College and Career Mathematics Winter Student Enrichment

Packet

Detroit Public Schools Community District Department of Curriculum and Instruction

Office of Mathematics

NOTE TO STUDENT

This Winter Student Enrichment Packet has been compiled to complement high school mathematics classroom instruction aligned to Michigan Standards for Mathematics. It is intended to be used for review and practice of previously taught and new concepts.

We strongly encourage you to work diligently to complete the activities in this packet. You may experience some difficulty with some problems in this packet, but we encourage you to explore and attempt to find a solution to the best of your ability.

 

   

1) Whatisthesumofthecomplexnumbers2 3 and 4 8 ,where √ 1?A) 17

B) 17i

C) 6+ l l i

D) 8+24i

2) 4 9

Intheequationabove,pandtareconstants.Whichofthefollowingcouldbethevalueofp?A) 2

B) 3

C) 4

D) 9

3)

Thevertexoftheparabolainthexy‐planeaboveis(0,c).Whichofthefollowingistrueabouttheparabolawiththeequationy= a(x b)2+c?A) Thevertexis(b,c)andthegraphopensupward.

B) Thevertexis(b,c)andthegraphopensdownward.

C) Thevertexis( b,c)andthegraphopensupward.

D) Thevertexis( b,c)andthegraphopensdownward.

4) Whichofthefollowingisequivalentto ?

A)

B 4

C

D 1

5)

Thetableaboveshowstheflavorsoficecreamandthetoppingschosenbythepeopleataparty.Eachpersonchoseoneflavoroficecreamandonetopping.Ofthepeoplewhochosevanillaicecream,whatfractionchosehotfudgeasatopping?

A)

B)

C)

D)

6) Thescatterplotbelowshowstheamountofelectricenergygenerated,inmillionsofmegawatt‐hours,bynuclearsourcesovera10‐yearperiod.

Ofthefollowingequations,whichbestmodelsthedatainthescatterplot?

A) 1.674 19.76 745.73

B) 1.674 19.76 745.73

C) 1.674 19.76 745.73

D) 1.674 19.76 745.73

7) 7 3 86 3 5

Forthesolution(x,y)tothesystemofequationabove,whatisthevalueof ?

A)

B)

C)

D)

8)

Whichofthefollowingequationsrelatesytoxforthevaluesinthetableabove?

A) ∙

B) 2 ∙

C) 2

D)

9)

TrianglesABCandDEFareshownabove.Whichofthefollowingisequaltotheratio ?A)

B)

C)

D)

10) In2008,therewere21stateswith10ormoreelectoralvotes,asshowninthetable.Basedonthetable,whatwasthemediannumberofelectoralvotesforthe21states?

A) 13

B) 15

C) 17

D) 20

11) Paulstartedtotrainforamarathon.ThetableshowsthenumberofmilesPaulranduringeachofthefirstthreeweeksafterhebegantraining.

Ifthispatterncontinues,whichofthelistedstatementscouldmodelthenumberofmilesPaulruns ,intermsofthenumberofweeks,n,afterhebegantraining?Selectallthatapply.A) 10 2 1

B) 10

C) 10 1.2

D) 10, 1.2

E) 10, 2

12) Whichgraphbestrepresentsthesolutiontothissystemofinequalities?6

2 8

A) B)

C) D)

13) Thefigureshowsagraphofthefunctionf(x)inthexy‐coordinateplane,withthevertexat(1,9)andthezeroesat‐2and4.

Thefunctiongisdefinedby 3 2.Whichstatementsaretrue?Selectallthatapply.

A) f(‐2)isgreaterthang(‐2).

B) f(‐1)islessthang(‐1).

C) f(0)isgreaterthang(0).

D) f(1)islessthang(1).

E) f(2)isgreaterthang(2).

14) Theapothemofaregularpolygonisthedistancefromthecentertoanyside.

Ifthelengthoftheapothemremainsconstantat10inches,theformulafortheperimeterofaregularpolygonasafunctionofthenumberofsidesnis

10 ° 2 .

