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RAMAPO---INDIANHILLSSCHOOLDISTRICT

DearRamapo---IndianHillsStudent:Pleasefindattachedthesummerpacketforyourupcomingmathcourse.Thepurposeofthesummerpacketistoprovideyouwithanopportunitytoreviewprerequisiteskillsandconceptsinpreparationforyournextyear’smathematicscourse.Whileyoumayfindsomeproblemsinthispackettobeeasy,youmayalsofindotherstobemoredifficult;therefore,youarenotnecessarilyexpectedtoanswereveryquestioncorrectly.Rather,theexpectationisforstudentstoputforththeirbesteffort,andworkdiligentlythrougheachproblem.Tothatend,youmaywishtoreviewnotesfrompriorcoursesoron-linevideos(www.KhanAcademy.com,www.glencoe.com,www.youtube.com)torefreshyourmemoryonhowtocompletetheseproblems.Werecommendyoucircleanyproblemsthatcauseyoudifficulty,andaskyourteacherstoreviewtherespectivequestionswhenyoureturntoschoolinSeptember.Again,giventhatmathbuildsonpriorconcepts,thepurposeofthispacketistohelpprepareyouforyourupcomingmathcoursebyreviewingtheseprerequisiteskills;therefore,thegreatereffortyouputforthonthispacket,thegreateritwillbenefityouwhenyoureturntoschool.PleasebringyourpacketandcompletedworktothefirstdayofclassinSeptember.Teacherswillplantoreviewconceptsfromthesummerpacketsinclassandwillalsobeavailabletoanswerquestionsduringtheirextrahelphoursafterschool.Teachersmayassessonthematerialinthesesummerpacketsafterreviewingwiththeclass.Ifthereareanyquestions,pleasedonothesitatetocontacttheMathSupervisorsatthenumbersnotedbelow.Enjoyyoursummer!RamapoHighSchoolMichaelKaplanmkaplan@rih.org(201)891-1500X2255IndianHillsHighSchoolAmandaZielenkieviczazielenkievicz@rih.org(201)337-0100X3355

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Name_________________________________________________________________________________________

Algebra1CPE-CPSummerReviewPacketRamapoIndianHills

ThispacketmustbecompletedthesummerbeforeenteringAlgebra1.Theseskillsarenecessaryforasuccessfulyearinthiscourse.Pleasereviewthenotesforeachsectionandcompleteallsubsequentpracticeproblems.Besuretoshowallofyourwork.Thispacketmustbecompletedinitsentiretyandbereadytobesubmitted at the beginning school.

I. WritingAlgebraicExpressions

Inalgebraicexpressions,letterssuchasxandwarecalledvariables.Avariableisusedtorepresentanunspecifiednumberorvalue.

Practice:Writeanalgebraicexpressionforeachverbalexpression.

1. Fourtimesanumberdecreasedbytwelve________________________

2. Threemorethantheproductoffiveandanumber____________________

3. Thequotientoftwomorethananumberandeight____________________

4. Sevenlessthantwiceanumber_______________________________

II. OrderofOperations

Toevaluatenumericalexpressionscontainingmorethanoneoperation,usetherulesfororderofoperations.TherulesareoftensummarizedusingtheexpressionPEMDAS

Examples:

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Practice:Evaluateeachexpression.

1.250÷[5(3•7+4)] 2.52 ⋅ 4− 5 ⋅ 42

5(4)

3.12⋅26−32 4.82÷(2•8)+2

5.5+ 30− (6−1)2"# $% 6.2 ⋅ 42 −8÷ 2(5+ 2) ⋅2

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III.EvaluatingAlgebraicExpressions

Toevaluatealgebraicexpressions,firstreplacethevariableswiththeirvalues.Then,useorderofoperationstocalculatethevalueoftheresultingnumericalexpression.Example:Evaluate!! − 5(! − !)if! = 6and! = 2!! − 5 ! − ! = 6 ! − 5(6− 2) = 6 ! − 5(4) =36− 5(4) =36− 20 =16Practice:Evaluateeachexpression.

1.5x2 − y whenx=4andy=24 2.3xy− 47x

whenx=2andy=3

3. (z÷ x)2 + 45x whenx=2andz=4 4.

y2 − 2z2

x + y− zwhenx=12,y=9,andz=4

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IV.TheRealNumberSystem

TheRealnumbersystemismadeupoftwomainsub-groupsRationalnumbersandIrrationalnumbers.Thesetofrationalnumbersincludesseveralsubsets:naturalnumbers,wholenumbers,andintegers.

