Answers - Ms Moon's Math Classes - Home€¦ · NEL Answers 595 Answers Chapter 1 ... The future value of option A is $7826.00 and the future value ... 13. e.g., In both cases, interest

NEL 595Answers

An

swers

Chapter 1 – Financial Mathematics: Investing MoneyLesson 1.1, page 14

1. a) $38400 b) $10500 c) $25250 d) $29760 2. a) 6% b) $5900 3. a) 25% b)A:$1365,25% 4. a) $4460 b) $4920 5. Brad;e.g.,Interestratesarealmostequal,butBrad’sGIChasaterm

of1moreyear. 6. a) 2.5% b) $16200 7. a) Theywillbeequal.e.g.,Theprincipal,interestrate,andtermare

equal.Bothearn$300ininterest.b)No.e.g.,Withsimpleinterest,thereisnoadvantagetohavingit

paidmoreoften.c) e.g.,Theymayneedtheinterestmoneytopayamonthlybill.

8. a) A:$12500,B:$11400,C:$11330,D:$10840b)No.e.g.,Theamountofinterestnotearnedinthelast1.5yearsis

insufficienttochangerankings.A:$11750,B:$11190,C:$11045,D:$10630

9. a)Desiree,$92.50 b) $7.50 c)Desiree:1.25%,Latoya:1.5%10. 8years11. a) $17241.38 b) about14.1years12. a) 12.5% b) $1410013. a) Increasetheinterestrate.e.g.,Thehighertheinterestrate,the

moremoneyearnedpertimeperiod.b)e.g.,Theybothhavethesameinterestrate,buttheyhavedifferent

principals.14. $5570.00 15. $24294.05

Lesson 1.2, page 19

1. Larry’sGICearns$49.96moreinterestthanEve’sGIC.e.g.,Larry’sGICearnsmoreinterestbecauseitiscompounded.

2. B.e.g.,ThefuturevalueofoptionAis$7826.00andthefuturevalueofoptionBis$7840.77.

3. a) e.g.,No,itisnotpossibletotell,astheprincipals,interestrates,andtimelinesalldiffer.

b)C

Lesson 1.3, page 30

1.Compound

Interest Rate per Annum (%)

Compounding Frequency Term

Interest Rate per Compounding Period, i (%)

Number of Compounding

Periods, n

10.2 semi-annually 4 years 5.1 8

4.1 monthly 6 years 0.3416… 72

13.2 quarterly 7 years 3.3 28

3.5 daily 9 months 0.009 589 e.g., 274

2. a) $744.83,$224.83 b) $4950.59,$3550.59 3. i) a)10.59years,10.54years b)7.83years,7.56years c)4.62years,4.45years d)26.67years,25.85years ii)a)$69999.01,$62999.01 b)$5314.63,$4464.63 c)$27236.58,$14736.58 d)$49572.41,$9572.41 4. a) $14151.36,$15067.91 b)

c)Ascompoundingfrequencyincreases,interestrategrowthincreases.

5. a) 15years,about14.78years b) 5yearssooner,about4.81yearssooner 6. $9590.25 7. C,B,A 8. a) 48years b) 24years 9. 6.5%,$80010. $54333.9611. $2655.4112. a) e.g.,Thehigherinterestrateispaymentinexchangeformoretime

beforematurity. b)i) Option1:$6884.47,Option2:$6494.71,e.g.,Interestrates

arecompoundedannually,interestratesremainthesamein5years,canreinvestall$5698.55in5years.

ii) e.g.,Option1:Higherreturnaslongasratesdonotrise,butmoneyislockedinfor10years.Option2:Ifratesrise,themoneycanbereinvestedafter5yearsatahigherrate,butifratesdonotrise,alowerreturnmayberealized.

3 6 9 12 18150

2 000

4 000

6 000

8 000

10 000

12 000

Years

Interest Earned

Inte

rest

ear

ned

($)

monthlycompounding

annualcompounding

Answers

8085_Ch01-08_West_ANS.indd 595 2/17/12 11:39 AM

NEL596 Answers

b) e.g.,Changedtheinterestrateto7.6%,compoundedannually.

31 000

29 000

27 000

0 2 10864

15 000

17 000

19 000

21 000

23 000

25 000

Years

GIC Investment Valueper Year

GIC

val

ue ($

)

3.8% interest

7.6% interest

13. e.g.,Inbothcases,interestisearnedontheprincipal.Forcompoundinterest,interestisalsoearnedontheinterest.

14. a) $2727.80 b) $5877.9615. $5168.65

Lesson 1.4, page 40

1. e.g.,OptionBwillrequireagreaterpresentvaluebecausethecompoundingfrequencyislessthanthatofoptionA.OptionA:$6071.61,OptionB:$6084.13.

2. a)A:1.647…,B:1.644… b) e.g.,Higherratiobecausetheinterestrateishigherandthe

principalislower. 3.

Future Value

(amount in $)

Present Value

(amount in $)

Interest Rate per Annum

(%)Compounding

Period

Invest- ment Term

(years)

2 500.00 1 370.85 7.8 annually 8

3 500.00 2 000.00 11.5 semi- annually

5

11 000.00 8 254.48 2.4 quarterly 12

100 000.00 609.35 13.6 annually 40

23 500.00 16 150.00 18.9 monthly 2

4. a) $48904.10 b) $201095.90 5. a) 33.1%;e.g.,No,itwouldbedifficulttofindaguaranteed

investmentwiththatinterestrate. b) about5.5years 6. $10073.39 7. a) A:32.49%,B:32.53%,C:32.36%;ChooseB.e.g.,Bhasthe

greatestrateofreturn. b) $5891.43 8. a) e.g.,InvestmentA

21 000

0 2 10864

15 000

16 000

17 000

18 000

19 000

20 000

Years


GIC

val

ue ($

)

c) e.g.,Changedtheinterestrateto1.9%,compoundedannually.

31 000

29 000

27 000

0 2 10864

15 000

17 000

19 000

21 000

23 000

25 000

Years


GIC

val

ue ($

)

1.9% interest

7.6% interest3.8% interest

d)e.g.,Changingtheinterestratechangestherateatwhichthevalueoftheinvestmentincreases.

9. C;e.g.,OptionChasthebestinterestratewithfrequentcompounding;optionArequires$8678.89,optionBrequires$9815.74,optionCrequires$5545.60,andoptionDrequires$9982.77.

