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# BASIC MATH 101

Eastern Washington University

GPA 3.9

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This 57 page Study Guide was uploaded by Hilbert Goldner on Sunday October 11, 2015. The Study Guide belongs to MATH 101 at Eastern Washington University taught by Staff in Fall. Since its upload, it has received 27 views. For similar materials see /class/221493/math-101-eastern-washington-university in Mathematics (M) at Eastern Washington University.

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Date Created: 10/11/15

ChapTer 3 STudy Guide MaTh 101 1 Make Time in your schedule To learn you cannoT Take shor TcuTs 2 Read each secTion in your Tebeook and answer39 The quesTions in The sTudy guide before you go To class 3 Take noTes in class Trying To under sTand as The Teacher pr esenTs examples and explains concest 4 Do your homework IT should be easier39 afTer39 The previous Two sTeps Make sure To under sTand whaT you are doing and be able To solve each problem compleTely and cor r echy by yourself 5 Carry on a conver saTion wiTh yourself as you work asking as you sTar T each problem WhaT is This WhaT is my goal WhaT should my answer39 look like when I am donequot Then as you work a problem ask WhaT pr oper Ty allows me To Take This sTepquot And aT The end Does my answer39 make sense How can I check Hquot 6 MainTain a gr eaT aTTiTude abouT lear ning Algebr a people who have a good aTTiTude find iT easier39 To learn and Those who learn algebr a well usually enjoy iT 7 Go To The lab or your insTr ucTor s office and geT help when you need iT SecTion 31 Solvinq Linear EquaTions Read secTion 31 pages 116 123 and answer39 The following quesTions as you read 1 WhaT is The goal of This secTion 2 WhaT is The sTandar d form of a linear equaTion in one variable 3 CompleTe The Table by deciding which are linear39 equaTions in one variable If H is noT explain how you know EquaTion YN If no why noT 6y7 59 14 2x3 4 4x 7y 9 7 42 2 4 WhaT are The Two sTages of solving an equaTion 5 Describe in words whaT is being done To x in each equaTion and whaT you musT do To solve a x 5 3 b x 48 C 5x10 6 In The examples 1 2 3 and 4 whaT is common abouT The fir sT sTep l WhaT would you do fir sT To solve each of The equaTions below a 2x 105x1 b 3y42y 7 SecTion 32 EquaTions ThaT Reduce To Linear For m Read secTion 32 pages 127 132 and answer39 The following quesTions as you read 1 N A 01 WhaT musT you do fir sT if a linear equaTion has grouping symbols WhaT pr oper Ty do you use To remove Them WhaT is The fir sT sTep in each of examples 1 2 3 4 and 5 In example 3 The second sTep is To subTr acT 2x fr om boTh sides Why do we need To do This sTep In example 4 afTer The disTr ibuTive pr oper Ty is used on The fir sT sTep whaT does The auThor39 do before adding a Ter m To each side Why Do you Think you will be wrong if you for geT This sTep WhaT is differ enT abouT example 5 from The previous examples How is This difference handled WhaT is meanT by clear ing The equaTion of fr acTionsquot Why would we wanT To do This 7 X 0 WhaT pr oper Ty are we using when we mulTiply boTh sides of an equaTion by a number In example 6 why are There par enTheses around The Terms on The lefT side of The equaTion in The fir sT sTep For The following equaTion A whaT number should you mulTiply boTh sides of The equaTion by B Rewr iTe The equaTion showing The mulTiplicaTion of boTh sides C Rewr iTe iT again disTr ibuTing The facTor you chose in A and D Simplify The equaTion so ThaT There are no fr39acTions 2x 5x TT 7 10 WhaT is crossmufpI39cafbn Use cr ossmulTiplicaTion To wr iTe The fir sT sTep of each of The following equaTions WhaT do you need To do wiTh b ThaT you do noT need To do wiTh a x 9 2x 3 4 a b 4 8 5 7 11 How do we clear an equaTion of decimals Clear The following equaTion of decimals 023x1 2805 SecTion 33 Problem Solving wiTh PercenTs Read secTion 33 pages 137 144 and answer The following quesTions as you read 1 Explain in words how To do each of The following Then make The conversion 3 a converT a fracTIon To a decImal g b converT a decimal To a percenT 0204 c converT a percenT To a decimal 92 d converT a percenT To a fracTion 33 2 WriTe an equaTion for each of The following quesTions a 35 is whaT percenT of 20 b WhaT number is 125 of 4 c 62 is 45 of whaT number 3 Refer to example 4 A real estate agency receives a commission of 421372 for the sale ofa 78000 house What percent commission is this a Write a verbal model b Write labels c Write an equation d Solve the equation Does your answer make sense X Explain in your own words what markup is and then write the verbal model given in the book If the cost of an item is 74 and the selling price is 90 What is the markup If the cost of an item is 590 and the markup is 400 What is the selling price What is the markup rate Write the verbal model How are the words cost and price different in business terms Explain in your own words what discount is and then write the verbal model given in the book What is discount rate Write the verbal model What is List Price Use The sTeps given in The box Guidelines for Solvinq Word Problems To solve The following A qualiTy conTr ol engineer TesTed sever al par Ts and found Tour To be defecTive The engineer r epor Ted ThaT 25 were