 What to Expect on the GED Mathematics Exam The GED Mathematics Exam measures your understanding of the mathematical knowledge needed in everyday life. The questions are based on information presented in words, diagrams, charts, graphs, and pictures. In addi- tion to testing your math skills, you will also be asked to demonstrate your problem-solving skills. Examples of some of the skills needed for the mathematical portion of the GED are: ■ understanding the question ■ organizing data and identifying important information ■ selecting problem-solving strategies ■ knowing when to use appropriate mathematical operations ■ setting up problems and estimating ■ computing the exact, correct answer ■ reflecting on the problem to ensure the answer you choose is reasonable This section will give you lots of practice in the basic math skills that you use every day as well as crucial problem-solving strategies. CHAPTER About the GED Mathematics Exam IN THIS chapter, you will learn all about the GED Mathematics Exam, including the number and type of questions, the topics and skills that will be tested, guidelines for the use of calculators, and recent changes in the test. 40 385 The GED Mathematics Test is given in two separate sections. The first section permits the use of a calculator; the second does not. The time limit for the GED is 90 minutes, meaning that you have 45 minutes to complete each section. The sections are timed separately but weighted equally. This means that you must complete both sections in one testing session to receive a passing grade. If only one section is completed, the entire test must be retaken. The test contains 40 multiple-choice questions and ten gridded-response questions for a total of 50 ques- tions overall. Multiple-choice questions give you several answers to choose from and gridded-response questions ask you to come up with the answer yourself. Each multiple-choice question has five answer choices, a through e. Gridded response questions use a standard grid or a coordinate plane grid. (The guidelines for entering a gridded-response question will be covered later in this section.) Test Topics The math section of the GED tests you on the following subjects: ■ measurement and geometry ■ algebra, functions, and patterns ■ number operations and number sense ■ data analysis, statistics, and probability Each of these subjects is detailed in this section along with tips and strategies for solving them. In addition, 100 practice problems and their solutions are given at the end of the subject lessons. Using Calculators The GED Mathematics Test is given in two separate booklets, Part I and Part II. The use of calculators is per- mitted on Part I only. You will not be allowed to use your own. The testing facility will provide a calculator for you. The calculator that will be used is the Casio fx-260. It is important for you to become familiar with this calcula- tor as well as how to use it. Use a calculator only when it will save you time or improve your accuracy. Formula Page A page with a list of common formulas is provided with all test forms. You are allowed to use this page when you are taking the test. It is necessary for you to become familiar with the formula page and to understand when and how to use each formula. An example of the formula page is on page 388 of this book. Gridded-Response and Set-Up Questions There are ten non-multiple-choice questions in the math portion of the GED. These questions require you to find an answer and to fill in circles on a grid or on a coordi- nate axis. STANDARD GRID-IN QUESTIONS When you are given a question with a grid like the one below, keep these guidelines in mind: ■ First, write your answer in the blank boxes at the top of the grid. This will help keep you organized as you “grid in” the bubbles and ensure that you fill them out correctly. ■ You can start in any column, but leave enough columns for your whole answer. ■ You do not have to use all of the columns. If your answer only takes up two or three columns, leave the others blank. ■ You can write your answer by using either frac- tions or decimals. For example, if your answer is ᎏ 1 4 ᎏ , you can enter it either as a fraction or as a decimal, .25. The slash “/” is used to signify the fraction bar