10. Franco,$204.2011. a) 8.56% b) 2.33;e.g,Ipredictitwilldecreasebecauseitiscompoundedless

frequentlysothefuturevaluedecreases,2.27.12. $185.3013. $2906.25


NEL 597Answers

An

swers

Lesson 1.5, page 55

1. a) $498526.60 b) $126127.32 c) $63820.79 d) $195389.47 2. a) 2.68% b) $250.00 c) 10.5years 3. $154030.54,$78430.54 4. A;e.g.,Thetotalamountisinvestedatthebeginningandearns

interestforthefullterm.A:$6691.13,B:$5637.09 5. $14150.77,$2150.77 6. $196.60 7. a) i) $76.22 ii) $568.60 b) i)3023.79% ii)318.74%;e.g.,Sheshouldchooseoptioni). 8. a) $1665.90 b) $1356.16 c)Aaron;e.g.,Hewillcontinuetoinvest$25eachmonthandhis

interestcompoundsmonthly;Aaron:$3720.33,Casey:$2046.39. 9. 6.13%10. 4.5years11. a)Dee:$66298.98,Pete:$73624.90 b) e.g.,Pete’smoneywasinvestedforalongerperiodoftime.12. Trey’sby$62.7513. No.e.g.,Hewillbeshort$78.87.14. a) $40006.80 b) $605469.2015. No.e.g.,Hewillbeshortby$35320.92.16. a) Same:Theamountinvested,interestrate,andtermareall

equal.Different:InvestmentAhasalumpsumpaymentwhileinvestmentBhasregularpayments.

b)

e.g.,InvestmentAisthebetterinvestment.InvestmentBgrowsatafasterrate,butdoesnothavetimetosurpassinvestmentA.

17. No.e.g.,Theprobabilitythathistipswillequalthesameamounteachmonthisveryunlikely.

18. $150.9319. $5522.3520. No.e.g.,Hewillbeshortby$1933.99.

Lesson 1.6, page 64

1. a) e.g.,Hecaninvestthe$300inaGICanddeposit$15intoahighinterestsavingsaccountsohehasaccesstofundsifrequired.

b)No;$27.21 2. $4078.92

240 48 72 96 120

500

1000

1500

2000

2500

Months

Investment Valueover Time

Valu

e of

inve

stm

ent

($)

investment A

investment B

14. e.g.,Inaninvestment,youagreetolendasumofmoneytoanotherentity(likeacompany);theamountyoulendiscalledthepresent valueoftheprincipal.Theinterest ratedictatestheamountofmoneytheypayyoufortheloan,foragiventimeperiod,calledtheterm.Simple interestpaysyouapercentageoftheloanedamountattheendoftheterm.Withcompound interest,theinterestispaidoutmoreoften,definedbythecompounding frequency.Youdon’tgetthecompound interestimmediately,buteffectivelylendtheentitytheinterestaswell,untiltheendoftheterm.Thepresent valueplustheinterestyouearniscalledthefuture value.Ahigherinterest rateandahighercompounding frequencywillearnyoumoreinterest.

15. 9.26%16. a) $1050.00 b) i) 4.94% ii) 4.91% iii) 4.89% c) e.g.,Itcouldhaveareturngreaterthananinvestmentwitha

higherinterestrateifcompoundedlessfrequently.

Mid-Chapter Review, page 45

1. 3years 2. a) 3.125years b) 4years c) 3.25years 3. a)Katherine:$12941.82,Brad:$10500.00 b)

c) e.g.,Theintersectionrepresentsthetimewhenbothinvestmentsareworththesameamount.

4. a) $5173.21 b) 25.44years,orabout26years c) i) e.g.,Futurevaluewouldincrease.$5245.18 ii)e.g.,Futurevaluewoulddecrease.$3961.69 d) 5.64% 5. $12947.39 6. AandD:$1340.10,B:$1338.23,C:$1283.35 7. a) $8356.45 b) $8374.84 8. a) i) $2382.91 ii) $2320.40 b)Higher;ratiofora)i)isabout4.62,ratiofora)ii)isabout4.74,

ratioforb)isabout4.85. 9. 4.47%10. e.g.,24years,about23.45yearsor23.5years

40 8 12 16 2420

5 000

6 000

7 000

8 000

9 000

12 000

13 000

10 000

11 000

Years

Comparing Brad’s andKatherine’s Investments

Valu

e of

inve

stm

ent

($)

Brad’sinvestment

Katherine’sinvestment


NEL598 Answers

3. a) e.g.,IpredictSoniabecauseithasamuchhigherinterestrate. b) Sonia:31.0%,Trent:30.2% c) e.g.,Sonia’sinterestratewasappliedontheprincipalonlywhile

Trent’sinterestratewasappliedtotheprincipalandanyaccruedinterest.

4. a) e.g.,Johnny,becauseitiscompoundedmorefrequently.James:$876.19,Johnny:$894.71

b) James:43.8%,Johnny:44.7% 5. 10.54% 6. a) Phil,$27027.06 b) $395323.07 7. a)Mel b)

c) e.g.,Mike’sinvestmentwillsoonbeworthmorebecauseitiscompoundedmorefrequently.

8. $2180.78 9. a) Josh:$212743.51,Jeff:$69827.91 b) $45000.00each c) Josh:$167743.51,Jeff:$24827.91 d) $9140.0510. a) e.g.,Theyhavedifferentcompoundingfrequenciesandpayments. b) John11. a) i) $31529.31 ii)37.1% b)No,shewillneedanextra$611.26forherfourthyear.12. a) e.g.,Portfolio2,the$25000portioniscompoundedmore

frequently,the$10000portioniscompoundedversussimpleinterest,andtheregularpaymentportionhasthesametotalinvestmentamountbutitisinvestedsoonereachyear.

b) Portfolio1:$105273.55,Portfolio2:$109852.24;Yes

13 000

12 000

11 000

0 2 10864

5 000

6 000

7 000

8 000

9 000

10 000

Years

Comparisons ofInvestments

Inve

stm

ent

valu

e ($

)

MelMike

3. $57125.96 4. a) $4788.51 b) Yes,shehas$2887.83. c) Shewillbeshortby$1080.55. 5. a) $2160.00 b)Gayla;e.g.,Fundswereinvestedforalongerperiodoftime.

