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Study Guide Precalculus

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Course
BIOLOGY 300

Institution
BIOLOGY 300

About the Author Janet Lee Adams received a Bachelor of Arts in Mathematics (secondary education) from Asbury College in Wilmore, Kentucky; a Master of Science in Operations Research from the University of Kentucky in Lexington, Kentucky; and a Master of Arts in Teaching Mathematics, also fr...

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Precalculus

Study Guide

Precalculus
By

Janet L. Adams

Reviewed By

Nathan C. Carter, Ph.D.

, About the Author
Janet Lee Adams received a Bachelor of Arts in Mathematics
(secondary education) from Asbury College in Wilmore, Kentucky;
a Master of Science in Operations Research from the University of
Kentucky in Lexington, Kentucky; and a Master of Arts in Teaching
Mathematics, also from the University of Kentucky. She taught a
variety of mathematics courses in high school for 15 years and
currently teaches classes at the Pennsylvania State University,
Worthington Scranton Campus. She has served as a speaker at
a number of mathematics conferences at the regional, state, and
national levels. Janet is a member of the Pennsylvania Council of
Teachers of Mathematics and of the Northeastern Council of
Teachers of Mathematics.

About the Reviewer
Nathan C. Carter received a Bachelor of Arts in both Mathematics
and Computer Science from the University of Scranton in Scranton,
Pennsylvania. He completed his postgraduate work at Indiana
University in Bloomington, Indiana, where he earned a Master
of Science in Computer Science and a doctorate in Mathematics.
Dr. Carter is currently teaching mathematics courses at Bentley
University, Waltham, Massachusetts. His research includes arti-
cles on mathematical logic and social network analysis, and
educational software development projects in group theory
visualization and teaching mathematical proofs.

All terms mentioned in this text that are known to be trademarks or service
marks have been appropriately capitalized. Use of a term in this text should not be
regarded as affecting the validity of any trademark or service mark.

Copyright © 2009 by Penn Foster, Inc.
All rights reserved. No part of the material protected by this copyright may be
reproduced or utilized in any form or by any means, electronic or mechanical,
including photocopying, recording, or by any information storage and retrieval
system, without permission in writing from the copyright owner.
Requests for permission to make copies of any part of the work should be

, Contents
INSTRUCTIONS TO STUDENTS 1

LESSON ASSIGNMENTS 7

LESSON 1: EXPONENTS, LOGARITHMS,
SEQUENCES, AND SERIES 9

EXAMINATION—LESSON 1 41

LESSON 2: TRIGONOMETRIC FUNCTIONS 47

EXAMINATION—LESSON 2 75

LESSON 3: ANALYTIC TRIGONOMETRY 81

EXAMINATION—LESSON 3 95

LESSON 4: ADDITIONAL TOPICS IN
TRIGONOMETRY 101

EXAMINATION—LESSON 4 123

LESSON 5: SYSTEMS OF EQUATIONS AND
INEQUALITIES 129

EXAMINATION—LESSON 5 147

iii

, YOUR COURSE

Instructions
Mathematicians generally consider a course in precalculus to
be an in-depth transition from the studies of algebra and
trigonometry to the study of calculus. Algebraic topics in pre-
calculus concentrate more on modeling real-world data than
do those in intermediate algebra. In precalculus, trigonome-
try (triangle measurement) is taken outside triangles and is
defined on a unit circle. In addition, you’ll be introduced to
advanced topics not covered in algebra or trigonometry. The
result is a course that will allow you to go beyond elementary
word problems to advanced applications of your knowledge.
You’ll apply the skills you learn to the areas of business,
manufacturing, scientific research, physics, and cycles in
nature and the human body—to name a few.
In addition, you’ll need the skills you learn in this course
to study calculus, which is without a doubt one of the most
important area of mathematics ever developed. Whether or
not you plan to continue in your study of mathematics, how-
ever, doesn’t mean that this course has no value in and of
itself. Any academic study in which you engage will make you
a better thinker and problem-solver for life.

OBJECTIVES
When you complete this course, you’ll be able to
■ Solve equations, including exponential, logarithmic, and
trigonometric

■ Graph exponential, logarithmic, and trigonometric equa-
tions and equations in polar form

■ Solve systems of equations using substitution and
addition methods

■ Graph solutions to inequalities in the coordinate plane

■ Graph solutions to systems of inequalities in the
coordinate plane

■ Compute sums of finite and infinite series

1

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