defecTive How many were TesTed SecTion 34 RaTio and Pr opor Tions Read secTion 34 pages 149 155 and answer The following quesTions as you read 1 N 4gt 0 WhaT is a r aTio If The r aTio of sTudenTs To compuTer s aT a school is whaT does This mean A speaker aT a conference announced ThaT aT a local elemenTar y school The r aTio of compuTer s To sTudenTs is 9 To 1 Do you Think This is True WhaT do you Think he meanT Wr iTe as a fr acTion in simplesT form The r aTio of children To candy bars is 7 To 4 If you are using a r aTio To compare Two measuremenTs whaT should be The same in The numer aTor and denominaTor Find a r aTio To compare The r elaTive size of 5 quar Ts To 6 gallons 7 How is The uniT price given as a r39aTio 8 If a 12pack of DieT Pop cosTs 495 whaT is The uniT and whaT is The uniT price 9 WhaT is a proporTion Explain how H is differ enT from a raTio 10 WhaT meThod do we use To solve pr opor Tions 11 Use The Consumer Price Index To find The 1991 value of a chair boughT in 1977 for 41 Wr iTe a verbal model labels and a pr opor Tion Then solve 12 WhaT is 7239 pi The r aTio of AfTer39 finishing your homework for This secTion answer39 The quesTions below 13 LisT The skills you used in This homewor k seT ThaT you learned in a previous secTion SecTion 35 GeomeTric and ScienTific ApplicaTions Read secTion 35 pages 161 168 and answer The following quesTions as you read 1 U1 0 Describe in your own words whaT The perimeTer of an objecT or shape is Describe in your own words whaT The area of an objecT or shape is Describe in your own words whaT The volume of an objecT or shape is If we wanT To find The area of a recTangular room and measure The engTh To be 15 feeT and The widTh To be 12 feeT whaT is The area of The room WhaT uniTs describe The area The volume of a righT circular cylinder is V 727 Find The volume of a righT circular cylinder ThaT has a radius of 4 feeT an a heighT of 6 feeT Draw a righT circular cylinder and wriTe The uniTs of measuremenT for your answer Use algebra To rewriTe The equaTion wiTh F alone on one side of The equal sign C gF 32 l X Wr iTe The formula for simple inTer esT and wr iTe whaT each leTTer39 r epr esenTs G WhaT is The r elaTionship beTween disTance r aTe and Time Refer To example 5 To answer39 The quesTions How do you find The ToTal cosT of 15 pounds of peanuTs ThaT cosT 4 per pound Wr iTe The expression ThaT r epr esenTs The ToTal cosT of 15 pounds of peanuTs How do you find The ToTal cosT of x pounds of cashews ThaT cosT 7 per pound Find an expression for The ToTal cosT of x pounds of cashews How much do x pounds of cashews and 15 pounds of peanuTs weighT when They are mixed TogeTher How do you find The ToTal cosT of x 15 pounds of mixed nuTs ThaT cosT 4 per pound Finish solving The problem and compare your work To The work in The example Does The answer39 make sense SecTion 36 Linear InegualiTies Read secTion 36 pages 174 182 and answer The following quesTions as you read 1 4gt l WhaT is a linear inequaliTy in one variable How is iT differenT from a linear equaTion in one variable WhaT does iT mean To solve an inequality Why do we graph soluTion seTs of inequaliTies Give an inequaliTy ThaT could have The soluTion seT graphed below Label Three poinTs on The number line ThaT correspond To soluTions Which properTies of inequaliTies are The same as The properTies of equaliTy Which properTies of inequaliTies are differenT from The properTies of equaliTy How are They differenT WriTe The words ThaT you say when you read xlx lt 4 WhaT is This noTaTion called 8 When do you reverse The inequaIiTy symbol Why does This work 9 How can you check your souTions afTer you solve an inequaIiTy 10 WhaT is a compound inequaliTy 11 WhaT Type of compound inequaIiTy can be wr iTTen as a double inequaIiTy 12 Give Thr ee number39s ThaT saTisfy xlt3 and xgt2 Gr aph The souTion seT Wr39iTe iT in seTnoTaTion 13 Give Thr ee number39s ThaT saTisfy xlt3 or xgt15 Gr aph The souTion seT Wr39iTe iT in seTnoTaTion 14 Wr39iTe an inequaIiTy for The sTaTemenT x is aT mosT 17 SecTion 37 AbsoluTe Value EquaTions and InequaliTies Read secTion 37 pages 186 189 and answer39 The following quesTions as you read 1 WhaT does x3 mean 2 WhaT are The soluTions To y7 Explain 3 Wr iTe The Two linear equaTions equivalenT To x12 4 Wr iTe The Two linear equaTions ThaT ar e equivalenT To l2 3xl 6 Then solve The equaTions 5 Wr iTe an absoluTe value equaTion ThaT has no soluTion Make up a differenT one Than The ones in The reading Explain why your39 equaTion has no soluTion 6 WhaT musT be done fir sT in example 3 before The absoluTe value is wr iTTen as Two equaTions wiThouT absoluTe value symbols How will you know when To Take This sTep 7 Rewr iTe each of The following absoluTe value inequaliTies as a compound inequaliTy If The sTaTemenT can also be wr iTTen as a double inequaliTy wr iTe The equivalenT double inequaliTy AbsoluTe value Compound inequaliTy Double inequaliTy if inequaliTy possible l4x 5l gt 2 3x 2 5 lt 1 3x 419 lx 6l gt 6 8 Do Dl39scussmg 15 Concepf in The blue box aT The boTTom of page 189 In general which absoluTe value inequaliTies and equaTions do noT have soluTions O WhaT is The midpoinT of The inTer val shown on The number line below All of The poinTs in The inTer val ar e aT mosT whaT disTance from The midpoinT Use your39 answer39s To wr iTe an