Gayla:$3940.98,Corey:$2622.73 6. $65078.24,160.3% 7. a) $38191.53 b)205.5% 8. a)No b) e.g.,Sheneedsabout$20perweek.Exactamountis$19.01. 9. A;e.g.,Itisworth$263.17more. 10. e.g.,Aninvestmentportfoliomayconsistofsinglepaymentinvestments

orregularpaymentinvestments.Someinvestmentsmaylockinfundsforaperiodoftime,limitingaccess,butoftenofferahigherinterestrate.Investmentsofferingalowerinterestrateusuallyallowaccesstothefunds.Ahigherinvestmentamountusuallytendstoofferhigherinterestrates.Thegreatertheprincipal,term,interestrate,andcompoundingfrequency,thefastertheinvestmentwillgrow.

11. a) $2121.31 b)$2374.0412. $143664

Chapter Self-Test, page 68

1. a) estimate12years;11.9years b) 16.67years 2. A;e.g.,OptionAwilltakeabout24yearsandoptionBwilltake

about28years. 3. a) $1200.00,$2256.24,88% b) $1388.25 c) $32.50 4. a)Alex:$12600.42,Jamie:$12064.27 b)Alex,at15.6%;e.g.,Alexusedinvestmentswithgreaterprincipals

thatcompoundedmoreoften.

Chapter Review, page 71

1. a) 15% b) $2850;e.g.,Shewillnotreceiveanyinterestforthelast6months. 2. a)Grandmother:$18190.00,Grandfather:$17374.00 b)

c) e.g.,Giventime,ahigherinterestratecancompensateforalowerinitialinvestment.

18 000

16 000

14 000

12 000

122 6 8 1040

2 000

4 000

6 000

8 000

10 000

Years

Comparisons ofInvestments

Inve

stm

ent

valu

e ($

)

Grandmother’sGICGrandfather’sCSB


NEL 599Answers

An

swers

Chapter 2 – Financial Mathematics: Borrowing MoneyLesson 2.1, page 92

1. a) $2560 b) $60 2. a) $1268.79 b) $68.79 3. a) $11154.61 b) $845.39 4. a) 31months b) $1140.33 5. a) $18845.60 b) i) More.e.g.,Heisborrowingthemoneyforalongerperiod

oftime,sohewillpaymoreinterest.Hewillpay$6522.73more.

ii) Less.e.g.,Heisborrowingmoneyforashorterperiodoftime,sohewillpaylessinterest.Hewillpay$2602.50less.

6. a) $11347.95 b) $652.05 7. a) $17990 d) 454weeksor8years38weeks b) $161910 e) $60101.74 c) $284.63 8. a) 42monthsor3years6months b) $695.61 9. a) $1275.15 b) $24.8510. $16545.6511. a) $2082.42

b) Payment Period

(half year)Payment

($)Interest Paid ($)

Principal Paid ($) Balance ($)

0 15 899.00

1 2082.42 166.94 1915.48 13 983.52

2 2082.42 146.83 1935.59 12 047.93

3 2082.42 126.50 1955.92 10 092.01

4 2082.42 105.97 1976.45 8 115.56

5 2082.42 85.21 1997.21 6 118.35

6 2082.42 64.24 2018.18 4 100.17

7 2082.42 43.05 2039.37 2 060.80

8 2082.42 21.64 2060.78 0.02

in2years6months c) $760.3812. a) $41278.72;$11278.72 b) i) $585.58 ii) $24740.54;$19134.42;$13158.79;$6789.31;$0.00 iii) $5134.8213. a) $406.87 b) i) 45months ii) $466.2614. a) $594.93 b) i) $29033.09 ii) $19999.61 iii) $10336.54 iv) $0.00 c) i) $2263.77 ii) $3938.98 iii) $4984.59 iv) $5356.7415. a) $2742.85 b) $2341.85 c) $401.00 d) e.g.,Mikewouldmakesmallerpaymentstothestoreeachmonth,

andhasoneadditionalyeartopayofftheloan.

16. a) bank:26months;investors:13months b) bank:$156.68;investors:$84.00 c) bank:$3156.68;investors:$3084.00 d) e.g.,Eliseshouldtaketheloanfromtheinvestors,ifshecan

makethe$250monthlypayments,becauseshepayslessinterest.17. a) optionA:$453.77;optionB:$456.89 b) optionA:$780.81;optionB:$447.88 c) e.g.,ConnorshouldtakeoptionB,ifhecanaffordthe$5000

downpayment,becausehepayslessinterest.18. principal 5 $5000;interestrateperperiod 5 2.25%;number

ofpayments 5 8;paymentamount 5 $689.93;totalinterestpaid 5 $519.38

19. e.g.,Payment ($)

Term (years)

Total Interest Paid ($)

Option A 8829.81/year 20 56 596.20

Option B 727.18/month 20 54 522.33

Option C 17 883.50/year 10 58 835.39

Option D 1455.93/month 10 54 711.74

ChooseOptionB,asithasamanageablemonthlypayment,ithasthelongestterm,anditincurstheleastamountofinterestoverthelifeoftheloan.

20. OptionBisthebetteroption,becauseGabewouldpay$71.77lessinterest.

21. a) $28797.46 b) 55monthsor4years7months c) 6monthssooner

Lesson 2.2, page 100

1. a) creditcard:$5933.80;bankloan:$5615.43 b) creditcard:$1053.80;bankloan:$615.43 c) creditcard:30monthsor2years6months;

bankloan:29monthsor2years5months d) e.g.,Sheshouldusethebankloan,becauseshewillpayitoff

soonerandpaylessoverall. 2. CardBlue.e.g.,Shewillpay$34.54less. 3. Annie’screditcard 4. a) cardA:$1261.56;cardB:$1327.49 b) i)


1. a) $1081.20 b) $1082.97 2. a) $445.05 b) i) $1249.37 ii) $244.34 c) e.g.,Forthefirstschedule,interestischargedonthefulloriginal

principaleverymonth.Forthesecondschedule,theremainingprincipalisreducedeverymonth,andthereforetheinterestisalsoreduced.

