GED MATH STUDY GUIDE. Last revision July 15, 2011

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1 GED MATH STUDY GUIDE Last revisin July 15, 2011 General Instructins If a student demnstrates that he r she is knwledgeable n a certain lessn r subject, yu can have them d every ther prblem instead f every prblem Always d the wrd prblems at the end. These are the best prblems t d within each lessn since they are mst like what will be n the test A key t understanding math is rganizatin and repetitin. Encurage students t shw their wrk in an rganized manner in their ntebks. Scratch paper can be used but the students shuld be able t refer back t their ntes if they frget hw t d a certain type f prblem. Math Basics Lessn 1 Whle Number Review Student shuld be able t identify and rund t place values Lessn 2 Operatins Review Student shuld knw hw t perfrm lng additin (including hw t carry), subtractin (including hw t brrw), multiplicatin (including placehlder use), and divisin (including remainders) by hand Example 1: Slve = 0 remainder 4 The first number f the dividend is divided by the divisr. The whle number result is placed at the tp. Any remainders are ignred at this pint = 0 The answer frm the first peratin is multiplied by the divisr. The result is placed under the number divided int. 4 0 = 4 Nw we take away the bttm number frm the tp number. Bring dwn the next number f the dividend.

2 43 25 = 1 remainder 18 Divide this number by the divisr. The whle number result is placed at the tp. Any remainders are ignred at this pint = 25 The answer frm the abve peratin is multiplied by the divisr. The result is placed under the last number divided int = 18 Nw we take away the bttm number frm the tp number. Bring dwn the next number f the dividend = 7 remainder 10 Divide this number by the divisr. The whle number result is placed at the tp. Any remainders are ignred at this pint.

3 25 7 = 175 The answer frm the abve peratin is multiplied by the divisr. The result is placed under the number divided int = 10 Nw we take away the bttm number frm the tp number. There is still 10 left ver but n mre numbers t bring dwn. With a lng divisin with remainders the answer is expressed as 17 remainder 10 as shwn in the diagram Answer: = 17 R 10 Lessn 3 Distance and Cst Frmulas This is the student s first intrductin t frmulas. Student shuld understand hw t use and manipulate cst and distance frmulas Skip Part A Lessn 4 Calculatrs n the GED Skip lessn 4 if student is familiar with calculatr. Student shuld knw hw t use the fllwing calculatr functins: Percent Psitive/negative buttn Fractin buttn Pwer/expnent Square rt Lessn 5 Filling in the Standard Grid. This shuld have been explained prir t the Math pre-test. Lessn 6 Prblem Slving: Estimatin

4 Pint ut key wrds t lk fr in prblems: Abut, estimate, apprximately, rund Als explain that smetimes prblems require yu t rund numbers befre perfrming calculatins and smetimes prblems require yu t perfrm the calculatin and then rund yur answer at the end Skip Part B Lessn 7 Prblem slving: Set-Up Prblems Order f Operatins Parentheses, Expnents, Multiplicatin, Divisin, Additin, Subtractin Use Please Excuse My Dear Aunt Sally r PEMDAS t remember Multiplicatin and Divisin are frm Left t Right AND Additin and Subtractin are frm Left t Right Example 1: 4(5 + 2) 9/3 Step 1: Parentheses 5 +2 = 7 4(7) 9/3 Step 2: Multiplicatin 4 x 7 = /3 Step 3: Divisin 9/3 = Step 4: Subtractin 28 3 = 25 The answer is 25 Example 2: x 2 Step 1: Multiplicatin 8 x 2 = Step 2: Subtractin (Remember rder f peratins calls that we d additin and subtractin frm left t right, s althugh A cmes befre S in PEMDAS, we must d subtractin first in this prblem. The same rule hlds true fr multiplicatin and divisin) = Step 3: Additin = 134 The answer is 134 Example 3: 5(2 + 6) 4(7 2) Calculate everything n tp f the divisin bar and the bttm f the divisin bar separately, and then the last step will be t divide. Step 1: Parentheses = 8 and 7 2 = 5 5(8) 4(5)

5 Step 2: Multiplicatin (Nte that number in frnt f a parentheses indicates multiplicatin) 5(8) = 40 and 4(5) = Step 3: Divisin = 20 The answer is 20 Decimals and Fractins Lessn 1 Decimal Basics Student shuld be able t identify and rund t place values Students shuld be able t cmpare decimals and rder decimals frm least t greatest and greatest t least Example 1: Write these numbers frm greatest t least: 5.07, 5.985, , 5.2 Step 1: Line the numbers vertically and in line by decimal pint Step 2: Add zers t each number t match the maximum number f place values. Nte that adding zers after the decimal pint des nt change the value f the number Step 3: Cmpare the numbers in each place value, mving frm left t right, until yu run ut f numbers t cmpare. Ones: 5 = 5 = 5 = 5 We must mve t the next place value Tenths: 0 = 0 < 2 < is the greatest number, 5.2 is the next greatest Hundredths: 0 < is the next greatest, is the least The answer is 5.985, 5.2, 5.07,