absoluTe value inequaliTy ThaT r epr esenTs The inTer val 10 WhaT skills in This secTion are new To you and which are skills you learned in previous secTions N Chap rer39 3 Review For each of The following equa rions a Wha r kind of equa rion or inequali ry is if b Wha r is your goal Wha r is your fir s r s rep Solve i r Check if 3x 2x 416 3 2x x l 5 6 x 2x 397 8 ON 8x24 p 246 3px gt7 3S4x8 5 ChapTer 3 PracTice TesT U1 wNH 0 l ConverT 635 To a fracTion in simplesT form ConverT 6 To a decimal WhaT number is 235 of 75 When Rod boughT his 6000 car The salesman offered him a 7 discounT or 500 off Which is The beTTer deal Show work Fay received a wholesale shipmenT of roses for ValenTine39s Day She paid 112 for each rose If she sells The roses for 225 each find The markup Then find The percenT of markup rounded To The nearesT hundredTh of a percenT In Mrs Adams39 class 25 ouT of 31 sTudenTs passed Their firsT maTh TesT In Mr Brown39s class 28 ouT of 34 passed Their firsT maTh TesT Mr Brown claimed boTh classes did equally well Is he righT If he is wrong whose class did beTTer Show work Solve The following proporTions 2x x x 4 x 2 a b 3 6 6 4 A 2802 Jar of peanuT buTTer sells for 449 a Find The uniT price rounded To The nearesT cenT Use appropriaTe uniTs in sTaTing your answer b If The uniT price remained The same how much would a 3202 Jar of peanuT buTTer cosT Express your answer using appropriaTe uniTs Jim found ThaT afTer working for 9 monThs he had earned 6 days of vacaTion Time How many days per year does he earn aT This raTe IdenTify a variable WriTe an algebraic equaTion Solve The equaTion 10 Solve for fin The following formula C 4t5 H H A fruiT drink is made by mixing fruiT Juices An apple Juice cockTail ThaT is 50 Juice is To be mixed wiTh a grape Juice cockTail ThaT is 30 Juice To geT 200 liTers of a mixTure ThaT is 45 Juice How much of each should be used IdenTify a variable WriTe an algebraic equaTion Solve The equaTion SamanTha and Tony operaTe a small laundry SamanTha working alone can clean a day39s laundry in 9 hours Tony can clean a day39s laundry in 8 hours ApproximaTely how long would iT Take Them if They work TogeTher ChapTer 4 STudy Guide MaTh 101 1 Make Time in your schedule To learn you cannoT Take shor TcuTs 2 Read each secTion in your Tebeook and answer39 The quesTions in The sTudy guide before you go To class 3 Take noTes in class Trying To under sTand as The Teacher pr esenTs examples and explains concest 4 Do your homework IT should be easier39 afTer39 The previous Two sTeps Make sure To under sTand whaT you are doing and be able To solve each problem compleTely and cor r echy by yourself 5 Carry on a conver saTion wiTh yourself as you work asking as you sTar T each problem WhaT is This WhaT is my goal WhaT should my answer39 look like when I am donequot Then as you work a problem ask WhaT pr oper Ty allows me To Take This sTepquot And aT The end Does my answer39 make sense How can I check Hquot 6 MainTain a gr eaT aTTiTude abouT lear ning Algebr a people who have a good aTTiTude find iT easier39 To learn and Those who learn algebr a well usually enjoy iT 7 Go To The lab or your insTr ucTor s office and geT help when you need iT SecTion 41 Ordered Pairs and Graphs Read secTion 41 pages 202 208 and answer The following quesTions as you read 1 Draw a recTangular coordinaTe sysTem label The origin The axes The quadranTs and The following ordered pairs 2 3 2 3 2 3 and 2 3 Use a ruler To make your work neaT N Why are The pairs of numbers called ordered pairs A Ordered pairs can be soluTions of equaTions How many variables musT an equaTion have in order To have soluTions ThaT are ordered pairs 39gt When is an ordered pair a soluTion To an equaTion U1 Is The ordered pair 1 2 a soluTion To The equaTion 2x3y24 Show how you know 0 Is The ordered pair 4 2 a soluTion To The equaTion x4y7 Show how you know 7 Looking aT example 6 if necessary To solve The following problem You are seTTing up a small business selling coffee in The MaTh Lab You spend a ToTal of 75 on a coffee poT and sTand and your uniT cosT To produce each cup of coffee cup coffee is 30 WriTe an equaTion ThaT relaTes your ToTal cosT To The number of cups of coffee produced Verbal Model Labels Algebraic Model Using This equaTion consTrucT The following Table of values x 5 20 50 100 500 WriTe a compleTe senTence describing whaT informaTion The Table is giving While doing your homework pick Three problems of differenT Types ThaT you eiTher couldn39T do by yourself or you found very hard and isT Them on The lasT page of This bookleT SecTion 42 Graphs of EquaTions in Two Variables Read secTion 42 pages 213 218 and answer The following quesTions as you read 1 Make a noTe card ThaT describes The relaTionship beTween an equaTion and iTs graph IT should conTain a sTaTemenT similar To The following Every ordered pair ThaT is a soluTion To The equaTion is an ordered pair on The graph of The equaTion and every ordered pair on The graph of The equaTion is a soluTion To The equaTion Show an example equaTion and iTs graph 2 If a b is on The graph of xy4 whaT can you say abouT The relaTionship beTween a and b 3 SkeTch The graph of 2x y 4 following example 1 Show your39 work on The IefT and wr iTe The sTeps you Take on The r ighT Need gr aph 4 How do we know when an equaTion in Two