3. a) 83weeksor1year31weeks b) Yes.e.g.,ittakes41weeks 4. a) 3.4% b) e.g.,Theinterestratewouldhavebeenless,becausetherate

wouldbeappliedtotheentirebalanceforayear. 5. a) $112.82 b) no c) $103.88 d) Yes.e.g.,It’sequivalenttohavingtwooftheoriginalloans. 6. Lauren’screditcard.e.g.,The2%cashbackismorethanthe

differenceininterestshewillpay.


NEL600 Answers

3. a)Rent.e.g.,Itischeaper. b) 78days c) 3years d) e.g.,Theymightneedtobuynewequipmentsoonerthan3years. 4. e.g.,Sheshouldpay$700perhalfdayifsheisconfidentshecan

finishin4daysorless,weatherpermitting,orsheshouldpay$6000fortheweeksoshehasafewextradaysforunforeseenproblemsthatmayarise.

5. a) about17years b) about47years 6. Jake:$84000;Archie:$49170.74 7. a) rent:$340permonth;buynew:$1302.80;buyused:$781.68 b) buyingused 8. a) $18715.15 b) $12520 c) $8085 d) e.g.,Lease,ifsheplanstousetheequipmentforonly2years,or

purchaseequipmentifsheplanstocontinuetousetheequipmentbeyondthe2years.

9. a) $9200.08 b) $6318.18,includingtrade-invalue c) $10920.00;leasing:profitof$1719.92;buying:profitof

$4601.82 d) e.g.,Ifthemanagerissureshewillstaywiththesamestoreafter

18months,sheshouldbuy.Otherwise,sheshouldleasetokeepheroptionsopen.

10. a) renting:$70000;buying:$43288.18;leasing:$40960.00 b) e.g.,Lease,itistheleastexpensiveoption.11. a) e.g.,Lease,becauseitseemscheaperthanrentingandnoneedto

purchase,becausetractorisonlyrequiredfor9months. b) buying:$19036.71;renting(275days):$16500;leasing:$14105 c) e.g.,Rentingisthemostflexibleoption;thetractormaynotbe

neededforthefull9months.Rentingisbetterthanbuyingifthedepreciatedvalueofthetractorislessthan$2536in9months.

12. a) $3788.69 b) about2.83% c) e.g.,Thebondislessrisky;ifheboughtthehouse,hewouldnot

needtopayrent. 13. a) $2071.00 b) $707.11 14. e.g.,Renting,buying,orleasingacarfor3years:Rentingmaybethe

bestoptionifonlyoccasionaluseisneeded.Eitherbuyingorleasingmaybethecheapestoption,dependingonfinancing,butleasingmaygivetheflexibilitytochangecarsearlier.

15. 9daysamonth16. e.g.,Equippinganofficewithacomputernetworkfor2years.

Option1:Buyingtheequipmentfor$7500financedat5.5%interest,compoundedmonthly,paidbackover2years,withdepreciationof40%peryearonresale;Option2:Leasingtheequipmentat$230permonth.Costofbuyingis$5237.22;costofleasingis$5520;buyingisslightlycheaper,butleasingavoidsthecostsanduncertaintiesofresale.


1. a) $5772.70;$772.70 b) $5751.28;$751.28 c) $5383.96;$383.96 2. a) $12043.83 b) $230.05;$1759.24 3. a) creditcard:$110.51;lineofcredit:$109.35 b) Lineofcredit.e.g.,Itwillbecheaper.

7. Storecreditcard.e.g.,Hewillpay$434.44less. 8. Storefinancing.e.g.,Hewillpay$113.58less.


1. a) $48.77 b) i) $38.89 ii) $118.56 2. a) dealershipfinancing:$827.34;bankloan:$694.76 b) dealershipfinancing:$39712.37;bankloan:$41685.80 c) dealershipfinancing:advantages:lowertotalinterest,lowertotal

payment,noshippingcharge,debtpaidoffsooner;disadvantages:highermonthlypayments;bankloan:advantages:lowermonthlypayments;disadvantages:highertotalinterest,highertotalpayment,mustpayshippingcharge,debttakeslongertopayoff

3. a) tireshop b) creditcard c) tireshop 4. a) creditcard:$524.53;lineofcredit:$514.24 b) creditcard:$329.82;lineofcredit:$226.94 5. a) 13months b) $26.37 6. a) 8months b) $12.22 c) $20.47more 7. No.e.g.,Withtherebate,Joannewillpaylessintotalwiththecredit

cardoption. 8. a) 9months b) Itwillnottakeheranylonger,butthelastpaymentwillbemore. 9. a) lineofcredit:72monthsor6years;creditcard:70monthsor

5years10months b) e.g.,lineofcredit,ashewouldpaylessoverall c) lineofcredit:$240.93;creditcard:$249.1710. $216.5911. a) $910 b) 85.3%simpleinterest12. a) $349.48;$17.22 b) 16months;$98.9813. a) 19.4% b) Clint;$25.4814. a) $99.95 d) $1240.34 b) $5602.70 e) $1190.68 c) 1.82% f) $1614.0815. e.g.,Interestrate:Thelowertheratethebetterthecreditoptionifall

otherfactorsareequal.Totalnumberofpayments:Thehigherthenumberoftotalpayments,themoreinterestispaidintotal.Astheinterestraterises,sodoesthetotalnumberofpayments.

16. e.g.,Lineofcreditpaymentsof$330willtake26monthstopayofftheloanof$8000,andthetotalinterestpaidwillbe$384.14.Artgalleryloanpaymentsof$311.05willtake26monthstopayofftheloanof$7500,andthetotalinterestpaidis$402.52.

17. a) bankloan:6months;creditcardA:42monthsor3years6months;creditcardB:30monthsor2years6months

b) 9months c) $594.66


1. a) e.g.,renting:costs(120days):$9000;benefits:cleaningservice,utilities

leasing:costs:$8500;benefits:$1600refundifnodamage b) e.g.,Iwouldrecommendleasing.Evenifthedepositislost,itis

lessexpensive. 2. a) leasing:costs:$23889.60;benefits:e.g.,couldupgradeearlierthan

3years;noneedtoresellequipment purchasing:costs:$28537.60;benefits:e.g.,ownequipment,

whichischeaperforthefourthyearonward b) e.g.,Itwouldbebettertolease,becausethetotalcostofleasingis

lessthanthatofpurchasing.