of the fraction. The numerator should be bubbled to the left of the fraction bar and the denominator should be bubbled in to the right. See the example on the next page. – ABOUT THE GED MATHEMATICS EXAM– 386 ■ When your answer is a mixed number, it must be represented on the standard grid in the form of an improper fraction. For example, for the answer 1 ᎏ 1 4 ᎏ , grid in ᎏ 5 4 ᎏ . ■ When you are asked to plot a point on a coordi- nate grid like the one below, simply fill in the bubble where the point should appear. SET -UP QUESTIONS These questions measure your ability to recognize the correct procedure for solving a problem. They ask you to choose an expression that represents how to “set up”the problem rather than asking you to choose the correct solution. About 25 percent of the questions on the GED Mathematics Test are set-up questions. Example: Samantha makes $24,000 per year at a new job. Which expression below shows how much she earns per month? a. $24,000 + 12 b. $24,000 − 12 c. $24,000 × 12 d. $24,000 ÷ 12 e. 12 ÷ $24,000 Answer: d. You know that there are 12 months in a year. To find Samantha’s monthly income, you would divide the total ($24,000) by the number of months (12). Option e is incorrect because it means 12 is divided by $24,000. Graphics Many questions on the GED Mathematics Test use diagrams, pie charts, graphs, tables, and other visual stimuli as references. Sometimes, more than one of these questions will be grouped under a single graphic. Do not let this confuse you. Learn to recognize question sets by reading both the questions and the directions carefully. What’s New for the GED? The structure of the GED Mathematics Test, revised in 2002, ensures that no more than two questions should include “not enough information is given” as a correct answer choice. Given this fact, it is important for you to pay attention to how many times you select this answer choice. If you find yourself selecting the “not enough information is given”for the third time, be sure to check the other questions for which you have selected this choice because one of them must be incorrect. The current GED has an increased focus on “math in everyday life.” This is emphasized by allowing the use of a calculator on Part I as well as by an increased empha- sis on data analysis and statistics. As a result, gridded- response questions and item sets are more common. The number of item sets varies. 1 2 −3 4 −5 −6 0 1 −2 3 4 5 6 −1 2 3 −4 5 −6 −1 −2−3−4 −5 6 1 2 3 4 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 55 6 7 8 9 0 / 1 3 4 6 7 88 9 0 • / 1 2 3 4 6 7 9 0 • 2 . 5 1 2 3 4 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 • / 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • 1 2 3 5 6 7 8 9 0 • – ABOUT THE GED MATHEMATICS EXAM– 387 Area of a: square Area = side 2 rectangle Area = length ϫ width parallelogram Area = base ϫ height triangle Area = ᎏ 1 2 ᎏ ϫ base ϫ height trapezoid Area = ᎏ 1 2 ᎏ ϫ (base 1 + base 2 ) ϫ height circle Area = π ϫ radius 2 ; π is approximately equal to 3.14 Perimeter of a: square Perimeter = 4 ϫ side rectangle Perimeter = 2 ϫ length + 2 ϫ width triangle Perimeter = side 1 + side 2 + side 3 Circumference of a circle Circumference = π ϫ diameter; π is approximately equal to 3.14 Volume of a: cube Volume = edge 3 rectangular solid Volume = length ϫ width ϫ height square pyramid Volume = ᎏ 1 3 ᎏ ϫ (base edge) 2 ϫ height cylinder π ϫ radius 2 ϫ height π is approximately equal to 3.14 cone Volume = ᎏ 1 3 ᎏ ϫ π ϫ radius 2 ϫ height; π is approximately equal to 3.14 Coordinate Geometry distance between points = ͙(x 2 – x ෆ 1 ) 2 + (y ෆ 2 – y 1 ) ෆ 2 ෆ ; (x 1 ,y 1 ) and (x 2 ,y 2 ) are two points in a plane slope of a line = ᎏ y x 2 2 – – y x 1 1 ᎏ ; (x 1 ,y 1 ) and (x 2 ,y 2 ) are two points on the line Pythagorean Relationship a 2 + b 2 = c 2 ; a and b are legs and c is the hypotenuse of a right triangle Measures of mean = ᎏ x 1 + x 2 + n +x n ᎏ , where the x's are the values for which a mean is desired, Central Tendency and n is the total number of values for x. median = the middle value of an odd number of ordered scores, and halfway between the two middle values of an even number of ordered scores. Simple Interest interest = principal ϫ rate ϫ time Distance distance = rate ϫ time Total Cost total cost = (number of units) ϫ (price per unit) Adapted from official GED materials. 