411 SAT Algebra & Geometry Questions

176 Pages·2008·3.22 MB·English

411 SAT
ALGEBRA AND
GEOMETRY
QUESTIONS

411 SAT
ALGEBRA AND
GEOMETRY
QUESTIONS
®
N E W Y O R K
Copyright © 2006 LearningExpress,LLC.
All rights reserved under International and Pan-American Copyright Conventions.
Published in the United States by LearningExpress,LLC.,New York.
Library ofCongress Cataloging-in-Publication Data:
411 SAT algebra and geometry questions.
p.cm.
ISBN1-57685-560-0
1.Algebra—Examinations,questions,etc. 2.Geometry—Examinations,questions,etc.
3.SAT(Educational test)—Study guides. I.LearningExpress (Organization).
II.Title:Four hundred eleven SATalgebra and geometry questions.
QA157.A14 2006
512.0076—dc22 2006005374
Printed in the United States ofAmerica
9 8 7 6 5 4 3 2 1
ISBN 1-57685-560-0
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Contents
INTRODUCTION 1
PRETEST 5
CHAPTER 1 Algebraic Expressions 13
CHAPTER 2 Solving Equations and Inequalities 19
CHAPTER 3 Quadratic Expressions and Equations 25
CHAPTER 4 Factoring and Multiplying Polynomials 33
CHAPTER 5 Radicals and Exponents 37
CHAPTER 6 Sequences 45
CHAPTER 7 Systems ofEquations 49
CHAPTER 8 Functions,Domain,and Range 55
CHAPTER 9 Angles 63
CHAPTER 10 Triangles 71
CHAPTER 11 Right Triangles 77
CHAPTER 12 Polygons 85
CHAPTER 13 Quadrilaterals 89
CHAPTER 14 Area and Volume 93
v
–CONTENTS–
CHAPTER 15 Circles 99
CHAPTER 16 Coordinate Geometry 107
POSTTEST 113
ANSWERS 121
vi
411 SAT
ALGEBRA AND
GEOMETRY
QUESTIONS

Introduction
I
hate math.”“Math is my worst subject.”“I’ll never understand math—it’s too hard.”
So many people approach math with an attitude that dooms them to failure before they even get started.
Your approach to math,or any subject,can make all the difference in the world.With the majority ofSAT
math questions involving algebra or geometry,this book is designed not only to give you the algebra and geom-
etry skills you need for the exam,but also to provide you with the confidence you require to score highly on
theexam.
You can’t study every possible word that may appear on the verbal portion ofthe SAT.No such list even exists.
However,all ofthe math skills that you will encounter on the math portion ofthe SAT are known,and the most
common ofthem are in this book.In this respect,it’s actually easier to study for the math sections ofthe SAT than
the verbal sections.
This book trains you for the SAT with 411 math questions.Every question can be solved using the skills
described in the following 16 chapters,and every answer is explained.Ifan explanation doesn’t make sense,review
the related material in the chapter,and then try the question again.
Don’t get discouraged.Use these chapters to gain an understanding ofthe algebra and geometry that’s given
you trouble in the past.With time and practice,you’ll become comfortable with math and enter the SAT with con-
fidence,believing you are prepared for any question.
1
–INTRODUCTION–
(cid:2) An Overview of This Book
This book is divided into an algebra section and a geometry section,each comprised ofeight chapters,plus a pretest
and a posttest.The tests are made up ofonly algebra and geometry questions.Use the pretest to identify the top-
ics in which you need improvement.Use the posttest to help you identify which topics you may need to review
again.The first eight chapters focus on algebra skills:
Chapter 1:Algebraic Expressions
Understand the parts ofalgebraic expressions,combine like and unlike terms,evaluate expressions using sub-
stitution,and evaluate one variable in terms ofanother.
Chapter 2:Solving Equations and Inequalities
Use basic arithmetic and cross multiplication to solve single- and multi-step equations,find the values that make
an expression undefined,and form algebraic equations from word problems.
Chapter 3:Quadratic Expressions and Equations
Multiply binomials,factor and solve quadratic equations,and analyze the graphs ofquadratic equations.
Chapter 4:Factoring and Multiplying Polynomials
Multiply,factor,and find the roots ofpolynomials.
Chapter 5:Radicals and Exponents
Add,subtract,multiply,divide,and simplify radicals and terms with exponents;rationalize denominators and
solve equations with radicals.Work with negative and fractional exponents,and raise exponents to exponents.
Chapter 6:Sequences
Solve arithmetic,geometric,and combination sequences for the next or missing term.
Chapter 7:Systems ofEquations
Solve systems oftwo equations with two variables using substitution and combination.
Chapter 8:Functions,Domain,and Range
Determine ifan equation is a function using the vertical line test,find the domain and range offunctions,solve
nested functions and evaluate functions with newly defined symbols.
The last eight chapters focus on geometry skills:
Chapter 9:Angles
Recognize and use the properties ofacute,obtuse,right,straight,complementary,supplementary,vertical,and
alternating angles.
2