Roadmap to the MCAS Grade 8 Math

About This Book

If Students Need to Know It, It’s in This Book
This book develops the math skills of eighth graders. It fosters skill
mastery that helps them succeed both in school and on the
Massachusetts Comprehensive Assessment System (MCAS).

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 Massachusetts Comprehensive
Assessment System
Our experts at The Princeton Review have analyzed the MCAS, and this book provides the most up-to-date,
thoroughly researched information possible. We break down the test into its 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 based on Massachusetts standards and objectives
• detailed lessons, complete with skill-specific activities
• 2 complete practice MCAS math tests.

Table of Contents

CONTENTS
Introduction for Parents and Teachers . . . . . . . . . . . . . . . . . . . . . . . . . 3
Introduction for Students. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Grade 8 MCAS Reference Sheet. . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Miles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Mile 1: Answering Multiple-Choice Questions. . . . . . . . . . . . . . . . 10
Mile 2: Answering Short-Answer Questions . . . . . . . . . . . . . . . . . 12
Mile 3: Answering Open-Response Questions . . . . . . . . . . . . . . . . 14
Mile 4: Real Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Mile 5: Properties of Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Mile 6: Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
Mile 7: Multiples and Factors. . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Mile 8: Exponents. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Mile 9: Order of Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
Mile 10: Scientific Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
Mile 11: Square Roots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Mile 12: Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
Mile 13: Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
Mile 14: Percents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
Mile 15: Fractions, Decimals, and Percents . . . . . . . . . . . . . . . . . 54
Mile 16: Estimation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
Mile 17: Ratios and Proportions . . . . . . . . . . . . . . . . . . . . . . . . . . 62
Mile 18: Number Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
Mile 19: Geometric Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
Mile 20: Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
Mile 21: Setting Up Equations and Inequalities . . . . . . . . . . . . . . . 76
Mile 22: Solving Algebraic Equations . . . . . . . . . . . . . . . . . . . . . . 80
Mile 23: Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
Mile 24: Graphing Linear Equations . . . . . . . . . . . . . . . . . . . . . . . 88
Mile 25: Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
MCAS_Gr8_Math 6/25/03 3:00 PM Page v
Mile 26: Properties of Polygons . . . . . . . . . . . . . . . . . . . . . . . . . . 94
Mile 27: Properties of Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
Mile 28: Congruence and Similarity . . . . . . . . . . . . . . . . . . . . . . 102
Mile 29: Rotations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
Mile 30: Reflections and Translations . . . . . . . . . . . . . . . . . . . . . 108
Mile 31: Pythagorean Theorem . . . . . . . . . . . . . . . . . . . . . . . . . 112
Mile 32: Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
Mile 33: Perimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
Mile 34: Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
Mile 35: Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
Mile 36: Mean, Median, Mode, and Range . . . . . . . . . . . . . . . . 128
Mile 37: Combinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
Mile 38: Probability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
Mile 39: Data with Graphs and Tables . . . . . . . . . . . . . . . . . . . . 138
Answer Key for Miles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
The Practice Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
How to Take the Practice Tests . . . . . . . . . . . . . . . . . . . . . . . . . 160
Practice Test One . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
Answer Sheet for Practice Test One . . . . . . . . . . . . . . . . . . . . . . 163
Mathematics Reference Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . 165
Practice Test Two . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
Answer Sheet for Practice Test Two . . . . . . . . . . . . . . . . . . . . . . 201
Mathematics Reference Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . 203
Answers and Explanations for Practice Tests . . . . . . . . . . . . . . . . . . 237
Practice Test One Answers and Explanations. . . . . . . . . . . . . . . . 239
Practice Test Two Answers and Explanations. . . . . . . . . . . . . . . . 253