Roadmap to 8th Grade Math, New York Edition

About This Book

If Students Need to Know It, It’s in This Book
This book develops the Math skills of eighth graders. It builds skills that will help them succeed in school and on the New York State test.

Why The Princeton Review?
We have more than 20 years of experience helping students master the skills needed to excel on standardized tests. Each year, we help more than 2 million students score higher and earn better grades.

We Know the New York State Testing Program
Our experts at The Princeton Review have analyzed the New York State test, and this book provides the most up-to-date, thoroughly researched practice possible for the Grade 8 Mathematics test. We break down the test into individual skills to familiarize students with the test’s structure, while increasing their overall skill level.

We Get Results
We know what it takes to succeed in the classroom and on tests. This book includes strategies that are proven to improve student performance. We provide

• content review, detailed lessons, and practice exercises modeled on the skills tested by the New York State Grade 8 Mathematics test
• engaging puzzles and word problems
• 2 complete practice New York State Math tests

Table of Contents

CONTENTS
Part I: Introduction
Introduction for Parents and Teachers . . . . . . . . . . . . . . . . . . . . . . . . . .3
Student Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5
Mile 1: Answering Multiple-Choice Questions . . . . . . . . . . . . . . . . . . . . .7
Mile 2: Answering Open-Response Questions . . . . . . . . . . . . . . . . . . . . .9
Part II: Math Review
Mile 3: Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13
Integers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13
Order of Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15
Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15
Divisibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15
Prime Factorization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16
Absolute Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16
Mile 4: Factors, Multiples, and Fractions . . . . . . . . . . . . . . . . . . . . . . .17
Greatest Common Factor (GCF) . . . . . . . . . . . . . . . . . . . . . . . .17
Least Common Multiple (LCM) . . . . . . . . . . . . . . . . . . . . . . . . .17
Rational Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18
Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18
Mile 5: Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .21
Variables, Expressions, and Equations . . . . . . . . . . . . . . . . . . .21
Distribution and Factoring . . . . . . . . . . . . . . . . . . . . . . . . . . . .22
Solving Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .22
Mile 6: Fractions, Decimals, and Percents . . . . . . . . . . . . . . . . . . . . . . .25
Percent Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .26
More on Percents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .27
Mile 7: Inequalities, Ratios, and Proportions . . . . . . . . . . . . . . . . . . . . .31
Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .31
Ratios and Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .32
Scale Drawings and Models . . . . . . . . . . . . . . . . . . . . . . . . . . .33
Proportions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .33
Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .34
Powers and Exponents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .35
Scientific Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .35
Square Roots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .36
The Real Number System . . . . . . . . . . . . . . . . . . . . . . . . . . . . .37
Mile 8: Lines, Angles, and Polygons . . . . . . . . . . . . . . . . . . . . . . . . . . . .39
Lines and Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .39
Classifying Quadrilaterals . . . . . . . . . . . . . . . . . . . . . . . . . . . .41
Perimeter and Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .43
Mile 9: Triangles, Congruence, and Similarity . . . . . . . . . . . . . . . . . . . .47
Classifying Triangles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .47
Similar Polygons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .50
Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .51
01-Part I/CH 1 8th Gr 6/23/03 11:11 AM Page v
Mile 10: The Pythagorean Theorem, Trigonometry, Circles, and Solids . .53
Pythagorean Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .53
Trigonometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .55
Circles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .56
Three-Dimensional Figures . . . . . . . . . . . . . . . . . . . . . . . . . . .57
Mile 11: The Coordinate System, Functions, and Transformations . . . . .59
The Coordinate System . . . . . . . . . . . . . . . . . . . . . . . . . . . . .59
Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .62
Translations, Reflections, Rotations . . . . . . . . . . . . . . . . . . . .63
Mile 12: Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .65
Graphs that Display Data . . . . . . . . . . . . . . . . . . . . . . . . . . . .65
Measures of Central Tendency . . . . . . . . . . . . . . . . . . . . . . . .67
Probability of Simple Events . . . . . . . . . . . . . . . . . . . . . . . . . .67
Probability of Compound Events . . . . . . . . . . . . . . . . . . . . . . .72
Answers to Review Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .75
Part III: The Practice Tests
How to Take the Practice Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .78
Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .79
Mathematics Reference Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .81
Bubble Sheets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .83
Practice Test One . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .87
Practice Test One Answers and Explanations . . . . . . . . . . . . . . . . . . .117
Practice Test Two . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .157
Practice Test Two Answers and Explanations . . . . . . . . . . . . . . . . . . .187