2018–2019 – summer assignment – algebra ii review...

2018–2019–SummerAssignment–AlgebraIIReviewForstudentsenteringPre-CalculusHonors

ThepurposeofthispacketistoensurethatstudentsarepreparedforthequickpaceofPre-Calculus.TheTopicscontainedinthispacketarethecoreAlgebraIandAlgebraIIconceptsthatstudentsmustunderstandtobesuccessfulinPre-Calculus.Thereare11conceptsaddressedinthispacket:

A.Distance&MidpointB.CirclesC.LinearFunctionsD.GraphingFunctionsE.FactoringF.EvaluatingFunctionsG.QuadraticFormulaH.SolvingInequalitiesI.Domain&RangeJ.PropertiesofExponentsK.SquareRootsandRationalizingDenominatorsForeachconceptlisted,thereisaproblemsetthatneedstobecompleted.Therearewebsitesgivenbelowwhereyoucangotofindexamples,videos,andextraproblemsthatdealwiththatparticulartopicifyouneedassistanceonworkingtheproblemsets.Ifyoutryasiteanditisnotworkingornolongeravailable,itisyourresponsibilitytodoasearchforanothersite.Itissuggestedthatyoucompletethispracticesetinthefewweekspriortoreturningtoschoolsothattheinformationwillbefresh.Pleasebringallofyourwork/solutionsONANOTHERSHEETOFPAPERtoclasswithyouontheFIRSTDAYOFSCHOOL.Youmustshowyourwork–justalistofanswerswillnotbeaccepted.Wewillgooverthematerialbrieflyandhaveasummativeassessment(test)withinthefirstfewweeksofschoolonthesetopics.IfithasbeenafewyearssinceyouhavehadAlgebraIIorifyouareuncomfortablewithanyofthetopicsaftercompletingtheproblemset,itisrecommendedthatyoufindsomeadditionalpracticefromthewebsitesbeloworelsewhere.http://www.purplemath.com/http://www.wtamu.edu/academic/anns/mps/math/mathlab/http://www.basic-mathematics.com/https://www.khanacademy.org/math/trigonometryhttp://www.khanacademy.org/math/algebra2http://www.regentsprep.org/Regents/math/ALGEBRA/math-ALGEBRA.htmhttp://patrickjmt.com/http://www.mathsisfun.com/algebra/index-2.htmlPleaseemailJulieVandiver(jvandiver@lexington1.net),KristyEason(keason@lexington1.net),orTiffanyRoach(troach@lexington1.net)ifyouhaveanyquestions.WelookforwardtoagreatyearinPreCalculus!!

PleasecompletethefollowingproblemsonANOTHERSHEETOFPAPER.Youshouldincludethedirections,problem,allworknecessaryandboxinyourfinalanswer.Theseproblemsshouldbedonewithintwoweeksofthestartofschool(pleasedonotdothematthebeginningofsummer).Bringallworkwithyoutothefirstdayofclass.

Feelfreetouseacalculatortocheckyourworkbutpleaseunderstandthattheexpectationisthatyoucancompletethefollowingwithouttheuseofacalculator.A.DistanceandMidpoint

DistanceFormula=2 2

2 1 2 1( ) ( )x x y y− + − MidpointFormula= 1 2 1 2,2 2

x x y y+ +⎛ ⎞⎜ ⎟⎝ ⎠

Problems:

Findthedistanceandmidpointbetweenthesepoints:1. ( ) ( )2, 3 & 4,7− 2. ( ) ( )1, 10 & 3, 9− − − B.Circles

FormulaofaCircle: 2 2 2( ) ( )x h y k r− + − = where(h,k)isthecenterandristheradius.

Problems:

Findthestandardformoftheequationofthespecifiedcircle:1.Center(-3,9)Radius=2 2.Endpointsofthediameter(8,2),(4,8)

3.Findthecenterandradius.Thengraphthecircle: 2 2( 2) ( 1) 16x y+ + − = C.LinearFunctions

ParallellineshavetheSameSlope PerpendicularlineshaveOppositeReciprocalSlopes

Slope= 2 1

2 1

y ymx x

−=−

Standardform:Ax By C+ =

Slope-InterceptForm: y mx b= + Point-Slopeform: 1 1( ) ( )y y m x x− = − Zeroslope=horizontalline(y=#) Undefinedslope=verticalline(x=#)Problems:Determinetheslopeofthelinepassingthroughthesepoints.1) ( ) ( )4, 1 & 8,2− − 2) ( ) ( )3, 1 & 3,4−

Writeanequationforthelinedescribedininthegiveninformation.