Astheregularpolygonchangesfromapentagon(5sides)toanoctagon(8sides),whatistheapproximateaveragerateofchangeintheperimeter?A) decreaseof0.80inchesforeachadditionalside

B) decreaseof2.13inchesforeachadditionalside

C) decreaseof4.56inchesforeachadditionalside

D) decreaseof6.38inchesforeachadditionalside

15) Thediagramshowstwocylinderswithbasesthathavethesamecenterandheightsof12millimeters.PartAWhichisafunctionforthevolume,V,thatisinsidethelargercylinderbutoutsidetheonewiththesmallerradius,r?A) 1,200 12

B) 120 12

C) 12

D) 12 10

PartBSupposethatthereisspacebetweentheinnerandoutercylindersandtheradiusoftheinnercylindermustbeanintegergreaterthanorequalto3.WhatisthedomainofV?A) allintegersgreaterthanorequalto3

B) 3,4,5,6,7,8,9,or10

C) 3,4,5,6,7,8,or9

D) 3 9

16) Thepolynomial 2 13 17 12 has 4 asafactor.Factorthepolynomialintothreelinearfactors.Describethestepsyouwouldusetosketchthegraphofthefunctiondefinedbythispolynomial.Identifyallinterceptsanddescribetheendbehaviorofthegraph.

17) Considerthepolynomialfunction 2 1 4 2 .PartAWhatisthey‐interceptofthegraphofthefunctioninthexy‐coordinateplane?PartBForwhatvaluesofxis 0?Selectallthatapply.A) 4

B) 4

C) 4 2

D) 2

E)

F) 2

PartCWhatistheendbehaviorofthegraphofthefunction?A) As → ∞, → ∞,andas → ∞, → ∞.

B) As → ∞, → ∞,andas → ∞, → ∞.

C) As → ∞, → ∞,andas → ∞, → ∞.

D) As → ∞, → ∞,andas → ∞, → ∞.

PartDHowmanyrelativemaximumsdoesthefunctionhave?A) none

B) one

C) two

D) three

18) PartAThehistogramsshowthedistributionofheartratesofrandomlyselectedadultmalesbetweentheagesof40and45after20minutesofcontinuousexercise.Theadultmaleswererandomlyassignedtouseeitheranewellipticalmachine(ExperimentalGroup)oratraditionaltreadmillmachine(ControlGroup).

Whatconclusionaboutthedifferencebetweenthedistributionsoftheheartratesforthesetwogroupscanbedrawn?Justifyyouranswer.

PartBAftertheparticipantsworkedoutthreetimesperweekforfourweekssolelyontheirassignedmachines,participants’heartrateswerecollectedagainafter20minutesofcontinuousexercise.Thedataareshowninthehistograms.

Whatconclusionaboutthedifferencebetweenthedistributionsoftheheartratesforthetwogroupscanbedrawn?Justifyyouranswer.Ifthetargetheartraterangeforadultmalesagedbetween40and45after20minutesofexerciseisaround175beatsperminute,whatrecommendationwouldyoumakeintermsofwhichmachinetouse?Justifyyouranswer.Baseduponthesedata,whatconclusionaboutexercisemachinesingeneralcanbemade?

19) PartAAbankoffersasavingsaccountthataccruessimpleinterestannuallybasedonaninitialdepositof$500.IfS(t)representsthemoneyintheaccountattheendoftyearsandS(5)=575,writeafunctionthatcouldbeusedtodeterminetheamountofmoneyintheaccountovertime.Showyourworkorexplainyourreasoning.PartBAnotherbankoffersasavingsaccountthataccruescompoundinterestannuallyatarateof3%.Whatistheinitialamountneededinthisaccountsothatitwillhavethesameamountofmoneyattheendof10yearsastheaccountinPartAattheendof10years?Showyourworkorexplainyourreasoning.

20) PhilandMattmadecookiesforafundraiserattheirhighschool. Philmade25%morecookiesthanMatt. Thecookiessoldfor$0.25each. Afterthesale,20%ofthecombinedtotaloftheircookiesremained.

PartACreateanequationtorepresentthetotalamountofmoneyMattandPhilearnedatthefundraiserbasedonthenumberofcookiesMattmade.Explainhowyoudeterminedyourequation.PartBPhilandMattmadeatotalof$72.00sellingthecookies.HowmanycookiesdidPhilmakeandhowmanycookiesdidMattmake?Showyourwork.PartCNextyear,PhilandMattmaysellthecookiesfor$0.50each.Theyplantomakethesametotalnumberofcookies,buttheypredictthattheywillonlysell70%ofthemgiventhepriceincrease.Basedontheirprediction,shouldPhilandMattraisethepriceofthecookies?Justifyyouranswer.