variables is a linear39 equaTion 5 Graph The equaTion having absoluTe value Y x2 IX 5 4 3 2 1 0 1 yrlx2 Need graph 6 WriTe Two noTe cards one wiTh The definiTion of The x inTercepT and one wiTh The definiTion of yinTercepT Be sure To include a graph and an example I Explain in compleTe senTences why we eT x0 when we wanT To find The yinTercepT and yO when we wanT To find The xinTercepT Does This work for equaTions whose graphs are noT lines X Find The x and y inTercest of 2x3y6 WriTe your answers as ordered pairs and label which is The xinTercepT and which is The y inTercepT O Summarize whaT you learned in This secTion Use compleTe senTences While doing your homework pick Three problems of differenT Types ThaT you eiTher couldn39T do by yourself or you found very hard and lisT Them on The lasT page of This bookleT SecTion 43 RelaTions FuncTions and Grc ohs Read secTion 43 pages 223 228 and answer The following quesTions as you read 1 Make four noTecards wiTh definiTions one for relaTions one for funcTion one for domain and one for me Be sure To include an example on each card 2 a Give a seT of five ordered pairs ThaT is a relaTion buT noT a funcTion STaTe why H is noT a funcTion STaTe The domain and The range b Give a seT of five ordered pairs ThaT is a funcTion STaTe how you know iT is a funcTion STaTe The domain and The range 3 Describe The verTical line TesT a Draw a graph of a relaTion ThaT is noT a funcTion How do you know iT is noT a funcTion by looking aT The graph b Draw a graph of a funcTion How do you know H is a funcTion by looking aT The graph 4 STaTe in words how The symbol gx is read Then explain whaT role x plays and whaT gx means 5 If fx32x find f2 f0 and f3 While doing your homework pick Three problems of differenT Types ThaT you eiTher couldn39T do by yourself or you found very hard and lisT Them on The lasT page of This bookleT SecTion 44 Slope and Graphs of Linear EquaTions Read secTion 44 pages 234 241 and answer The following quesTions as you read A l Make a noTe card for The word slope Include The verbal definiTion The formula and a graph Include an example of how The slope is found Also include ThaT The slope is a rafe afchange a In example 1a The slope is a posiTive number Describe The direcTion The line is going as you look aT iT from lefT To righT b In example 1b The slope is zero describe The sTeepness of The line b In example 1c The slope is a negaTive number Describe The direcTion The line is going as you look aT H from lefT To righT WhaT Type of line has an undefined slope Why Make a noTe card for slopeinTercepT form of The equaTion of a line Be sure To include whaT m and b mean and how you can skeTch a line once you know m and b Make a noTe card for parallel lines Describe how you can Tell wheTher Two lines are parallel Include a graph and an example Make a noTe card for perpendicular lines Describe how you can Tell wheTher Two lines are perpendicular Include a graph and an example Use an illusTraTion To summarize whaT you learned This secTion and how The concest are relaTed While doing your39 homework pick Thr ee problems of differ enT Types ThaT you eiTher couldn39T do by yourself or you found very hard and lisT Them on The lasT page of This bookleT SecTion 45 EguaTions of Lines Read secTion 45 pages 246 252 and answer39 The following quesTions as you read 1 N 0 Describe whaT is meanT by AnalyTic GeomeTr y In example 1 you are asked To find The equaTion of a line when you are given The slope and one poinT Say we knew The equaTion whaT do you know abouT The r elaTionship beTween The poinT and The equaTion Make a noTe card for poinTslope form of The equaTion of a line Include an example and give sTeps for finding The equaTion of a line using This form when you have been given a slope and a poinT If you are given Two poinTs insTead of a slope and one poinT whaT addiTional sTep do you have To Take To find The equaTion How is infor maTion from The lasT secTion used in examples 4 and 5 Give The equaTion of The hor izonTal line Thr ough 14 0 Give The equaTion of The verTical line Through 14 Make a noTe card for horizonTal lines Include a graphical example whaT you know abouT The slope of every horizonTal line and whaT The equaTion always looks like Make a noTe card for verTical lines Include a graphical example whaT you know abouT The slope of every verTical line and whaT The equaTion always looks like To summarize how To wriTe The equaTion of a line given one or Two poinTs describe each of The differenT cases below and how you know whaT To do Describe any ThaT are similar and how They are similar Find The equaTions a A verTical line Through 34 039 A horizonTal line Through 34 c A line Through 12 and 34 0 A line Through 12 wiTh slope 2 e A line Through 12 and 32 f A line Through 12 and 1 3 11 STudy example 7 and Then work This similar problem During The firsT year of operaTion a company had sales of 72 million During The Third year The company had sales of 82 million Using This informaTion only and assuming This Trend conTinues whaT would you esTimaTe The sales To be during The fifTh year The sevenTh year SoluTion WhaT should yrepresenT WhaT should frepresenT WhaT should The horizonTal axis of The graph represenT WhaT should The verTical axis of The graph represenT Give Two ordered pairs T y from The sTaTemenT of