3)(5,4)m= 23

− 4) ( )2,4− m= 3− 5)passesthrough ( )6, 3− − and ( )2, 5− −

6) ( )2, 1− m=0 7) ( )1,5− andperpendicularto 2 5x y− + =

D.GraphingFunctions

Problems:Sketchagraphofthefollowingfunctions:(Graphpaperonbackofpacketifneeded)

1. 2 4 8x y− = 2. 3 5y x= − + 3. ( ) ( )22 13

y x+ = −

4. 2y x= 5. y x= 6. 3y x= 7. 3y x= 8. y x= 9. 3y = −

10. ( )22 4y x= − − + 11. 1 3y x= + − 12. 2 3y x= −

E.Factoring

Problems:Factorthefollowingcompletely:1. 22 11 15x x− + 2. 25 180x − 3. 25 25x x− 4. 2 6 40x x+ − 5. 2 2 8x x− − 6. 2 4x − 7. 23x 75− 8. 2 9 20+ +x x 9. 2 16−x

10. 24x 4x 15− − 11. 22x 7x 4+ − 12. 2x 2x 35− −

13. 2 12 36m m− + 14. 22 18p − 15. 26 15x x+ −

16. 321 35−x x 17. 215 2y y− − 18. 26 10 4c c− −

19. 23 12s − 20. 218 9 1z z+ + 21. 215 16 4− +r r

22. 3 23 12 4w w w− − + 23. 3 24 12 3y y y+ − − 24. 3 22 12 18− +n n n

F.EvaluatingFunctionsProblems:Evaluatethefunctionatthevaluesgivenina,b,andc.Simplifywherepossible.Youshouldhaveananswerforparta,b,andcforeachquestion.

1. ( ) 5 2f x x= − a. ( )3f b. ( )5f − c. ( )2f r −

2. ( ) 2 3h x x x= + a. ( )2h − b. ( )7h c. ( )h x−

3. ( )2 2, 01 4, 02

x xg x

x x

⎧ − ≤⎪= ⎨+ >⎪

⎩

a. ( )0g b. ( )10g − c. ( )2g

G.QuadraticFormula QuadraticFormula:2 42

b b acxa

− ± −=

Problems:Solveusingthequadraticformula.Answersshouldbeinsimplestradicalform–nodecimals.

1. 22 6 1 0x x+ + = 2. 23 5 2x x− =

H.SolvingInequalities

Problems:Solveandgraphonanumberline.1.4( 3) 44x + ≤ 2. 7(3 7) 21 50x x− − + ≥ 3.4 16 or 12 144x x< > 4. 6 2 4 12x− < − <

I.DomainandRange

Problems:1.Findthedomainandrangeoftherelationbelowthendetermineiftherelationisafunction. {( 3,2),( 2,0),( 1, 1),(2,1),(2,3),(4,1)}− − − − Determinethedomainandrangeofthefunctionsbelow:2.Domain:__________Range:___________ 3.Domain:__________Range:__________

J.PropertiesofExponents

Supposemandnarepositiveintegersandaandbarerealnumbers.Thenthefollowingpropertieshold.

Problems:Simplifythefollowingusingpropertiesofexponents.Makesureallanswerscontainonlypositiveexponents.

1. 3 24 2x x− ⋅ 2. 4 34 2n n−⋅ 3. 3 2 4 34 3a b a b− −⋅ 4. ( )234a

5. 3 24x xy⋅ 6. ( )404r 7. ( )443x 8. ( ) 24 32x y−−

9.2

32yy

10.4 4 3

2 3 4

23x y zx y z

− −

− 11.( )43 4

32x xx

−

− 12. ( )2 22 2y y⋅

13.( )

4

34

2

2

m

m

−

− 14.

43x

− 15. ( )

13 215xy 16. ( ) 253x

−−

K.SquareRootsandRationalizingDenominators

Problems:Simplify.

1. 4 3288x y 2.1259

3. 53 128x− 4.7 33

23

2502x yx y

Rationalize.

5.82x

6.5 35

7.72 3

8.12

= ≠0 1, 0a a +=gm n m na a a −=m

m nn

a aa

− = 1nna

a

( ) =n n nab a b ⎛ ⎞ =⎜ ⎟⎝ ⎠

n n

n

a ab b

( ) =nm mna a

1

nna a= ( )m m m

mn nn na a or a a= =

GraphPaperforPartD–GraphingFunctionsifyouwanttouseit.