NEL 601Answers

An

swers

4. e.g.,SheshouldpurchasetheLaser,becauseitischeaper,andkeepitifsheplanstoreturntothecottageinthefuture.Sheshouldsellitwhenshewillnolongergotothecottage


1. a) 6.76% b) $33.75 2. a) 14months b) 25months c) $224.71 3. a) $189.78 b) i) No.e.g.,Hewouldstillsave$68.93usingcardA. ii) Yes.e.g.,Hewouldsave$50.97usingcardB. 4. Bankloan.e.g.,Shewillpay$1.41lessoverall. 5. $1670.00 6. e.g.,Caseyshouldpurchaseasnowplow;itislessexpensivethan

leasingorrentingover2years. 7. Rent.e.g.,Itischeaper.

Cumulative Review, Chapters 1–2, page 140

1. a) $24200,$4200 b) $5896,$396 2. 4years 3. a) $5773.18,$773.18 b) $43536.44,$19536.44 4. B.e.g.,Ithasamorefrequentcompoundingperiodthatearnsmore

interest. 5. estimate:$4000;actual:$3970.31 6. $1330.78 7. a)Emma b) Hans 8. a) $5449.90 b) $449.90 9. $243.2910. OptionB.e.g.,OptionAisworth$28613.14andoptionBisworth

$29245.11.11. a) $1536.33 b) $36.3312. a) $462.67 b) $2760.3713. a) 26months b) 14monthssooner c) $662.1614. a)Misty’sparents:$48000;Danielle’sparents:$86135.48 b) e.g.,Danielle’sparents,becauseiftheyresellthehousetheyshould

makeaprofit.

Chapter 3 – Set Theory and LogicLesson 3.1, page 154

1. a) Yes b) e.g., •C 5 5produce6 •O 5 5orangeproduce6 5 5oranges,carrots6 •Y 5 5yellowproduce6 5 5bananas,pineapples,corn6 •G 5 5greenproduce6 5 5apples,peas,beans6 •B 5 5brownproduce6 5 5potatoes,pears6 c) e.g.,S ( F becauseallfruitsyoucaneatwithoutpeelingare

alsofruits.S ( C becauseallfruitsyoucaneatwithoutpeelingarealsoproduce.

d)SandV,FandV e) Yes.e.g.,C 5 5F andV },soF r 5 V . f ) n 1V 2 5 5 g) oranges,pineapples,bananas,peas,carrots,corn,beans,potatoes 2. a)

b)EandS,FandS c) i) True.e.g.,Multiplesof8arealsomultiplesof4. ii) False.e.g.,Notallmultiplesof4aremultiplesof8. iii) True.e.g.,Allmultiplesof8aremultiplesof8. iv) False.e.g.,F r 5 {allnumbersfrom1to40thatarenot

multiplesof4} v) True.e.g.,Theuniversalsetincludesnaturalnumbersfrom

1to40. 3. a)

b) e.g.,N ( T meansthatallthefishfoundinNunavutarealsofoundintheNorthwestTerritories.T X N meansthatnotallthefishfoundintheNorthwestTerritoriesarefoundinNunavut.

U

E

F

4 12 20

28 36

8 16 24

32 40

1 2 3 5 6 7 9 1011 13 14 15 1819 21 22 23 2526 27 29 30 3133 35 37 38 39

S

17 34

T

inconnu

N

walleye

lake trout

Arctic grayling

northern pike

Arctic char

lake whitefish


NEL602 Answers

4. a)

b)CandS c)Hand D d) Yes.e.g.,Acardcannotbebothaspadeandaclub. e) Yes.e.g.,Youcannotdrawacardthatisaheartandadiamondat

thesametime. f ) Yes.e.g.,n(SorD) 5 26(thereare26cardsthatarespadesor

diamonds) 5 thenumberofcardsthatarespades(13)plusthenumberofcardsthatarediamonds 1132 5 n 1S2 1 n 1D2 .

5. a) e.g.,C 5 {allclothes},S 5 {summerclothes},W 5 {winterclothes},H 5 {summerheadgear}

b)C c)No.e.g.,Síncludesjacket,butWdoesnot. d)S andW,HandW e) e.g.,C 5 {clothes},H 5 5headgear6 5 5cap,sunglasses,toque6, B 5 5clothingforbody6 5 5shirt,shorts,coat,jacket6, F 5 5footwear6 5 5sandals,insulatedboots6 6. 99988 7. notpossible;e.g.,Theremaybesomeelementsthatareinboth

XandY. 8. 76 9. a)S 5 5A,E,F,H,I,K,L,M,N,T,V,W,X,Y,Z6 C 5 5C,O,S6 b) False.e.g.,BisnotinSorC.10. e.g.,

U

W

LA

airplaneshot-air balloons

power boatscanoes

walking bikingskiing drivingbuses horses

U

A♣2♣3♣4♣5♣6♣7♣8♣9♣10♣J♣Q♣K♣

C

A♠2♠3♠4♠5♠6♠7♠8♠9♠10♠J♠Q♠K♠

S

A♥2♥3♥4♥5♥6♥7♥8♥9♥10♥J♥Q♥K♥

H

A♦2♦3♦4♦5♦6♦7♦8♦9♦10♦J♦Q♦K♦

D

RB

11. a)

b)AandB c) i) False.e.g.,1isnotinB. ii) False.e.g.,21isnotinA. iii) False.e.g.,0isinA rbutnotinB. iv) True.e.g.,n 1A2 5 10,n 1B2 5 10 v) True.e.g.,Nointegerfrom220to215isinU.12. a) S 5 54,6,9,10,14,15,21,22,25,26,33,34,35,38,39,46,496 W 5 51,2,3,5,7,8,11,12,13,16,17,18,19,20,23,24,27, 28,29,30,31,32,36,37,40,41,42,43,44,45,47,48,506 b) e.g.,E 5 5evensemiprimenumbers6

E 5 54,6,10,14,22,26,34,38,466 c) 33 d)No.e.g.,Thereisaninfinitenumberofprimenumbers,sothereis

aninfinitenumberofsemiprimenumbers.13. e.g.,

14. e.g.,Agree.Thenumberofelementsinasubsetmustbeequaltoorlessthanthenumberofelementsintheset.