The problem Find The slope of The line conTaining The Two poinTs you gave Use The form of The equaTion of a line To find The equaTion ThaT gives The relaTionship beTween years and ToTal sales Using This model find The esTimaTe of sales during The fifTh year Use The model again To find The esTimaTe of sales during The sevenTh year 12 You have learned Two forms of The equaTion of a line WhaT are They a Which one is mosT convenienT for finding an equaTion b Which one is mosT convenienT for graphing a line While doing your homework pick Three problems of differenT Types ThaT you eiTher couldn39T do by yourself or you found very hard and lisT Them on The lasT page of This bookleT SecTion 46 Graphs of Linear InequaliTies Read secTion 46 pages 257 261 and answer The following quesTions as you read 1 Make a noTe card for linear inegualiTy in Two variables Include whaT a soluTion To a linear inequaliTy in Two variables is 2 Decide wheTher The poinT 2 3 is a soluTion To The linear inequaliTy in example 1 Show your work 3 WriTe The sTeps for graphing a linear inequaliTy in Two variables Include how you can check your soluTion 4 Give one soluTion for xgt2 from The graph of example 2a 5 0 Looking aT The graph of The soluTion seT in example 3 give Three soluTions STudy example 5 and Then work This similar problem You have Two parTTime Jobs One is aT a car wash which pays 8 per hour Tips included and The oTher is planTing Trees in a naTional foresT which pays 7 per hour and you feel good abouT yourself Since you don39T wanT To Jeopardize your financial aid nexT year beTween The Two Jobs you wanT To earn no more Than 150 a week WriTe an inequaliTy ThaT shows The number of hours ThaT you can work Then skeTch a graph of The inequaliTy SoluTion WriTe a verbal model To describe The relaTionship beTween The amounTs of money you make aT each Job and The maximum you wanT To earn Labels Algebraic inequal iTy SkeTch The graph Find a soluTion in your graphed soluTion seT and describe whaT iT means ChapTer 4 Review LisT The problems from each secTion here Ask sTudy parTners To see problems They isTed if They are differenT Types Than you have isTed below copy Theirs Use This isT as a pracTice TesT a couple of days before your chapTer 4 TesT ChapTer 5 STudy Guide MaTh 101 1 Make Time in your schedule To learn you cannoT Take shor TcuTs 2 Read each secTion in your Tebeook and answer39 The quesTions in The sTudy guide before you go To class 3 Take noTes in class Trying To under sTand as The Teacher39 pr esenTs examples and explains concest 4 Do your homework IT should be easier afTer39 The previous Two sTeps Make sure To under sTand whaT you are doing and be able To solve each problem compleTely and cor r echy by yourself 5 Carry on a conver saTion wiTh yourself as you work asking as you sTar T each problem WhaT is This WhaT is my goal WhaT should my answer39 look like when I am donequot Then as you work a problem ask WhaT pr oper Ty allows me To Take This sTepquot And aT The end Does my answer39 make sense How can I check iTquot 6 MainTain a gr eaT aTTiTude abouT lear ning Algebr a people who have a good aTTiTude find iT easier39 To learn and Those who learn algebr a well usually enjoy iT 7 Go To The lab or your insTr ucTor s office and geT help when you need iT SecTion 51 Addinq and SubTr acTinq Polynomials Read secTion 51 pages 274 279 and answer39 The following quesTions as you read 1 WhaT is a polynomial 2 Which of The following is noT a polynomial Why a 2x5 b3x4 8x27 C x9 6 d x 2 81x5 e 8 3 For each of The polynomials puT iT in sTandar39d for m idenTify The degree of The polynomial and idenTify The leading coefficienT Polynomial STandar d For m Degree of Leading The coefficienT polynomial 6 7x2 5x2 4 3x3 8x 5x5 2x34x 3x25 4 Give an example of a A monomial b A binomial c A Tr inomial d A polynomial ThaT is noT a monomial binomial or Tr inomial 5 Add The polynomials a 5x24 3x38x 5x52x34x 3x25 5x3 7x2 3x 39 6x3 5x 9 6 SubTr acT The polynomials a 5x2 4 3x3 8x 5x5 2x3 4x 3x2 5 5x3 7x2 3x b39 6x3 5x 9 7 Find a polynomial ThaT r epr esenTs The area of The shaded r egion SecTion 52 MulTiplyinq Polynomials Read secTion 52 pages 284 291 and answer39 The following quesTions as you read 1 MulTiply The monomials and Then sTaTe in words how you mulTiply monomials a 2x23x5 b 5xx4 Words 2 MulTiply The monomial by The binomials a 2x33x25x b 2x253x WhaT pr oper Ty did you use Explain clearly how you know when To add exponenTs 3 A deck is 8 feeT by 8 feeT A builder39 wanTs To add 4 feeT To The lengTh and 6 feeT To The widTh How much addiTional area is added To The deck Draw and label a picTur e To r epr esenT The siTuaTion 4 Use The disTribuTive properTy To mulTiply x4x6 5 Use The foil meThod To mulTiply 2x13x6 6 MulTiply The polynomials by firsT rewriTing Them verTically 3x34x12x2x7 7 Describe The special producT producT of The sum and difference of Two Terms How do you recognize iT Give an and mulTiply Them 8 Describe The special producT sguare of a binomial How do you recognize iT Give an example and mulTiply SecTion 53 Neanive ExponenTs and ScienTific NoTaTion Read secTion 53 pages 297 301 and answer The following quesTions as you read 1 RewriTe wiTh posiTive exponenTs and simplify 3 72 a 2393 b 2x392 c 74 d x 1 x 6y39 e 4xO N Review The rules of exponenTs cards you made earlier