AP Calculus (AB)
Introductory Information
June 2012
Mr. Lajoie
Welcome to AP Calculus 2012-2013!
Topic 1: Textbook
You are required to purchase the textbook for this course as soon as possible.
The information for ordering is below:
Title: Calculus: Early Transcendentals, Eighth Edition
Authors: Howard Anton, Irl Bivens, Stephen Davis
ISBN#: 978-0-471-47244-5
It is imperative that you order this exact edition. CHECK THE ISBN NUMBER!!! There
are different editions of the 8th edition, so the correct ISBN number is crucial! Do not
attempt to purchase an older version or the newer version – it must be the 8th edition!
How to order:
I strongly urge you to purchase a used version of the textbook online, which you can
do at most sites that sell books. It is available at many sites for as low as $10 – $20.
Some students have purchased two textbooks (one for home, one for school).
You may also order it by contacting the publisher at 1(800)-CALL-WILEY (225-5945).
The book covers material through Multivariable Calculus, which is the third semester of
college calculus. It will be of incredible use to you in the future.
Topic 2: Summer Assignment
You are required to complete the attached assignment before the first day of school. An
assessment on this material will be taken within the first two weeks of the school year.
The material is a review of concepts learned in Algebra II and Pre-Calculus. The
intention of this assignment is not to make your summer miserable. The assignment is
meant to provide you an opportunity to determine your readiness for Calculus, and to
shed light on topics from past math classes that have particular importance in Calculus.
Please note: This is a substantial assignment which should be worked on throughout
the summer. Waiting until August to begin the assignment is strongly discouraged.
Collaboration is allowed; however, it would be more beneficial for you to work on the
assignment independently and only work with peers if absolutely necessary. The
assignment is intended to be a way for myself but particularly for you to assess your
mathematical ability and your preparedness for AP Calculus (AB).
Page |1
AP Calculus (AB)
Introductory Information
June 2012
Mr. Lajoie
An outline of the assignment is below:
Part/Title
A: Trigonometry
Number of
Part/Title
Questions
45
H: Isolating Variables
Number of
Questions
4
B: Logarithms and Exponentials
30
I: Domain
8
C: Rational Expressions,
Functions, and Equations
D: Polynomials
15
J: Difference Quotient
3
10
K: Inverse Functions
3
E: Lines
5
L: Parametric Equations
5
F: Irrational Expressions
5
M: Graphing Functions
9
G: Inequalities
5
N: Similarity
2
*Please complete this assignment in an orderly fashion using either a
COMPOSITION BOOK purchased on your own or using provided BLUE BOOKS.
*I will not accept anything written on the actual assignment or on extra loose-leaf paper.
*You may certainly “jump around” as you set out on completing it; but when you submit
it, please label the top of each page with “Part A”, “Part B”, etc.
Topic 3: Summer Review Sessions
There will be two optional review sessions over the summer. This is an opportunity for
you to come prepared with questions on the exercises from the assignment. The
sessions are informal and will be a good opportunity to come together as a group and to
begin the wonderful work we will be doing next year together. You may come for as little
or as long as you want to either or both sessions! The tentative dates, times, and
locations of the session are below. Please check your student e-mail over the summer
for any changes to these dates, times, and/or locations:
Monday, August 6th, 2012, 12:00PM – 3:00PM, Room ND403
Wednesday, August 8th, 2012, 12:00PM – 3:00PM, Room ND403
Topic 4: Attitude
AP Calculus (AB) is meant to be a challenge. However, with the right attitude (namely: a
positive outlook, a willingness to learn, enthusiasm for the learning process, dedication,
and a determination to succeed), I am confident that you will be more than able to rise
to that challenge. I am looking forward to an extraordinary year with you; I hope you are
as well! Enjoy the summer!
Mr. Lajoie (jlajoie@stalux.org)
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A.P. Calculus (AB): Summer Assignment 2012
Part A: Trigonometry
Directions: Evaluate each expression below without using a calculator.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
Directions: Solve the trigonometric equations over the specified interval.
29.
30.
ALL WORK MUST BE COMPLETED IN SEPARATE COMPOSITION BOOK OR BLUE BOOKS
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A.P. Calculus (AB): Summer Assignment 2012
Directions: Graph at least two cycles of each trigonometric function below without a calculator.
31.
32.
33.
34.
35.
36.
Directions: Prove (verify) the trigonometric identities below. Work with one side only.
