AP CALCULUS AB and CALCULUS SUMMER PREPARATION
Objectives:All students will….
o Become familiar with the features and style of the textbook.
o Be proficient the TI 83/84 graphing calculator and be familiar with the features.
o Review important terminology and concepts learned in prior math classes.
Required Materials:
o Text Book: Calculus – Single Variable 4e by Hughes-Hallett, Gleason, McCallum
o TI 83/84 graphing calculator
QUOTES TO PONDER:
S. Gudder:
The essence of mathematics is not to make simple things complicated, but to
make complicated things simple.
Dean Schlicter:
Go down deep enough into anything and you will find mathematics.
Gottfried Leibniz:
Music is the pleasure the human mind experiences from counting without being
aware that it is counting.
Israel Herstein:
The value of a problem is not so much coming up with the answer as in the
ideas and attempted ideas it forces on the would be solver.
Hermann Hankel:
In most sciences one generation tears down what another has built and what
one has established another undoes. In mathematics alone each generations
adds a new story to the old structure.
Sir Winston Churchill:
I had a feeling once about Mathematics - that I saw it all. Depth beyond depth
was revealed to me - the Byss and Abyss. I saw - as one might see the transit of
Venus or even the Lord Mayor's Show - a quantity passing through infinity and
changing its sign from plus to minus. I saw exactly why it happened and why
the tergiversation was inevitable, but it was after dinner and I let it go.
Dear Future Calculus Student,
As Churchill notes, we are often on the verge of understanding, but get distracted by something (like dinner
or a Celtics game) and ‘let it go’. In calculus, most of the trouble experienced by students does not come
from the concepts in calculus, but from forgotten basics of algebra, geometry and trigonometry. Therefore,
you will be required to spend some time this summer reviewing the fundamentals of the courses that have
brought you to this class called calculus!
Attached to this letter is a book assignment and worksheet. You are expected to read the text book. You
have an awesome book and the sooner you get used to reading a math textbook the better! As you read
the book, take time to follow the examples and study the graphs and tables. If you read something
confusing, go back and read it again. Read the terminology. We assume that at this point you have
mastered the basic skills in algebra … being able to solve equations, work with algebraic expressions and
complete basic factoring, for example. If not, you should not be going into AP Calculus.
DON’T FAKE YOUR WAY THROUGH THE PROCESS JUST TO GET AN ANSWER. Refer to the Herstein quote
… it is the process that is important! Be sure to understand the path to the correct answer so that you can
follow it again the next time you encounter a similar problem. Also realize that many of these topics are
interrelated. Finding Domain may require you to be an expert at working with inequalities, while solving
quadratic equations may involve the same techniques used in solving fractional equations.
IT IS A MISTAKE TO COMPLETE THIS ASSIGNMENT AT THE BEGINNING OF THE SUMMER. Let it go until
mid-summer. We want these techniques to be relatively fresh in your mind in the fall. Also, do NOT wait
to do them at the last minute. These will take time. If you complete two concepts per day, the whole packet
will take you about a week to complete.
IT IS A MISTAKE TO RELY ON YOUR CALCULATOR. While a calculator will be required for many types of
problems, the problems in this packet should not fall into that category and therefore you should work
with only paper and pencil techniques to solve these problems. Much of both courses (Calculus and AP
Calculus AB) next year will be done without a calculator. For those of you in the AP version of the course,
half of your AP Exam will be done without a calculator and many of your exams will have sections where
calculator use is prohibited. Therefore, you need to make sure that you can complete appropriate problems
without the use of your calculator in order to guarantee your success.
QUESTIONS? If you have questions about any of these problems or the techniques used in solving them,
you should start by visiting the following websites:
For most algebra topics: http://www.purplemath.com/modules/index.htm
For most trigonometry topics: http://www.mathematicshelpcentral.com/index.html
Additionally, you can contact us through the school e-mail system at the following addresses:
Ane Swift: aswift@sprise.com
SUPPLIES NEEDED FOR NEXT YEAR:
 You are required to have a graphing calculator. If you do not, please try to purchase one this
summer. We would recommend a TI-83 or TI-84. It is easy to use, and has all the necessary
functions built in. There are some available to borrow from the info center, but they are limited to
in-school use only. (NOTE: The TI-89 is very nice, but it is prohibited on the AP Calculus exam and
therefore is NOT currently recommended for Calculus class.)
 A dedicated notebook for this course with dividers to organize a minimum of notes, homework and
assessments. You will get a lot of worksheets that you will need to keep in some organized manner.
We expect, at this point, for you to not lose your handouts and therefore do not make extra copies.
 A composition book
We are looking forward to seeing each of you in class next fall. Have a great summer and do some
mathematics!
Ane Swift
One last quote, describing your upcoming year in calculus …
TO INFINITY … AND BEYOND! ~Buzz Lightyear
Please consider the reader when completing your assignments. Including the following for each assignment
will do this:
 Heading: name, assignment number, page number, problems and date completed.
 Problem numbers: these should be easy to see so that you can quickly locate problems.
 WORK: without showing your work as you solve a problem, you cannot see where your errors are
when they occur.
 Solutions: please make your solutions stand out so that you can quickly check them against the answers
in the book or those given in class.
HW
#
Page
#’s
LOF
WS
1
7-9
2
14-16
3
21-23
4
27-28
5
35-36
6
42-44
9
58-62
10
62-63
Section Title
 Assigned Problems
Library of Functions
 Graphing Translations Practice
Section 1.1 – Functions and Change
 1, 8, 11, 13, 15, 16, 20, 25, 28, 32, 35, 36
Section 1.2 – Exponential Functions
 1, 4, 6, 11, 14, 16, 18, 21-23, 30, 31, 34, 37
Section 1.3 – New Functions from Old
 3, 9-13, 15, 21, 27, 29, 30-37, 42, 43, 46, 50, 53
Section 1.4 – Logarithmic Functions
 3-30(x3), 32, 39, 41-43, 46
Section 1.5 – Trigonometric Functions
 3-24 (x3), 28, 29, 32, 38, 43, 45
Section 1.6 – Powers, Polynomials, and Rational Functions
 2, 5, 6, 7, 10, 12, 14, 15, 19, 22, 24, 25, 29, 32
Review Exercises and Problems
 1 – 23, 34 - 36
Check Your Understanding
 1-30, 37 – 40, 41 – 45, 49 
Date
Completed
AP Calculus
Graphing Translations Practice
Sketch each of the following and state the domain and range.
1. y = (x + 3)2
2. y = ex – 5
1
x 1
3. y = -x3+ 1
4. y =
5. y = ½x – 4+ 4
6. y = 3sin(x + 1) –2
7. y =
x 5 3
8. y = -2ln x