388 Formulas T HE USE OF measurement enables you to form a connection between mathematics and the real world. To measure any object, assign a unit of measure. For instance, when a fish is caught, it is often weighed in ounces and its length measured in inches. This lesson will help you become more familiar with the types, conversions, and units of measurement. Also required for the GED Mathematics Test is knowledge of fundamental, practical geometry. Geometry is the study of shapes and the relationships among them. A comprehensive review of geometry vocabulary and con- cepts, after this measurement lesson, will strengthen your grasp on geometry. CHAPTER Measurement and Geometry THE GED Mathematics Test emphasizes real-life applications of math concepts, and this is especially true of questions about meas- urement and geometry. This chapter will review the basics of meas- urement systems used in the United States and other countries, performing mathematical operations with units of measurement, and the process of converting between different units. It will also review geometry concepts you’ll need to know for the exam, such as prop- erties of angles, lines, polygons, triangles, and circles, as well as the formulas for area, volume, and perimeter. 41 389  Types of Measurements The types of measurements used most frequently in the United States are listed below: Units of Length 12 inches (in.) = 1 foot (ft.) 3 feet = 36 inches = 1 yard (yd.) 5,280 feet = 1,760 yards = 1 mile (mi.) Units of Volume 8 ounces* (oz.) = 1 cup (c.) 2 cups = 16 ounces = 1 pint (pt.) 2 pints = 4 cups = 32 ounces = 1 quart (qt.) 4 quarts = 8 pints = 16 cups = 128 ounces = 1 gallon (gal.) Units of Weight 16 ounces* (oz.) = 1 pound (lb.) 2,000 pounds = 1 ton (T.) Units of Time 60 seconds (sec.) = 1 minute (min.) 60 minutes = 1 hour (hr.) 24 hours = 1 day 7 days = 1 week 52 weeks = 1 year (yr.) 12 months = 1 year 365 days = 1 year *Notice that ounces are used to measure both the volume and weight.  Converting Units When performing mathematical operations, it is neces- sary to convert units of measure to simplify a problem. Units of measure are converted by using either multipli- cation or division: ■ To change a larger unit to a smaller unit, simply multiply the specific number of larger units by the number of smaller units that makes up one of the larger units. For example, to find the number of inches in 5 feet, simply multiply 5, the number of larger units, by 12, the number of inches in one foot: 5 feet = how many inches? 5 feet × 12 inches (the number of inches in a single foot) = 60 inches Therefore, there are 60 inches in 5 feet. Try another: Change 3.5 tons to pounds. 3.5 tons = how many pounds? 3.5 tons × 2,000 pounds (the number of pounds in a single ton) = 6,500 pounds Therefore, there are 6,500 pounds in 3.5 tons. ■ To change a smaller unit to a larger unit, simply divide the specific number of smaller units by the number of smaller units in only one of the larger units. For example, to find the number of pints in 64 ounces, simply divide 64, the smaller unit, by 16, the number of ounces in one pint. = 4 pints Therefore, 64 ounces are equal to four pints. Here is one more: Change 24 ounces to pounds. = 2 pounds Therefore, 32 ounces are equal to two pounds.  Basic Operations with Measurement It will be necessary for you to review how to add, sub- tract, multiply, and divide with measurement. The mathematical rules needed for each of these operations with measurement follow. Addition with Measurements To add measurements, follow these two steps: 1. Add like units. 2. Simplify the answer. 32 ounces ᎏᎏ 16 ounces 64 ounces ᎏᎏ 16 ounces specific number of the smaller unit ᎏᎏᎏᎏᎏ the number of smaller units in one larger unit – MEASUREMENT AND GEOMETRY– 390 . subjects is detailed in this section along with tips and strategies for solving them. In addition, 100 practice problems and their solutions are given at the end of the subject lessons. Using Calculators The. grouped under a single graphic. Do not let this confuse you. Learn to recognize question sets by reading both the questions and the directions carefully. What’s New for the GED? The structure of