Add The new rules A Work each of The problems in example 3 p 299 covering up The soluTions unTil you are done Go back and check your work If you missed any of Them explain in words whaT concepT you did noT apply correchy 4gt WriTe The form of a number in scienTific noTaTion U1 ConverT To scienTific noTaTion a 7540000 b 0000000367 0 ConverT To decimal noTaTion a 243x10395 b 5441x1o4 SecTion 54 Dividing Polynomials Read secTion 54 pages 305 311 and answer The following quesTions as you read 1 Which rules of exponenTs do we use when we divide monomials 2 Simplify 6x6 b 23x4 14xy2 a W szs c 7 5 4 y x A Perform The division and simplify 6x 9 2x3 8x a b 7 3 4x 4gt Divide using long division Explain To a s rudy buddy wha r you are doing each s rep 156024 5 Divide using long division Explain To a s rudy buddy wha r you are doing each s rep 18x23x286x7 We do no r lear n syn rhe ric division in Ma rh 101 ChapTer 5 Review Go Through The chapTer review exercises on p 316 wiThouT a paper and pencil describing whaT your firsT sTep and your sTraTegy would be in each of The problems Circle The problems ThaT you do noT know how To sTarT WriTe five hard39 problems differenT Types below To work ChapTer 1 STudy Guide MaTh 101 1 Make Time in your schedule To learn you cannoT Take shor TcuTs 2 Read each secTion in your Tebeook and answer39 The quesTions in The sTudy guide before you go To class 3 Take noTes in class Trying To under sTand as The Teacher pr esenTs examples and explains concest 4 Do your homework IT should be easier39 afTer39 The previous Two sTeps Make sure To under sTand whaT you are doing and be able To solve each problem compleTely and cor r echy by yourself 5 Carry on a conver saTion wiTh yourself as you work asking as you sTar T each problem WhaT is This WhaT is my goal WhaT should my answer39 look like when I am donequot Then as you work a problem ask WhaT pr oper Ty allows me To Take This sTepquot And aT The end Does my answer39 make sense How can I check Hquot 6 MainTain a gr eaT aTTiTude abouT lear ning Algebr a people who have a good aTTiTude find iT easier39 To learn and Those who learn algebr a well usually enjoy iT 7 Go To The lab or your insTr ucTor s office and geT help when you need iT HOW To read Cl maTh book Preview The secTion by reading each bold wor d sTudy Tip and example heading Doing so will give you an idea of whaT you are going To read and help you see The big picTur39e39 Then go back and read carefully working The examples fill in missing sTeps and making noTe cards for vocabular y SecTion 11 RealNumber s Order and AbsoluTe Value Preview The secTion secTion 11 pages 1 8 by reading each bold wor d sTudy Tip and example heading Doing so will give you an idea of whaT you are going To read and help you see The big picTur e39 Now go back and read carefully answer ing The following quesTions as you read 1 Make a noTe card for each seT of numbers real numbers naTur al number39s whole numbers r aTional number39s ir r aTional number39s inTeger s On each card give The name of The seT and a verbal descr ipTion N Show wiTh a diagram how The seTs of numbers are r elaTed Be sure To give a couple of examples for each Type of number39 3 CompleTe The Table by checking The boxes ThaT idenTify The Type of number39 number NaTur al Whole InTeger RaTional Ir r a fioml Ral 3 42 TE 32 0 4 If a number is a whole number iT musT also be cir cle all ThaT apply NaTur al Whole RaTional Ir r aTional InTeger Real 5 If a number is a Real number iT musT be eiTher cir cle all ThaT apply NaTur al Whole RaTional Ir r aTional InTeger Real 6 Give an example of a number ThaT is r aTional buT noT an inTeger 7 Give an example of a number ThaT is an inTeger buT is wriTTen as a fracTion 8 WhaT kind of decimals are raTional numbers 9 WhaT kind of decimals are irraTional numbers 10 Draw a real number line and label The inTeger poinTs from 3 To 3 Then ploT The numbers 8 14 and 52 11 PuT an inequaliTy symbol beTween The Two numbers and Then wriTe The name of The symbol less Than or greaTer Than A 3 7 B 12 21 C 12 21 D 56 E 125 1205 12 Make a noTe card for opposiTes be sure To include a couple of examples and a number line illusTraTing The idea of opposiTes OpposiTes are also called inverses 13 Make a noTe card for absoluTe value Include a descripTion of whaT iT means as well as some examples 14 WhaT is an expression SecTion 12 OperaTions wiTh InTeqers Read secTion 12 pages 11 23 and answer The following quesTions as you read 1 STaTe The rule for adding inTegers wiTh The same sign Then perform The addiTions a 1742 b 31 23 N a 17 42 A b 23 32 STaTe The rule for subTr acTing inTeger s STaTe The rule for adding inTeger s wiTh opposiTe signs Then perform The addiTions 4 Rewr iTe each of The subTr acTions as an addiTion using The rule you wr oTe in 3 Then simplify find The answer SubTr acTion EquivalenT Same sign or Answer addiTion opposiTe signs 7 8 7 8 7 8 7 8 5 Look aT example 5 If The TemperaTur e dr ops anoTher39 6 degrees whaT TemperaTur e will iT be Wr iTe The oper aTion you use 6 Wr iTe The rules for mulTiplying inTeger s 7 Find The sums and pr oducTs a 26 b 2 6 c 2 6 d 2 6 8 Wr iTe The division 87 as a fr acTion 9 Wr iTe The fr acTion 613 as a division 10 Consider The following To under sTand why division by zero is undefined We sTar T wiTh a True sTaTemenT 6 2 3 