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# TCAP Tennessee 8th Grade Achievement Test (REA) - The Best Test Prep for the TCAP

**by**Hearne, Stephen

### 9780738601069

0738601063

Paperback

5/15/2005

Research & Education Assn

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## Summary

Score high and succeed on the Tennessee TCAP Grade 8 mathematics exam! REA gets students ready for exam day! Our all-new test prep for the TCAP provides all the instruction and practice students need to pass and excel on this important state-required math exam. The book's comprehensive math review features numerous examples, diagrams, and charts that illustrate and reinforce key math lessons. Use the book's diagnostic tests to pinpoint the areas where your students need to invest more time and practice. REA's test prep also features one full-length practice TCAP exam so you can familiarize yourself with the content and format of the actual TCAP exam. Each practice exam question is fully explained to help reinforce important math concepts. You can prepare even more for exam day by following REA's proven test-taking techniques, powerhouse drills and targeted homework assignments. DETAILS - The best math TCAP test prep available for Tennessee students in the 8th grade - Features a comprehensive review of every mathematics topic to appear on the TCAP exam - All math problems in the review are clearly explained - many problems feature color charts, diagrams and illustrations - Includes a full-length practice TCAP exam complete with answer key and detailed explanations for each test question - Dynamic diagnostic tests pinpoint a student's math strengths and weaknesses - Packed with proven test tips, sound strategies and powerhouse drills to help students score high - Contains student-friendly classroom and homework assignments that target and reinforce key math concepts - Fully aligned with the core curriculum standards of the state of Tennessee.