• RealNumbers-anynumberthatcanberepresentedonanumber-line.o RationalNumbers-anumberthatcanbewrittenastheratiooftwointegers

(thisincludesdecimalsthathaveadefiniteendorrepeatingpattern)

Examples:2,−5,!!! ,!!,0.253,0. 3

§ Integers-positiveandnegativewholenumbersand0Examples:−5,−3,0,8…

§ WholeNumbers–thecountingnumbersfrom0toinfinityExamples:{0,1,2,3,4,….}

§ NaturalNumbers-thecountingnumbersfrom1toinfinityExamples:{1,2,3,4…}

o IrrationalNumbers-Non-terminating,non-repeatingdecimals(includingπ,andthesquarerootofanynumberthatisnotaperfectsquare.)Examples:2!, 3, 23,3.21211211121111….

Practice:Nameallthesetstowhicheachnumberbelongs.

1.-4.2______________________________________2.

€

3 5 _______________________________________

3.

€

53 ________________________________________

4.

€

9 __________________________________________

5.

€

16 ________________________________________

6.− 82___________________________________________

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V.Fractions Add,subtract,multiplyordivide.Simplifyfully.Writeyouranswerasanimproperfractioninsimplestform,notadecimal.

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VI.TheDistributiveProperty

TheDistributivePropertystatesforanynumbera,b,andc:

1. a(b+ c) = ab+ ac or (b+ c)a = ba+ ca

2. a(b− c) = ab− ac or (b− c)a = ba− ca

Practice:Rewriteeachexpressionusingthedistributiveproperty.

1.7(h-3) 2.-3(2x+5)

3.(5x–9)4 4.1214− 6y( )

5.3(7x2 −3x + 2) 6.1416x −12y+ 4z( )

7. 9− 2! + 3!" ∙−4 8.0.3(40! + 10! − 5)

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VII.CombiningLike-Terms

Termsinalgebraarenumbers,variablesortheproductofnumbersandvariables.Inalgebraicexpressionstermsareseparatedbyaddition(+)orsubtraction(-)symbols.Termscanbecombinedusingadditionandsubtractioniftheyarelike-terms.Like-termshavethesamevariablestothesamepower.

Exampleoflike-terms:5x2 and−6x2

ExampleoftermsthatareNOTlike-terms:9x2 and15xAlthoughbothtermshavethevariablex,theyarenotbeingraisedtothesamepower

Tocombinelike-termsusingadditionandsubtraction,addorsubtractthenumericalfactor

Example:Simplifytheexpressionbycombininglike-terms 8x2 + 9x −12x + 7x2 = (8+ 7)x2 + (9−12)x =15x2 +−3x =15x2 −3x Practice:Simplifyeachexpression1.5x − 9x + 2 2.3q2 + q− q2 3. c2 + 4d 2 − 7d 2 4.5x2 + 6x −12x2 − 9x + 2 5.2(3x − 4y)+ 5(x +3y) 6.10xy− 4(xy+ 2x2y)

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VIII.SolvingEquationswithVariablesonOne-SidePractice:Solveeachequation.1.98 = b+34 2.−14+ y = −2

3.8k = −64 4.25x = 6

5.14n−8 = 34 6.8+ n12

=13

7.3k − 75

=16 8.−d6+12 = −7

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IX.SolvingEquationswithVariablesonEach-Side:Tosolveanequationwiththesamevariableoneachside,writeanequivalentequationthathasthevariableonjustonesideoftheequation.Thensolve.Practice:Solveeachequation.1.5+3r = 5r −19 2.8x +12 = 4(3+ 2x) 3.−5x −10 = 2− (x + 4) 4.6(−3m+1) = 5(−2m− 2) 5.3(d −8)− 5= 9(d + 2)+1

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XII.SolvingForaSpecificVariable

Practice:Solveeachequationorformulaforthevariablespecified.

1. 15! + 1 = !for!

2. ! 4− ! = !for!

3. 7! + 3! = !for!

4. ! = 2! + 2!for!

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XVI.SolvingWordProblemsPractice:Writeanalgebraicequationtomodeleachsituation.Thensolvetheequationandanswerthequestion.

1. Avideostorechargesaone-timemembershipfeeof$11.75plus$1.50pervideorental.HowmanyvideosdidStewartrentifhespends$72.00?

2. Darelwenttothemallandspent$41.Heboughtseveralt-shirtsthatachcost$12andhebought1pairofsocksfor$5.Howmanyt-shirtsdidDarelbuy?

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3. Nickis30yearslessthan3timesRay’sage.Ifthesumoftheiragesis74,howoldareeachofthemen?

4. Three-fourthsofthestudentbodyattendedthepep-rally.Iftherewere1230studentsatthepeprally,howmanystudentsarethereinall?

5. Sarahdrove3hoursmorethanMichaelontheirtriptoTexas.Ifthetriptook37hours,howlongdidSarahandMichaeleachdrive?

6. Bicyclecitymakescustombicycles.Theycharge$160plus$80foreachdaythatittakestobuildthebicycle.Ifyouhave$480tospendonyournewbicycle,howmanydayscanittakeBicycleCitytobuildthebike?