And because mulTiplicaTion is The inverse oper aTion of division we have The True sTaTemenT 2x326 Now if 60O is True Then The mulTiplicaTion Ogtlt06 musT be Tr ue BUT of course H is noT Tr ue So we cannoT divide 6 by O For The same reason we cannoT divide any number including 0 by O WhaT par T of a fr acTion cannoT be zero 11 Label each number in The following sTaTemenT as eiTher a facTor or a pr oducT 89 72 12 Make a noTe card for prime number and anoTher39 for composiTe number 13 Find The prime facTor izaTion of 342 SecTion 13 Oper aTions wiTh RaTional Number s Read secTion 13 pages 29 39 and answer39 The following quesTions as you read H N A 4gt 0 l X Label The parTs of The fracTion WriTe Three fracTions equivalenT To Find The greaTesT common facTor of 32 and 48 WriTe The fracTion 3248 in simplesT form Show your work Describe in words how you can add or subTracT Two fracTions wiTh unlike denominaTors Find The leasT common mulTiple of 32 and 48 Add 332 and 548 WriTe The mixed number 2 as an improper fracTion Show your work Draw a picTure represenTing onehalf of a pizza Then shade Three fourThs of The half of pizza WhaT parT of a whole pizza have you shaded WriTe a number sTaTemenT To iusTraTe This acTiviTy Describe in words how you mulTiply Two fracTions Describe in words how you divide Two fracTions Make a noTe card for reciprocal Include The oTher words used To describe The reciprocal and some examples Also include whaT The producT of a number and iTs reciprocal is A flow charT is a graphic organizer ThaT helps you make decisions when performing a series of sTeps CompleTe The following by inserTing The phrases below in The appropriaTe boxes To make a flow charT To show whaT To do when you musT perform an operaTion beTween Two fracTions QuesTions go in The diamond shapes STaTemenTs go in The recTangles I see an operation between two fractions Which operation is it AddiTion or subTracTion l MulTiplicaTion or division l Do They have a common denominaTor Find a common denominaTor Is iT mulTiplicaTion or division RewriTe problem wiTh equivalenT fracTions MulTiplicaTion and common denominaTors Division simplify InverT second fracTion and rewriTe problem MulTiply numeraTors mulTiply denominaTors Add numeraTors keep denominaTor SecTion 14 ExponenTs Order of OperaTions and ProperTies of Real Numbers Read secTion 14 pages 44 50 and answer The following quesTions as you read 1 WhaT form of a number describes repeaTed mulTiplicaTion N Name The parTs of The exponenTial form 35 WriTe iT as a repeaTed mulTiplicaTion 3 WhaT power is undersTood when you don39T see a power Give an example and explain in a compleTe senTence 4gt Find each of The following by firsT wriTing The expression as a repeaTed mulTiplicaTion a 34 b 233 c 34 U1 Explain why your answers for 4a and 4c are noT The same 6 Why do we need an order of operaTions l Use The following memory device To remember your order of operaTions PEMA or Please Excuse My AunT The P sTands for parenTheses or any oTher grouping symbol LisT all The grouping symbols you know X 0 The E sTands for exponenTs The M sTands for mulTiplicaTion and division since division is mulTiplying by The reciprocal We perform all mulTiplicaTion and division as we come To Them from To The A sTands for AddiTion and subTracTion since subTracTion is adding The opposiTe We perform all addiTion and subTracTion as we come To Them from To Use The order of operaTions To correchy simplify 2082x45 Make a noTe card for each of The ProperTies of Real Numbers on page 48 Describe in your own words whaT each properTy means 10 STaTe which properTy is being used and how you know a 16355163 a3bab3 c a3bb3a 16351635 039 Q 11 Go Through examples 6 and 7 covering up The soluTions unTil you have come up wiTh your own answer Then compare your answer To The book39s soluTion 12 Why isn39T CommuTaTive ProperTy of SubTracTion lisTed in The Pro perTies WiTh The oTher members of your group make a concepT map ThaT describes The r elaTionships beTween The following key Terms in chapTer 1 AbsoluTe value NaTur al number Whole number InTeger RaTional number Real number Ir r aTional number Real number line InequaliTy symbol AddiTive Inver se OpposiTes ChapTer 2 STudy Guide MaTh 101 1 Make Time in your schedule To learn you cannoT Take shor TcuTs 2 Read each secTion in your Tebeook and answer39 The quesTions in The sTudy guide before you go To class 3 Take noTes in class Trying To under sTand as The Teacher39 pr esenTs examples and explains concest 4 Do your homework IT should be easier afTer39 The previous Two sTeps Make sure To under sTand whaT you are doing and be able To solve each problem compleTely and cor r echy by yourself 5 Carry on a conver saTion wiTh yourself as you work asking as you sTar T each problem WhaT is This WhaT is my goal WhaT should my answer39 look like when I am donequot Then as you work a problem ask WhaT pr oper Ty allows me To Take This sTepquot And aT The end Does my answer39 make sense How can I check iTquot 6 MainTain a gr eaT aTTiTude abouT lear ning Algebr a people who have a good aTTiTude find iT easier39 To learn and Those who learn algebr a well usually enjoy iT 7 Go To The lab or your insTr ucTor s office and geT help when you need iT SecTion 21 WriTinq and evaluaTinq Alqebraic Expressions Read secTion 21 pages 62 67 and answer