## Table of Contents

About Our Editors | p. v |

About Research & Education Association | p. v |

Succeeding on the TCAP Assessment in Mathematics | |

About this Book | p. xvii |

About the TCAP | p. xvii |

About the Reviews & Drills | p. xviii |

Tips for the Student | p. xix |

Sound Advice for Test Day | p. xx |

Tips for Parents | p. xxi |

Arithmetic Review | |

Integers and Real Numbers | p. 1 |

Rational and Irrational Numbers | p. 2 |

Absolute Value | p. 5 |

Positive and Negative Numbers | p. 7 |

Order of Operations | p. 9 |

Drill: Integers and Real Numbers | p. 9 |

Fractions | p. 12 |

Operations With Fractions | p. 12 |

Drill: Fractions | p. 18 |

Decimals | p. 22 |

Operations With Decimals | p. 24 |

Drill: Decimals | p. 30 |

Ratio and Proportion | p. 33 |

Ratio | p. 33 |

Proportion | p. 33 |

Percentages | p. 48 |

Equivalent Forms of a Number | p. 49 |

Drill: Percentages | p. 59 |

Radicals | p. 62 |

Operations With Radicals | p. 62 |

Drill: Radicals | p. 66 |

Exponents | p. 68 |

General Laws of Exponents | p. 69 |

Power to a Power | p. 71 |

Drill: Exponents | p. 71 |

Scientific Notation | p. 73 |

Averages | p. 74 |

Mean | p. 74 |

Median | p. 75 |

Mode | p. 75 |

Drill: Averages | p. 76 |

Estimation | p. 78 |

Significant Digits | p. 80 |

Money Notation | p. 81 |

Counting and Sorting | p. 83 |

Game Strategies | p. 86 |

Networks | p. 88 |

Algorithms | p. 90 |

Flow Charts | p. 91 |

More Estimation | p. 93 |

Arithmetic Drills Answer Key | p. 94 |

Algebra Review | |

Operations With Polynomials | p. 98 |

Drill: Operations With Polynomials | p. 100 |

Simplifying Algebraic Expressions | p. 102 |

Commutative Laws (Addition, Multiplication) | p. 105 |

Associative Laws (Addition, Multiplication) | p. 105 |

Distributive Law | p. 106 |

Drill: Simplifying Algebraic Expressions | p. 116 |

Equations | p. 117 |

Linear Equations | p. 121 |

Drill: Linear Equations | p. 126 |

Two Linear Equations | p. 127 |

Drill: Two Linear Equations | p. 132 |

Quadratic Equations | p. 134 |

Drill: Quadratic Equations | p. 137 |

Absolute Value Equations | p. 139 |

Drill: Absolute Value Equations | p. 139 |

Inequalities | p. 140 |

Properties of Inequalities | p. 141 |

Drill: Inequalities | p. 147 |

Ratios and Proportions | p. 148 |

Drill: Ratios and Proportions | p. 150 |

Permutation, Combination, and Probability | p. 151 |

Trees | p. 159 |

Iteration | p. 161 |

Recursion | p. 163 |

Growth | p. 164 |

Graphs of Functions | p. 165 |

Algebra Drills Answer Key | p. 167 |

Geometry Review | |

Points, Lines, and Angles | p. 169 |

Intersection Lines and Angles | p. 170 |

Types of Angles | p. 170 |

Perpendicular Lines | p. 175 |

Parallel Lines | p. 176 |

Drill: Lines and Angles | p. 180 |

Polygons (Convex) | p. 182 |

Drill: Regular Polygons | p. 184 |

Triangles | p. 185 |

Drill: Triangles | p. 192 |

Change in Linear Dimension | p. 194 |

The Pythagorean Theorem | p. 195 |

Quadrilaterals | p. 197 |

Parallelograms | p. 197 |

Rectangles | p. 198 |

Rhombi | p. 198 |

Squares | p. 199 |

Trapezoids | p. 199 |

Drill: Quadrilaterals | p. 201 |

Circles | p. 204 |

Drill: Circles | p. 209 |

Solids | p. 211 |

Rectangular Solids | p. 211 |

Drill: Solids | p. 212 |

Perimeters, Areas, Volumes | p. 212 |

Coordinate Geometry, Plotting, and Graphing | p. 217 |

Drill: Coordinate Geometry | p. 227 |

Fractals | p. 230 |

Geometry Drills Answer Key | p. 232 |

Word Problems Review | |

Algebraic | p. 235 |

Drill: Algebraic | p. 248 |

Rate | p. 249 |

Drill: Rate | p. 250 |

Work | p. 250 |

Drill: Work | p. 251 |

Mixture | p. 251 |

Drill: Mixture | p. 252 |

Interest | p. 252 |

Drill: Interest | p. 253 |

Discount | p. 254 |

Drill: Discount | p. 255 |

Profit | p. 255 |

Drill: Profit | p. 256 |

Sets | p. 256 |

Drill: Sets | p. 257 |

Geometry | p. 258 |

Drill: Geometry | p. 259 |

Measurement | p. 259 |

Drill: Measurement | p. 264 |

Data Interpretation | p. 265 |

Drill: Data Interpretation | p. 267 |

Scaled Drawings | p. 269 |

Problems with Missing or Misleading Information | p. 271 |

Making Inferences | p. 272 |

Word Problem Drills Answer Key | p. 274 |

Quantitative Ability | |

Quantitative Comparison | p. 275 |

Discrete Quantitative | p. 277 |

Spatial Sense/Relationships | |

Spatial Sense/Relationships | p. 279 |

Drill: Spatial Sense/Relationships | p. 283 |

Spatial Sense/Relationships Drill Answer Key | p. 286 |

Statistics | |

What is Statistics? | p. 287 |

Variables | p. 287 |

Functions | p. 288 |

Data Description: Graphs | p. 288 |

Frequency Distributions | p. 291 |

Frequency Histograms and Relative Frequency Histograms | p. 293 |

Cumulative Frequency Distributions | p. 294 |

Types of Frequency Curves | p. 295 |

Deductive and Inductive Reasoning | p. 298 |

Sampling | p. 298 |

Statistical Plots and Graphs | p. 298 |

Diagnostic Tests for Class and Homework Assignments | |

Arithmetic Diagnostic Test | p. 306 |

Algebra Diagnostic Test | p. 313 |

Geometry Diagnostic Test | p. 321 |

Word Problems Diagnostic Test | p. 332 |

Tcap Mathematics Practice Test | p. 343 |

Answer Sheet | p. 356 |

Answer Key | p. 357 |

Detailed Explanations of Answers | p. 358 |

Index | p. 367 |

Table of Contents provided by Ingram. All Rights Reserved. |

## Excerpts

SUCCEEDING ON THE TCAP ACHIEVEMENT TEST - GRADE 8 MATHEMATICS ABOUT THIS BOOK Our book provides excellent preparation for the TCAP Achievement Test - Grade 8 Mathematics. Inside you will find reviews and drills that are designed to provide students with the instruction, practice, and strategies needed to do well on this achievement test, which is part of the Tennessee Comprehensive Assessment Program, or TCAP. We also provide a full-length practice test, so students can get a good idea of what to expect on test day. Detailed explanations follow the practice test. Our Teacher's Answer Guide contains full explanations for the "Class and Homework Assignment" questions in the diagnostic tests at the back of this book. Teachers may obtain the answer guide by contacting REA. ABOUT THE TCAP The purpose of Tennessee's assessment program and achievement tests is to ensure that all students are progressing and successfully meeting the state's academic content standards. The eighth grade achievement tests are among the key tools used to gauge whether the student is on track to perform well at the high school level; the tests are also used to identify students who need additional instruction to master the knowledge and skills as set forth by the state of Tennessee. The Grade 8 mathematics test contains 64 multiple-choice questions and is administered in two 40-minute sections, with a break between sections. Schools can decide whether to allow students to use a four-function calculator but all test items are calculator-neutral, designed to be solved without the use of a calculator. Students also receive a punch-out ruler to help solve certain problems. The questions are designed to test student mastery of these seven key standards for Grade 8 mathematics: 1. Number and Operations 2. Algebraic Thinking 3. Graphs and Graphing 4. Real World Problem Solving 5. Data Analysis and Probability 6. Measurement 7. Geometry For comprehensive official information on the TCAP Achievement Tests, visit the Tennessee State Education Department online at http://www.state.tn.us/education/assessment. ABOUT THE REVIEWS & DRILLS The reviews in this book are designed to help students sharpen the basic skills needed to approach the exam, as well as to provide strategies for solving each type of question. Students will also find exercises to reinforce what has been learned. By using the reviews in conjunction with the drills and practice test, students will be in a better position to master the exam. TIPS FOR THE STUDENT There are plenty of things students can do before and during the actual test to improve their test-taking performance. The good thing is most of the tips described in the following pages are easy! Preparing for the Test Test Anxiety Do you get nervous when your teacher talks about taking a test? A certain amount of anxiety is normal and it actually may help you prepare better for the test by getting you motivated. But too much anxiety is a bad thing and may keep you from properly preparing for the test. Here are some things to consider that may help relieve test anxiety: - Share how you are feeling with your parents and your teachers.They may have ways of helping you deal with how you are feeling. - Keep on top of your game.Are you behind in your math homework and class assignments? A lot of your classwork-related anxiety and stress will simply go away if you keep up with your homework assignments and classwork. And then you can focus on the test with a clearer mind. - Relax. Take a deep breath or two. You should do this especially if you get anxious while taking the test. Study Tips & Taking The Test - Learn the Test's Format. Don't be surprised. By t