write in this class as a lot of questions will ask you to explain your reasoning.

The next page is where your summer assignment begins. On a separate piece of paper complete the

questions. Please label each section (EX: Review #1, Review #2,…ect) and SHOW ALL WORK no matter

how simple it may seem. If you are using a formula show the formula you are using and show how you

used the formula. NO WORK= NO CREDIT. NO EXCEPTIONS! This will be due the FIRST DAY of school.

I look forward to seeing you guys next year!

AP Calculus AB - Pre-Calculus Review 1 Name:___________________________

Write the equation of the line with the given information.

1. slope is and 2. passes through 3. perpendicular to

passes through and and passes

through

4. Given the function,

, for what values of is ?

I.

II.

III.

A. I only

B. II only

C. I and II only

D. II and III only

E. I, II, and III

Evaluate without a calculator.

5.

6.

7.

AP Calculus AB - Pre-Calculus Review 2 Name:___________________________

1. Write the equation of the line with a slope of that passes through the point .

2. Evaluate without a calculator:

.

A) B)

C) D)

E)

3. Consider the function .

a) Find the vertex, -intercept and -intercepts of .

b) Find the point(s) of intersection of and the line

4. Given the function,

, what is the minimum value of ?

A) B) C) D) E)

5. Solve for :

AP Calculus AB - Pre-Calculus Review 3 Name:___________________________

(minutes)

0 1 4 7 9

(meters)

0 20 120 250 350

1. Find the rate at which a train’s distance from the station is changing on the interval from

to using the data from the table above. Please indicate units of measure.

2. Given , find each of the following.

a) b) c) d)

3. A bug begins to crawl along a horizontal wire at time minutes. The graph of the bug’s

velocity, , for , is shown below. At what time(s), in minutes, does the bug change

directions?

A)

B) and

C) and

D) , , and

E) , , , and

4. Solve for :

5. Evaluate without a calculator:

.

A) B)

C)

D)

E)

AP Calculus AB - Pre-Calculus Review 4 Name:___________________________

1. Write the equation of the line parallel to the line

that passes through the point

.

2. Given , find each of the following.

a) b) when c) d)

3. Use the tables below to find .

1 2 3 4 5

4 3 5 2 1

1 2 3 4 5

3 5 2 1 4

A) B) C) D) E)

4. A parabola has -intercepts of and and passes through the point . On which

interval is the graph of the parabola increasing?

A) B) C) D) E)

5. Evaluate without a calculator:

.

AP Calculus AB - Pre-Calculus Review 5 Name:___________________________

1. Write an equation for the line containing the points: and .

2. Solve for .

a) b)

c)

d)

3. Identify all the discontinuities of each function. Label each discontinuity as either a vertical

asymptote or a hole.

a)

b)

c)

4. Given , find

.

A) B)

C) D) E)

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PRECALCULUS Name___________________________________

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Limits Review

Evaluate each limit.

1)

lim

r→−3

(

−

r + 2) 2)

lim

w →0

(

w3 − 3

w2 + 5)

3)

lim

t→−3

−2

t + 44)

lim

r→0

r − 7

r2 + 3

r + 2

5)

lim

r→−1 −

−

r + 1

r

f(r)

−8 −6 −4 −2 2 4 6

−8

−6

−4

−2

2

4

6

8

6)

lim

r→0 +

h(

r),

h(

r) = {

−

r2 − 4

r − 3,

r < 0

−

r − 1,

r ≥ 0

r

h(r)

−8 −6 −4 −2 2 4 6 8

−10

−8

−6

−4

−2

2

4

6

7)

lim

x→−1

2

x + 2

x + 1

x

h(x)

−8 −6 −4 −2 2 4 6

−8

−6

−4

−2

2

4

6

8

8)

lim

r→−2

f (

r),

f (

r) = {−3,

r < −2

−

r − 5,

r ≥ −2

r

f(r)

−10 −8 −6 −4 −2 2 4 6

−10

−8

−6

−4

−2

2

4

9)

lim

x→−2

x2 − 4

x + 210)

lim

s→1

−

s − 1

s2 + 2

s − 3

11)

lim

w→2

g(

w),

g(

w) = {

−

w2 + 2

w + 1,

w ≠ 2

4,

w = 212)

lim

x →1−

3

x2 − 1

13)

lim

t→−2 +

−

t + 2

t2 + 5

t + 614)

lim

t →

−

∞

−6

t2 + 3

15)

lim

s→

−

∞

−

s4

4

s2 − 1

16)

lim

x →

−

∞

2

x

x + 2

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Answers to Limits Review

1) 5 2) 5 3) 104)

−7

2

5) 0 6) −1 7) Does not exist. 8) −3

9) −410)

−1

4

11) 1 12) −

∞

13) −1 14) 0 15) −

∞ 16) 2