6 *Nte that althugh sme numbers may have mre digits, this des nt necessarily mean that the number is greater than a number with fewer digits Lessn 2 Decimal Operatins Student shuld knw hw t perfrm lng additin, subtractin, multiplicatin and divisin with decimals by hand Lessn 3 Fractin Basics Students shuld knw hw t g frm mixed numbers t imprper fractins and frm imprper fractins t mixed numbers. Students shuld als be able t reduce a fractin t its lwest term. Lessn 4 Fractin Operatins Lessn 5 Slving Prblems Using a Calculatr Lessn 6 Filling in the Answer Grid Lessn 7 Prblem Slving: Fractin and Decimal Equivalencies Students shuld knw hw t g frm decimals t fractins and frm fractins t decimals. Example 1: Cnvert 0.42 t a fractin Ntice that the last digit (2) is in the hundredth place. Simply place 42 ver = 42 = Example 2: Cnvert t a decimal Yu shuld knw that a fractin is als a divisin prblem. Simply divide numeratr by the denminatr: 3 5 = 0.6 Rati, Prprtin, and Percent Lessn 1 Using Rati and Prprtin t Slve Prblems Students shuld knw hw t write ratis and shuld knw that prprtins are setting tw ratis equal t each ther. Students shuld als knw that in rder t slve a prprtin that yu need t crss multiply. Lessn 2 Understanding Percents Percent means per cent r per cent r ut f a hundred.

7 Lessn 3 Using the Percent Frmula Ignre the percent diagram/bx unless it is easy fr yu t understand. Instead student shuld understand hw t translate wrds t parts f an equatin. What r a number r what amunt variable such as y is equal sign = 10% 10 per cent r 10 ut f /100 f means t multiply, we use x as the multiplicatin sign Example 1: What is 15% f 200? What y is = 15% 15/100 f x y = (15/100) x 200 y = 30 15% f 200 is 30 Example 2: 3 is what percent f 60? is = what y percent /100 f x 60 3 = (y/100) x 60 3 x 100 = y x = 60y y = 5 3 is 5% f 60 Example 3: 150 is 40% f what amunt? is = 40% 40/100 f x what amunt y 150 = (40/100) x (y) 150 x 100 = 40 x (y) = 40y y = is 40% f 375 Lessn 4 Slving Prblems Using a Calculatr

8 Skip this lessn Lessn 5 Simple Interest Smetimes when yu brrw smene else s mney, they will charge yu interest r extra mney t use their mney. Student shuld knw hw t use the simple interest frmula (which will be prvided n the given frmula sheet during the GED test). Student shuld als remember that time needs t be written in terms f years, s mnths shuld be written as a fractin f a year (i.e. 3 mnths is 3/12) Als be careful t answer the questin!! Yu may be asked fr the interest charged fr brrwing the mney (use the interest frmula i = prt ), r the ttal amunt that is needed t be paid back (principal + interest). Lessn 6 Percent f Change This is used t determine hw much change happened when ne number changed t anther number. A cmmn percent f change prblem is determining the change when an item f clthing ges n sale fr say a certain percentage. When slving percent decrease r percent increase prblems, always start with the riginal number, r the number befre the change, and then subtract the final number, r the number after the change. Then divide the difference by the riginal number. Lessn 7 Prblem Slving Data Analysis Lessns 1-6 Students shuld nt spend t much time n this sectin, as there will nt be many data analysis questins n the test. In general, students shuld knw hw t read and interpret data in graphs and tables. Students als shuld knw hw t calculate mean (average), median (middle number in set f numbers), and mde (mst frequent number in set f numbers). Measurement Lessns 1-4 Students shuld nt spend t much time n this sectin, as there will nt be many measurement questins n the test. In general, students shuld knw hw t cnvert between units f measure. Algebra Lessns 1 The Number Line and Signed Numbers Psitive plus psitive equals psitive ( +) + (+) = (+) Negative plus negative equals negative (-) + (-) = (-) T add a psitive and a negative number, subtract and take the sign f the largest number

9 Example 1: = 6 The largest number 9 is psitive, s the answer is psitive 6 Psitive times/divided by psitive equals psitive ( +) x (+) = (+) Negative times/divided by negative equals psitive (-) x (-) = (+) Negative times/divided by psitive equals negative (-) x (+) = (-) Als remember that subtracting is the same as adding a negative number. Yu can use this t change any subtractin prblem t an additin prblem Example 2: = 3 Als remember that tw negatives side by side cancel each ther ut t equal a psitive Example 3: = 28 Lessns 2 Pwers and Rts Any number raised t the 1 pwer is the number itself (i.e. 4¹ = 4) Any number raised t the 0 pwer is 1 (i.e. 10 = 1) Student shuld memrize the fllwing squares: 1² = 1 8² = 64 2² = 4 9² = 81 3² = 9 10² = 100 4² = 16 11² = 121 5² = 25 12² = 144 6² = 36 15² = 225 7² = 49 25² = 625 Square rt is the ppsite f squares. Fr example, 8² = 64 s the square rt f 64 is 8. This is why it is imprtant t try t memrize the squares abve. A number raised t a negative number is equal t a fractin with a numeratr f 1. Example 1: (5)ˉ² = 1 = 1 (5)² 25 Lessns 3 Scientific Ntatin Students shuld knw hw t write a number in scientific ntatin and cnvert frm scientific ntatin t standard ntatin. Lessns 4 The Order f Operatins See instructins abve n PEMDAS

