The Mathematical Reasoning section of the GED® test measures your ability to solve problems using essential concepts of high school mathematics. The test is 115 minutes long and includes items in a variety of formats. There is a short section of approximately five questions in which a calculator is not allowed, but for most of the test a calculator is allowed. The calculator is available on the computer screen or you may bring your own TI-30XS Multiview Scientific Calculator. No other calculator model is allowed. You will also be provided with a list of essential mathematical formulas that you can use to solve problems.
About half of the test focuses on quantitative problem solving, and about half focuses on basic algebraic problem solving. There are also some geometry questions. Some of the questions simply require mathematical calculations, but others present hypothetical real-world situations, and you must decide which problem-solving technique will enable you to arrive at the correct answer. Many questions refer to diagrams, charts, coordinate grids, or other graphics.
Most Mathematical Reasoning questions are multiple choice with four answer choices. However, some questions use interactive formats such as drag and drop and drop-down. In some questions, you will be asked to type your answer in a box on the computer screen. Other questions may ask you to click on the screen in order to plot points on a coordinate grid. See “Introducing the GED® Test” at the beginning of this book for an explanation and samples of these formats.
The following section of this book presents a comprehensive review of the skills that are tested on the Mathematical Reasoning test. There are short review sections on all of the essential mathematical concepts that you need to know. Each review section ends with an exercise that you can use to test your mastery of the concept. You will also see sample questions like the ones you will encounter on test day. Pay careful attention to the explanations for each question. They will help you become familiar with all the Mathematical Reasoning question types, and you will learn test-taking strategies that can raise your score. If you have already taken the Mathematical Reasoning Pretest at the start of this book, make sure to study those sections that cover the types of questions you missed or found difficult.
This Mathematical Reasoning review section is organized as follows:
Mathematical Reasoning
Chapter 1 Whole Numbers and Operations
Chapter 2 Exponents, Roots, and Number Properties
Chapter 3 Decimal Numbers and Operations
Chapter 4 Fractions and Operations
Chapter 5 Ratios, Rates, and Proportions
Chapter 6 Percents and Applications
Chapter 7 The Number Line and Negative Numbers
Chapter 8 Probability and Counting
Chapter 9 Statistics and Data Analysis
Chapter 10 Algebraic Expressions
Chapter 11 Solving Equations and Inequalities
Answers and explanations for all of the practice questions in this section are located at the end of the section.
Use this list as a guide for your studies. Be sure to study and practice each topic until you feel that you have mastered it.
1. Place Value and Rounding: Know how to identify digits by place value and round values to a place value.
2. Number Line and Negatives: Know how to read a number line and understand negative numbers.
3. Order of Operations: Follow the order of operations (PEMDAS) when doing calculations.
4. Roots and Exponents: Perform operations with exponents, including negative exponents. Know the value of basic square roots and cube roots. Simplify roots.
5. Fractions: Perform operations with fractions, change between improper and mixed fractions, and convert fractions to decimals and percents.
6. Decimals: Perform operations with decimals and convert decimals to fractions and percents.
7. Ratios and Proportions: Understand how ratios and proportions work; do word problems involving ratios and proportions; reduce ratios; find the missing value in a proportion.
8. Rates: Understand how rates work; do word problems involving rate; reduce rates.
9. Percent: Convert percents to decimals and fractions. Solve problems involving percent, including calculating interest.
10. Measures of Central Tendency: Find the mean, median, mode, and range of a data set.
11. Probability and Combinations: Understand probability; find the probability of a single event; find the probability of compound events; find the number of possible combinations of things.
12. 2-Dimensional Figures: Find the area and perimeter of 2D figures.
13. 3-Dimensional Figures: Find the area, surface area, and volume of 3D figures.
14. Polynomials: Combine like terms; add and subtract polynomials.
15. Multiplying Polynomials: Multiply single terms; use the FOIL method to multiply binomials; multiply polynomials with more than two terms.
16. Factoring Polynomials: Factor out the GCF; use reverse FOIL; use the difference of squares.
17. Rational Expressions: Simplify, add, subtract, multiply, and divide rational expressions.
18. Equations and Inequalities: Write and solve linear equations and inequalities; graph inequalities.
19. Systems of Equations: Solve systems of two equations with two unknowns.
20. Quadratic Equations: Solve quadratic equations with the square root rule, by factoring, and with the quadratic formula.
21. Translating Word Problems: Turn a word problem into a mathematical calculation or equation and solve it.
22. Graphing: Plot points; graph lines; find the intercepts of a line.
23. Line Equations: Find the equation of a line from two points or from one point and the slope.
24. Slope: Find the slope of a line from a graph of the line, from the equation of the line, or with two points on the line.
25. Functions: Evaluate functions (find the given value); recognize a function from a table or a graph; identify when a graphed function is positive, negative, increasing, or decreasing; determine the period of a function from a graph.