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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 proble

 W h a t t o E x p e c t o n t h e G E D M a t h e m a t i c s E x a m

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

C H A P T E R

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

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 quesques-tions 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 calculacalcula-tor 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

S TANDARD G RID - IN Q UESTIONS

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 14, 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

– A B O U T T H E G E D M AT H E M AT I C S E X A M –

■ 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 114, grid in 54

■ 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

S ET -U P Q UESTIONS

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 analyempha-sis and statistics As a result, gridded-response questions and item sets are more common The

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– A B O U T T H E G E D M AT H E M AT I C S E X A M –

Area of a:

square Area = side2

rectangle Area = length  width

parallelogram Area = base  height

triangle Area = 12 base  height

trapezoid Area = 12 (base1+ base2)  height

circle Area = π  radius2; π is approximately equal to 3.14

Perimeter of a:

square Perimeter = 4  side

rectangle Perimeter = 2  length + 2  width

triangle Perimeter = side1+ side2+ side3

Circumference of a circle Circumference = π  diameter; π is approximately equal to 3.14

Volume of a:

cube Volume = edge3

rectangular solid Volume = length  width  height

square pyramid Volume = 13 (base edge)2 height

cylinder π  radius2 height π is approximately equal to 3.14

cone Volume = 13 π  radius2 height; π is approximately equal to 3.14

Coordinate Geometry distance between points = (x2– x1)2+ (y2– y1)2; (x1,y1) and (x2,y2) are two points

in a plane slope of a line = y x2

2

– –

y x

1 1

; (x1,y1) and (x2,y2) are two points on the line

Pythagorean Relationship a2+ b2= c2; a and b are legs and c is the hypotenuse of a right triangle

Measures of mean = x1+ x2 +

n

+ x n

, 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  rate  time

Distance distance = rate  time

Total Cost total cost = (number of units)  (price per unit)

Adapted from official GED materials

Formulas

TH E U S E O F 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

C H A P T E R

Measurement and Geometry

THE GED Mathematics Test emphasizes real-life applications of

math concepts, and this is especially true of questions about 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

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 Ty p e s o f M e a s u r e m e n t s

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.

 C o n v e r t i n g U n i t s

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

 B a s i c O p e r a t i o n s w i t h

M e a s u r e m e n t

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

16 ounces

64 ounces

16 ounces

specific number of the smaller unit

 the number of smaller units in one larger unit

– M E A S U R E M E N T A N D G E O M E T R Y –