## Mathematical Reasoning Workbook For The Ged® Test, Fourth Edition

By McGraw-Hill Education

**Contents**

Introduction v

How to Use This Workbook v

The GED® Mathematical Reasoning Test vi

Calculators and the GED® Mathematical Reasoning Test vii

The Top 25 Things You Need to Know for the GED® Mathematical Reasoning Test viii

Mathematical Reasoning Pretest 3

Answers and Solutions 9

Evaluation Chart 13

CHAPTER 1 Whole Numbers and Integers 15

CHAPTER 2 Exponents, Roots, and Properties of Numbers 21

CHAPTER 3 Fractions and Operations 25

CHAPTER 4 **Decimal Numbers** and Operations 31

CHAPTER 5 Ratios, Rates, and Proportions 37

CHAPTER 6 Percents and Applications 43

CHAPTER 7 Statistics 49

CHAPTER 8 Probability and Counting 55

CHAPTER 9 Geometry 63

CHAPTER 10 Polynomial and Rational Expressions 69

CHAPTER 11 Solving Equations and Inequalities 75

CHAPTER 12 **Graphing Equations** 81

CHAPTER 13 Functions 97

Answers and Solutions 107

Mathematical Reasoning Posttest 151

Answers and Solutions 157

Evaluation Chart 160

Glossary 161

Introduction

How to Use This Workbook

This workbook contains practice problems to help you sharpen your mathematical skills in preparation for taking the GED® Mathematical Reasoning test.

Start your mathematics practice by taking the Mathematical Reasoning Pretest at the beginning of this book. It will help you decide which chapters of the workbook will be most valuable to you. You will also see some samples of the technology-enhanced question formats that appear on the actual exam. Take the pretest in a controlled environment, with as few distractions as possible. Use a calculator, and if you want to more closely simulate testing conditions, limit yourself to 115 minutes, although you may prefer taking the test untimed in order to get a chance to think about every problem. When you are done, or when time is up, check your answers in the Answers and Solutions directly following the pretest, where you will find short explanations of a correct approach to each problem. Next, find the problem numbers you answered incorrectly in the Evaluation Chart to identify the chapters on which you need to concentrate.

Each of the 13 chapters in the book consists of an exercise of 50 problems on a different individual topic in mathematics. The number of problems is intended to expose you to the variety of contexts and situations in which various mathematical problems arise. The questions have also been carefully designed to match each of the following:

- The test content
- The “depth of knowledge” (DOK) levels that measure how well you understand each topic
- The Common Core State Standards (CCSS) that you are expected to have mastered

The exercises are not intended to be timed, but if you find that you are familiar with a topic, you could try timing yourself on a few problems, attempting to correctly work 5 problems in 10 minutes, for example. Answers and Solutions for the problems in the exercises are located directly following the last chapter.

Finally, when you have completed the last exercise, take the Mathematical Reasoning Posttest at the back of this book. This test can help you to reevaluate yourself after practicing in the workbook as much as you feel is necessary. It also contains more samples of the technology-enhanced question formats used on the actual exam. Answers and Solutions and an Evaluation Chart are located at the end of the posttest, which can help you decide if you are ready to take the GED® Mathematical Reasoning test or if you need further practice.

The GED® Mathematical Reasoning Test

The GED® Mathematical Reasoning test is divided into two parts. Part I consists of approximately 5 questions to be completed without a calculator. A calculator is available for Part II, which consists of approximately 41 questions. Once you have started working on Part II, you will not be able to return to Part I. The individual parts are not timed, but the entire test is limited to 115 minutes.

The GED® Mathematical Reasoning test is a computer-based test, which allows for a broad range of item types. There are many multiple-choice items, each of which has four answer choices from which to choose. There are also many technology-enhanced items with formats such as fill-in-theblank, drop-down, hot spot, and drag-and-drop.

- Fill-in-the-blank: These are short-answer items in which a numerical response may be entered directly from the keyboard or in which an expression, equation, or inequality may be entered using an on-screen character selector with mathematical symbols not found on the keyboard.
- Drop-down: A list of possible responses is displayed when the response area is clicked with the mouse. These may occur more than once in a sentence or question.
- Hot spot: Images on the screen have one or more areas where a response is entered by clicking with the mouse. For example, a line in a coordinate system is entered by clicking the locations of two points on the line.
- Drag-and-drop: Small images, words, equations, or other elements are moved around the screen by pointing at them with the mouse, holding the mouse button down, and then releasing the button when the element is positioned over an area on the screen. Such items are used for sorting, classifying, or ordering questions.

About 45 percent of the problems on the test are quantitative, including problems using whole numbers, negative numbers, fractions, decimals, and percentages to answer questions on calculations, conversions, exponents, word problems, rates, ratios, proportions, counting, probability, statistics, data analysis, the Pythagorean theorem, and the perimeter, area, surface area, and volume of geometric objects. These topics are covered in chapters 1 through 9 of this workbook. The remaining 55 percent of the problems on the test are algebraic, covering algebraic expressions, polynomials, rational expressions, equations, inequalities, graphing, and functions. These topics are covered in chapters 10 through 13 of this workbook. Due to the nature of mathematics, there will be overlap; for instance, an algebraic expression might be partially expressed with fractions, or an equation might involve using decimals.

Visit http://www.ged.com for more about the GED® test.