The following quesTions as you read 1 WhaT are symbols used To represenT in Algebra 2 WhaT is an algebraic expression Give Two examples of algebraic expressions differenT from The examples in The book 3 CompleTe The Table by idenTifying The Terms of The expressions Expression How many LisT The Terms separaTed by Terms commas 6y7 5x2 3 x 2x34x 3x25 4x 7y 9 7x 42 4 IdenTify The coefficienTs of The following Terms a x b 5x c E 7 5 a WriTe 35 as repeaTed mulTiplicaTion b WriTe 34 as repeaTed mulTiplicaTion c WriTe 34 as repeaTed mulTiplicaTion d WriTe 34 as repeaTed mulTiplicaTion d WriTe 3x4 as repeaTed mulTiplicaTion e WriTe 3x4 as repeaTed mulTiplicaTion f WriTe 3x4 as repeaTed mulTiplicaTion 6 WhaT does iT mean To evaluaTe an expression For each of The following show your work neale 7 EvaluaTe The expression in example 5 e when y2 8 EvaluaTe The expression in example 6 d when x5 and y2 9 EvaluaTe The expression in 7a when x5 y2 and 223 10 Example 8 which is abouT if The Table included one more xvalue whaT would iT be WhaT is The value of 5x2 for39 This x SecTion 22 Simplifying Alqebr aic Expr essions Read secTion 22 pages 71 79 and answer39 The following quesTions as you read 1 Make Thr ee noTe car ds one for each rule of exponenT on page 71 Be sure To include on each noTe card a verbal descr ipTion of The expression To be simplified and aT leasT Two examples 2 Simplify each of The following expressions if possible If H is noT possible explain why a xzx5 b d A 39gt 01 0 l xy23 If you made noTe cards in chapTer 1 for each of The properTies geT Them ouT and add an algebraic example To each one If you did noT make cards in chapTer 1 make one now for each properTy You should have nine cards when you are done Be sure To include a way To remember each properTy Use The DisTribuTive properTy To rewriTe The following expressions a 3x7 b 3x7 c 3xx7 Draw an area model like Those in example 5 for The mulTiplicaTion 3a2ab WhaT is The definiTion of like Terms IdenTify The like Terms in each of The following expressions by underlining Terms ThaT are like If oTher Terms are also like Terms double underline Them Example 21 4y3z2x2 9y 3l a 361213 71362 14ab2 25b2a b 6rt 3r2t2rt2 4rt 2m 8 Combine like Terms in The lasT problem a b 9 Simplify each expression a 26x b 212 3 3 10 WhaT number musT we mulTiply by gx To geT x HinT look aT example 10a WhaT properTy are we using 11 Example 11 Talks abouT symbols of grouping LisT all grouping symbols you know of 12 To simplify an algebraic expression means To remove symbols of grouping and combine like Terms Simplify The following expressions a 5 46x2x3 y b le 15 SecTion 23 Algebra and Problem Solving Read secTion 23 pages 85 95 and answer The following quesTions as you read 1 WhaT is algebra 2 How do you Tell an eguaTion from an expression A 4gt U1 0 N You are parTicipaTing in a fundraiser where your employer pays 2 for each mile you run and 150 for each mile you bike ride for a week wriTe an expression ThaT represenTs The ToTal amounT of money your employer will pay The chariTy Declare variables and wriTe a verbal model firsT WriTe The operaTion indicaTed by each of The following words a Sum b ProducT c Difference TranslaTe The phrases inTo algebraic expressions a The sum of 12 and a number b The producT of a number and 5 c 5 less Than a number d A number less Than 5 e 10 less Than The producT of 3 and a number WriTe a verbal descripTion for each of The following algebraic expressions a 2x4 b 2x4 In example 6a give a verbal descripTion of The value of nickel39 mulTiplied by number of nickels39 ThaT is afTer The mulTiplicaTion how can you describe The meaning of The quanTiTy 8 If you drive 60 miles per hour for Three hours how far have you gone If you Tr avel r miles per hour for T hour39s wr iTe an expression for how far you have gone SecTion 24 InTr oducTion To EquaTions Read secTion 24 pages 99 104 and answer39 The following quesTions as you read 1 A 4gt U1 WhaT is an eguaTion WhaT does iT mean To solve an equaTion WhaT is an idenTiTy WhaT is a condiTional eguaTion STaTe wheTher each of The following is an expression an idenTiTy or a condiTional equaTion and sTaTe how you know a 2x42x2 b 83x4x7 c x73 a DeTer mine wheTher 3 is a soluTion To The equaTion x 5 2 b DeTer mine wheTher 3 is a soluTion To 44x4 7 WhaT ar e eguivalenT eguaTions 8 LisT The four ways an equaTion can be Transformed inTo an equivalenT equaTion 9 To solve each of The following equaTions sTaTe your goal sTaTe The sTep you are going To Take and why you are going To Take iT Then solve The equaTion Example X42 My goal is To geT x on one side of The equaTion by iTself I am going To subTr acT 4 from each side since 4 is being added To x X4424 X2 a x 35 b 2x5 c x315 10 WriTe a verbal model for each of The problems a The sale price of a fooTball is 15 The sale price is 4 less Than The original price WhaT is The original price b The original price of a shirT is 45 The original price is marked down by 12 WhaT is The sale price ChapTer 2 Review 1 WhaT is differenT abouT solving equaTions and simplifying expressions 2 WhaT properTies can you use To solve equaTions ThaT you cannoT use To simplify expressions 3 WhaT Topics in chapTer 2 are sTill confusing To you you may lisT problems you do noT undersTand

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