15. a) S 5 5x 021000 # x # 1000,x [ I6 T 5 5t 0 t 5 25x,240 # x # 40,x [ I6 F 5 5 f 0 f 5 50x,220 # x # 20,x [ I6 F ( T ( S b)

16. a)U 5 5HHH,HHT,HTH,THH,HTT,THT,TTH,TTT6 b)E 5 5HTH,HTT,TTH,TTT6 c)n 1U 2 5 8;n 1E 2 5 4 d) Yes.e.g.,

U

0

A

�10 �9 �8 �7 �6�5 �4 �3 �2 �1

1 2 3 4 56 7 8 9 10

B

ST

F

UE

HTH HTTTTH TTT

HHH HHTTHH THT


NEL 603Answers

An

swers

e) e.g.,EísthesetofelementsofUwherethesecondcointurnsupheads;n 1E r2 5 n 1U 2 2 n 1E 2 5 8 2 4 5 4;

E r 5 5HHH,HHT,THH,THT6 f ) Yes.e.g.,Acoincannotshowbothheadsandtailsatthe

sametime.17. a)

b) e.g., N risthesetofallnon-naturalnumbers.W risthesetofallnon-wholenumbers.Iísthesetofnon-integernumbers.Q risthesetofnumbersthatcannotbedescribedasaratiooftwointegers.Q risthesetofnumbersthatcanbedescribedasaratiooftwointegers.

c)NandQ,WandQ,IandQ,QandQ d) Yes.e.g.,Q risthesetofnumbersthatcannotbedescribedasa

ratiooftwointegers,whichisthesetofirrationalnumbers. e)W,I, Q, R f )No.e.g.,TheareaofaregioninaVenndiagramisnotrelatedto

thenumberofelementsintheset.18. a) 8 b) 9 c) 28319. a) e.g.,A ( B ifallelementsofAarealsoinB.Forexample,all

weekdaysarealsodaysoftheweek,soweekdaysisasubsetofdaysoftheweek.

b) e.g.,A rconsistsofalltheelementsintheuniversalsetbutnotinA.Forexample,alldaysoftheweekthatarenotweekdaysareweekenddays.Soweekenddaysisthecomplementofweekdays.

20. e.g.,Disagree;sinceboththesubsetsareempty,theybothcontainthesameelementsandarethereforethesamesubset.


1. a)

b)i) 5 ii) 3 iii) 7 iv) 5 v) 2 vi) 10 vii)5 2. a) 8 b) 11;6 c) 19;14 d) 25 e) 13

RQ–

N

W

Q

I

3. a) 5 b) 24 c)

4. a) 11 b) 14 c) 21 5. a)n 1AandB2 5 2,n 1Aonly2 5 11,n 1Bonly2 5 8 b)


1. a) 5210,28,26,24,22,0,1,2,3,4,5,6,7,8,9,106 b) 16 c) {0,2,4,6,8,10} d) 6 2. a) union 5 {Arcticfox,caribou,ermine,muskox,polarbear,

grizzlybear,baldeagle,Canadianlynx,greywolf,long-earedowl,wolverine}

intersection 5 {grizzlybear} b)

3. a) AcC 5 5210,28,26,24,22,0,2,4,6,8,10,12,14,166; n 1AcC 2 5 14 A d C 5 52,4,6,8,106;n 1A d C 2 5 5 b)


NEL604 Answers

4. a) {half-tons,quarter-tons,vans,SUVs,crossovers,4-doorsedans,2-doorcoupes,sportscars,hybrids}

b) 9 c) {crossovers} 5. a)

b) union 5 5lion,giraffe,hippo,camel,elephant,tiger,takin6 intersection 5 5camel,elephant6 6. a)

b) AcB 5 5212,29,26,24,23,22,0,2,3,4,6,8,9,10, 12,156;n 1AcB2 5 16 A d B 5 526,0,6,126;n 1A d B2 5 4 7. 6;10;5 8. 40 9. 1210. e.g.,ShecoulddrawaVenndiagramshowingthesetofmultiplesof2

andthesetofmultiplesof3.Theintersectionofthesetswouldbethemultiplesof6.

11. a)U 5 5allcustomerssurveyed6,C 5 5customersorderingcoffee6, D 5 5customersorderingdoughnuts6, N 5 5customersorderingneithercoffeenordoughnuts6 b) e.g.,

c) 20

12. 3313. 1014. 1615. 616. No.e.g.,Somestudentstakeabusbutdonotdriveacar.Sothese

regionsshouldonlybepartiallyoverlapping.ThetotalnumberofstudentsinBeyondé’sdiagramisonly43.

17. a)AandB b)AandC c) Yes;BandC;e.g.,CintersectingAandAandBbeingdisjoint

saysnothingabouttheintersection,ifany,ofBandC.18. e.g.,Theunionoftwosetsismoreliketheadditionoftwonumbers

becausealltheelementsofeachsetarecountedtogether,insteadofjustthosepresentinbothsets.

19. a) e.g.,indoor,outdoor,races b) e.g.,U 5 {allsports},I 5 {indoorsports} 5 {badminton,basketball,

curling,figureskating,gymnastics,hockey,indoorsoccer,speedskating,tabletennis,volleyball,wrestling,ArcticSports,DeneGames},O 5 {outdoorsports} 5 {alpineskiing,cross-countryskiing,freestyleskiing,snowshoebiathlon,skibiathlon,dogmushing,snowboarding,snowshoeing,DeneGames},R 5

{races} 5 {speedskating,alpineskiing,cross-countryskiing,biathlon,dogmushing,snowboarding,snowshoeing}

c) e.g.,

d) Yes


1. a)V ( N,M ( N,F ( N,F ( M b) e.g.,N 5 {allfoods},V 5 {fruitsandvegetables},M 5 {meats},

F 5 {fish} c)No.e.g.,PastaisnotpartofMorV. d)VandM,VandF


NEL 605Answers

An

swers

2. a)

b)SandF c) i) False.e.g.,6isinEbutnotinF. ii) True.e.g.,AllelementsinSareinE. iii) False.e.g.,9isnotamultipleof15. iv) True.e.g.,F 5 {15,30} v) True.e.g.,Asetisasubsetofitself. 3. e.g.,

4. a) 17 b) 18 c)

5. a) 4 b) 9 c) 2

U

1 2 4 5 7 8 1011 13 14 16 1719 20 22 23 2526 28 29 31 3234 35 37 38 40

S9 18 27 36

F15 30

E

3 6 2112

24 33 39

6. a) e.g.,TanyadidnotputanyelementsintheintersectionofAandB.

b)

7. 0


1. e.g.,p 5 14,q 5 9,r 5 12 2. a) 32 b) 27 c) 63 d) 7 3. e.g.,StaffcouldlookathowmanyDavidSmithswereonthatbus

routeortheycouldlookatthebooksinthebagandseehowmanyDavidSmithsaretakingcoursesthatusethosebooks.