10 Lessns 5 Algebraic Expressins Students shuld knw hw t g frm wrds t numbers and expressins Students shuld als be able t identify like terms and hw t simplify expressins by cmbining like terms Example 1: Simplify this expressin x + 5x² + 8x y 3 We have tw sets f like terms: 3x, 8x and 10, 3 Rewrite expressin gruping like terms: (10 3) + (3x + 8x) + 5x² - y Subtract/add like terms: x + 5x² - y This is the answer since there are n additinal like terms t cmbine. Nte that 5x² and y did nt have like terms s just leave thse terms alne. Students shuld als be able t distribute when simplifying expressins. When yu see a number utside f a parentheses (i.e. 3(8y + 5) ) yu need t distribute Example 2: Simplify this expressin 3(8y + 5) Distribute the 3 t bth terms 3 * 8y = 24yand 3 * 5 = 15 24y + 15 Lessns 6 Algebraic Expressins and the Calculatr Lessn 7 Equatins Students shuld knw hw t slve equatins by islating the variable, r making sure the variable is by itself n ne side f the equal sign Lessns 8 Cmmn Algebra Wrd Prblems Lessns 9 Patterns and Functins Lessns 10 Functin Applicatins Lessn 11 Inequalities Slve these just as yu wuld slve equatins with equal signs. Remember t flip the sign f the inequality if yu multiply r divide by a negative number Lessn 12 Quadratic Equatins Students shuld be able t use FOIL and t factr quadratic expressins Lessn 13 The Crdinate Plane

11 Students shuld be able t identify the rdered pair fr a pint in the crdinate plane. They shuld als be able t plt pints n the crdinate plane if given an rdered pair. Lessn 14 Linear Equatins Students shuld be able t graph a given equatin by picking values fr x and slving fr y Students shuld als understand that a pint falls n a line in the crdinate plane if it satisfies the equatin Example 1: Will the graph f the equatin y = 3x + 1 pass thrugh the pint (2,1)? Plug in the values f x and y in the equatin and see if the equatin is true (2,1) Des 1 = 3(2) + 1 Des 1 = 7? NO, s y = 3x + 1 des NOT pass thrugh pint Lessn 15 Slpe f a Line Students shuld be able identify slpe by: Using the slpe frmula Using rise ver run in the crdinate plane Lking at an equatin in y = mx + b frmat (m is slpe) Lessn 16 Distance Between Pints Students shuld be able t use the distance frmula which is n the frmula sheet Lessn 17 Special Crdinate Grid Items Lessn 18 Prblem Slving Gemetry Lessn 1 Pints, Lines, and Angles A straight line is half f a circle, s it has a ttal f 180 degrees. If anther line bisects a straight line, the tw angles that it creates (called supplementary angles) have t add up t 180 degrees A right angle has 90 degrees. If anther line bisects a right angle, the tw angles that it creates (called cmplementary angles) have t add up t 90 degrees Lessn 2 Parallel Lines and Transversals When a line passes thrugh parallel lines it creates 8 different angles. A student shuld be able t find all 8 angles if given ne angle given that vertical angles are equal and that angles at a straight line add up t 180 degrees. It desn t matter if students remember what the angles are called Lessn 3 Quadrilaterals Students shuld knw that angles in quadrilaterals add up t 360 degrees

12 Lessn 4 Triangles Students shuld knw that angles in triangles add up t 180 degrees. Students shuld als be able t identify sides and angles f equilateral and issceles triangles Lessn 5 Cngruent and Similar Triangles Lessn 6 Similar Triangle Applicatins Frm these tw lessns, students shuld be able t set up ratis between similar triangles and slve fr the missing part in the rati Lessn 7 Perimeter and Area Student shuld be able t use the frmula sheet t slve fr perimeter and area in quadrilaterals and triangles Lessn 8 Circles Students shuld be able t use the frmula sheet t slve fr circumference and area f circles Remember that radius is half f diameter Lessn 9 Vlume Students shuld be able t use the frmula sheet t slve fr vlumes f different figures Lessn 10 Irregular Figures Students shuld be able t break irregular figures apart int familiar figures in rder t slve fr perimeter, area, and vlume f irregular figures Lessn 11 Pythagrean Relatinship Students shuld be able t use the Pythagrean frmula that is n the frmula sheet t slve fr the missing side in a right triangle Lessn 12 Using the Frmulas Page Lessn 13 Using the Calculatr Lessn 12 Prblem Slving