37.
38.
Directions: Suppose you are told
and that
39.
40.
41.
. Find the exact value of:
42.
43.
Directions: Find the exact value of each expression below without a calculator. Draw a diagram
to assist you.
44.
45. (Express answer in terms of ).
ALL WORK MUST BE COMPLETED IN SEPARATE COMPOSITION BOOK OR BLUE BOOKS
Page 2
A.P. Calculus (AB): Summer Assignment 2012
Part B: Logarithms and Exponentials
Directions: Evaluate each expression below without using a calculator.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
Directions: Expand (16) and condense (17) the logarithmic expressions below.
16.
17.
Directions: Solve the logarithmic equations below without a calculator.
18.
19.
20.
Directions: Simplify the power expressions below. Use positive exponents only.
21.
22.
23.
24.
Directions: Solve the exponential equations below without a calculator.
25.
26.
27.
28.
ALL WORK MUST BE COMPLETED IN SEPARATE COMPOSITION BOOK OR BLUE BOOKS
Page 3
A.P. Calculus (AB): Summer Assignment 2012
Directions: Graph each function below without using a calculator.
29.
30.
Part C: Rational Expressions, Functions, and Equations
Directions: Simplify the rational expressions below.
1.
2.
3.
4.
5.
Directions: Multiply (6), divide (7), and add/subtract (8) the rational expressions below.
6.
7.
8.
Directions: Graph each rational function below. Determine intercepts, asymptotes, holes, etc.
9.
10.
Directions: Solve the rational equation below.
11.
Directions: Write the partial fraction decomposition of each rational expression below.
12.
13.
14.
15.
ALL WORK MUST BE COMPLETED IN SEPARATE COMPOSITION BOOK OR BLUE BOOKS
Page 4
A.P. Calculus (AB): Summer Assignment 2012
Part D: Polynomials
Directions: Find the quotient and remainder by performing synthetic (1) and long (2) division.
1.
2.
Directions: Find all solutions to the higher-degree polynomial equations below.
3.
4.
5.
Directions: Factor the polynomial expressions below.
6.
7.
8.
9.
10.
Part E: Lines
1. Find the equation of the line through the points
and
in both slope-intercept
and standard form.
2. Find the equation of the line through the point
and parallel to the line
in both slope-intercept and standard form.
3. Find the equation of the line through the point
and perpendicular to the line
in both slope-intercept and standard form.
4. The point
lies on a circle centered at
. Find the equation of the circle.
5. Find the equation of the line tangent to the circle in the previous problem at
.
Part F: Irrational Expressions
Directions: Rationalize the denominator for each expression below.
1.
2.
3.
4.
ALL WORK MUST BE COMPLETED IN SEPARATE COMPOSITION BOOK OR BLUE BOOKS
5.
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A.P. Calculus (AB): Summer Assignment 2012
Part G: Inequalities
Directions: Solve the inequalities below (use a sign-line when necessary).
1.
2.
4.
3.
5.
Part H: Isolating Variables
Directions: Solve for the specified variable in each equation below.
1. Solve for :
2. Solve for :
3. Solve for :
4. Solve for :
Part I: Domain
Directions: Find the domain of each function below.
1.
2.
3.
4.
5.
6.
7.
8.
ALL WORK MUST BE COMPLETED IN SEPARATE COMPOSITION BOOK OR BLUE BOOKS
Page 6
A.P. Calculus (AB): Summer Assignment 2012
Part J: Difference Quotient
Directions: Simplify the difference quotient for each expression below.
Recall the difference quotient:
1.
2.
3.
Part K: Inverse Functions
Directions: Find the inverse function associated with each function below.
1.
2.
3.
Part L: Parametric Equations
Directions: Find an equation in
and
1.
2.
4.
for the parametric equations below.
3.
5.
ALL WORK MUST BE COMPLETED IN SEPARATE COMPOSITION BOOK OR BLUE BOOKS
Page 7
A.P. Calculus (AB): Summer Assignment 2012
Part M: Graphing Functions
Directions: Graph each of the functions below.
1.
2.
3.
4. Complete the square and
convert to vertex form to graph:
5.
6.
7.
8.
9.
Part N: Similarity
Directions: Express
in terms of the other variables in the picture.
ALL WORK MUST BE COMPLETED IN SEPARATE COMPOSITION BOOK OR BLUE BOOKS
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