4. C 5 {contactlenswearers},G 5 {glasseswearers};n 1C d G2 5 51orabout10.8%

5. e.g.,“CanadianRockies,”“skiaccommodations,”“weatherforecast,”“Whistler.”Bycombiningtwoormoreoftheseterms,Jacquescansearchfortheintersectionofwebpagesrelatedtotheseterms.Forexample,“skiaccommodations”and“CanadianRockies”ismorelikelytogivehimusefulinformationforhistripthaneitherofthosetermsonitsown.

6. 7 7. e.g.,

8. a) e.g.,Thedealermightuseexteriorcolour,interiorcolour,oryear. b) e.g.,Thedealermightprioritizethesearchaccordingtooptions

TraviswantsorbydistancefromwhereTravislives. 9. e.g.,Hecountedthestudentswholiketwoofthethreerestaurants

andundercountedthosethatlikeallthree.6310. a) e.g.,Hecansearchforcolleges and (CalgaryorEdmonton). b) “and” c) “or” d) e.g.,colleges and (CalgaryorEdmonton)and “athletics programs”-

university e) e.g.,about1500


NEL606 Answers

f ) e.g.,

11.

12. a) 81 c) 27 e) 45 b) 27 d) 54 f) 1813. a) 36;e.g.,35sitesdealwithboats.21sitesdealwithfishing,

20ofwhichalsodealwithboats,soonly1dealswithjustfishing.

b) e.g.,Becausefishing and boatswillturnupsitesthatdealwithboatsandfishing,butnotjustfishingboats.

c) 1

Set 1:

Set 2:

Set 3:

Set 4:

Set 5:

Set 6:

14. e.g.,No,theydidnotgetthesameresults.ElinorgotallofJames’results,plusothersdealingwitheitherstringorbean,butnotboth.

15. a)andb)e.g.,

c) e.g.,1 5 A\ 1BcCcD2 ;2 5 B\ 1AcCcD2 ; 3 5 C \ 1AcBcD2 ;4 5 D\ 1AcBcC2 ; 5 5 1A d B2 \ 1CcD2 ;6 5 1A d C 2 \ 1BcD2 ; 7 5 1A d D2 \ 1BcC 2 ;8 5 1B d C 2 \ 1AcD2 ; 9 5 1B d D2 \ 1AcC2 ;10 5 1C d D2 \ 1AcB2 ; 11 5 1A d B d C 2 \ D;12 5 1A d B d D2 \C; 13 5 1A d C d D2 \ B;14 5 1B d C dD2 \ A; 15 5 A d B d C d D16. e.g.,LetB 5 {blue},Y 5 {yellow},R 5 {red},andG 5 {green}.

Thereisnoarearepresenting 1B d R2 \ 1GcY2 or 1G d Y 2 \ 1BcR2 .


1. a)p 5 Iamswimmingintheocean;q 5 Iamswimminginsaltwater

b)True c) IfIamswimminginsaltwater,thenIamswimmingintheocean.

False.e.g.,Someswimmingpoolsaresaltwater. 2. a) Yes b) Ifanumberisdivisibleby2,thenitisdivisibleby4;false c) e.g.,Acounterexampleoftheconverseisthenumber2. 3. a) Ifitisanequilateraltriangle,thenithasthreeequalsides. b) Ifithasthreeequalsides,thenitisanequilateraltriangle. c)True;true d) Yes.e.g.,Thestatementanditsconversearebothtrue. 4. a) e.g.,Ifwecannotgetwhatwelike,thenletuslikewhatweget. b)Hypothesis:Wecannotgetwhatwelike.;Conclusion:Letuslike

whatweget.


NEL 607Answers

An

swers

5. a)No b) Ifanumber’sfinaldigitis0,thenitisdivisibleby5. c) Yes.e.g.,

6. a) notbiconditional;e.g.,YoumightliveinMexico. b) biconditional;e.g.,YouliveinthecapitalofCanadaifandonlyif

youliveinOttawa. 7. biconditional;e.g.,

"x2 5 x x is not negative "x2 5 x 1 x is not negative

true true true

true false false

false true true

false false true

8. a) Ifaglassishalf-empty,thenitishalf-full.Aglassishalf-emptyifandonlyiftheglassishalf-full.

b) Ifapolygonisarhombus,thenithasequaloppositeangles.Notbiconditional;e.g.,arectangle.

c) Ifanumberisarepeatingdecimal,itcanbeexpressedasafraction.

Notbiconditional;e.g.,0.3canbeexpressedas3

10,butitisnota

repeatingdecimal. 9. a) IfABandCDareparallel,thenthealternateanglesareequal.Ifthe

alternateanglesareequal,thenABandCDareparallel. b)True.e.g.,SinceABandCDareparallel,tintersectsthematthe

sameangle,andthealternateanglesmustbeequal.Sincethealternateanglesareequal,tmustintersectbothABandCDatthesameangle,soABandCDmustbeparallel.

c)True.e.g.,Boththeconditionalstatementanditsconversearetrue.10. a) Ifyourpetisadog,thenitbarks.Itisnotbiconditional. b) Ifyourpetwagsitstail,thenitisadog.Itisnotbiconditional.11. a)True b)True12. e.g.,Ifanumberappearsinthesamerow,column,orlargesquareas

theshadedsquare,thenitisnotintheshadedsquare.Thenumbersinthecolumnshouldbe,fromtoptobottom:8,3,9,5,6,4,1,7,2.

13. a) i) Ifafigureisasquare,thenithasfourrightangles. ii) Ifafigurehasfourrightangles,thenitisasquare. iii)True;false.e.g.,Arectanglehasfourrightangles. iv) n/a b) i) Ifafigureisarighttriangle,thena2 1 b2 5 c 2. ii) Ifa2 1 b2 5 c 2,thenthefigureisarighttriangle. iii)True;true iv) Afigureisarighttriangleifandonlyifa2 1 b2 5 c 2. c) i) Ifashapeisatrapezoid,thenithastwosidesthatareparallel. ii) Ifashapehastwosidesthatareparallel,thenitisatrapezoid. iii)True;false.e.g.,Aregularhexagonhastwosidesthatareparallel. iv) n/a

ULast digit is 0

Divisible by 5..., 10, 20, 30, ... ..., 5, 15,

25, 35, ...

14. a) i) $1674.56 ii) $836.16 b) 2164;e.g.,Ifyoucanaffordtomakeyourmortgagepayments

morefrequently,thenyouwillsavealotofmoneyoninterest.15. a) e.g.,IfitisDecember,thenitiswinter.Ifanumberiseven,then

itisdivisibleby2. b) e.g.,

c) e.g.,Ifthesetsarethesame(i.e.,thereisoneareaintheVenndiagram),thentheconverseistrue.IftherearetwoormoreareasintheVenndiagram,thentheconverseisfalse.

16. a) e.g.,Ifthefirstletterisaconsonant,thenthesecondletterisavowel.

b)Howwonderfulitisthatnobodyneedwaitasinglemomentbeforestartingtoimprovetheworld.–AnneFrank

17. a) 231 b) $38850

Lesson 3.6, page 214 1. a) converse:Ifyouarelookinginadictionary,thenyouwillfind

successbeforework. inverse:Ifyoudonotfindsuccessbeforework,thenyouarenot

lookinginadictionary. contrapositive:Ifyouarenotlookinginadictionary,thenyouwill

notfindsuccessbeforework. b) converse:Ifyoucandrive,thenyouareover16. inverse:Ifyouarenotover16,thenyoucannotdrive. contrapositive:Ifyoucannotdrive,thenyouarenotover16. c) converse:Ifaquadrilateral’sdiagonalsareperpendicular,thenitis

asquare. inverse:Ifaquadrilateralisnotasquare,thenitsdiagonalsarenot

perpendicular. contrapositive:Ifaquadrilateral’sdiagonalsarenotperpendicular,

thenitisnotasquare. d) converse:If2nisanevennumber,thennisanaturalnumber. inverse:Ifnisnotanaturalnumber,then2nisnotanevennumber. contrapositive:If2nisnotanevennumber,thennisnotanatural

number. 2. a) converse:Ifananimalisagiraffe,thenithasalongneck. contrapositive:Ifananimalisnotagiraffe,thenitdoesnothavea

longneck. b)No.e.g.,Ostricheshavelongnecks.No.e.g.,Llamashavelongnecks. 3. a) converse:Ifapolygonisapentagon,thenithasfivesides. inverse:Ifapolygondoesnothavefivesides,thenitisnota

pentagon. b) Yes.e.g.,Thedefinitionofapentagonisthatithasfivesides. 4. a)Disagree.e.g.,xcouldbe25. b) Yes.e.g.,Ifx 5 5,thenx2 5 25. c) Yes.e.g.,Ifx2isnot25,thenxisnotequalto5. d)No.e.g., 12522 5 25 5. a) i) True ii) IfyouareintheNorthwestTerritories,thenyouareinHay

River;false. iii)IfyouarenotinHayRiver,thenyouarenotintheNorthwest

Territories;false. iv) IfyouarenotintheNorthwestTerritories,thenyouarenotin

HayRiver;true.

M

D

UW E

D


NEL608 Answers

b) i) True ii) Ifapuppyisnotfemale,thenitismale;true iii)Ifapuppyisnotmale,thenitisfemale;true iv) Ifapuppyisfemale,thenitisnotmale;true c) i) True ii) IftheEdmontonEskimoswerenumber1intheWest,then

theywouldhavewoneverygame;false iii)IftheEdmontonEskimosdidnotwineverygamethisseason,

thentheywouldnotbenumber1intheWest;false iv) IftheEdmontonEskimoswerenotnumber1intheWest,

thentheywouldnothavewoneverygame;true d) i) False.e.g.,Thenumbercouldbezero. ii) Ifanintegerispositive,thenitisnotnegative;true iii)Ifanintegerisnegative,thenitisnotpositive;true iv) Ifanintegerisnotpositive,thenitisnegative;false 6.

Conditional Statement

Inverse

Converse

Contrapositive

a) true false false true

b) true true true true

c) true false false true

d) false true true false

7. a)Theyareeitherbothtrueorbothfalse. b)Theyareeitherbothtrueorbothfalse. 8. a) e.g.,noconclusion b) e.g.,noconclusion 9. a) converse:Ifapolygonisaquadrilateral,thenitisasquare. inverse:Ifapolygonisnotasquare,thenitisnotaquadrilateral. contrapositive:Ifapolygonisnotaquadrilateral,thenitisnota

square. b) conditionalstatement:True converse:False;e.g.,trapezoid inverse:False;e.g.,trapezoid contrapositive:True,e.g.,Asquareisaquadrilateral.10. a) converse:Ifthey-interceptis2,thentheequationofthelineis

y 5 5x 1 2. inverse:Iftheequationofthelineisnoty 5 5x 1 2,thenthe

y-interceptisnot2. contrapositive:Ifthey-interceptisnot2,thentheequationofthe

lineisnoty 5 5x 1 2. b) converse:False;e.g.,y 5 x 1 2 inverse:False;e.g.,y 5 x 1 2 contrapositive:True11. e.g.,Itisbiconditional.12. a) i) e.g.,False.Apinwillnotburstahotairballoon. ii) False.e.g.,Apincanburstabubble. iii)False.e.g.,TheMooncouldbeabubble. iv) e.g.,False.TheMooncouldbeahotairballoon. b) i) True ii) True iii)True iv) True c) i) True ii) False;e.g.,3isnotaperfectsquare. iii)False,e.g.,3isnotaperfectsquare. iv) True

d) i) True

ii) False.e.g.,13

cannotbewrittenasadecimal.

iii)False.e.g.,13

cannotbewrittenasadecimal. iv) True e) i) True ii) False.e.g.,y 5 x2

iii)False.e.g.,y 5 x2

iv) True f ) i) False.e.g.,21isnotawholenumber. ii) True iii)True iv) False.e.g.,21isaninteger. g) i) True ii) False.e.g.,Imightbe20. iii)False.e.g.,Imightbe20. iv) True h) i) False.e.g.,SomeCanadiansdonotenjoyhockey. ii) False.e.g.,SomeAmericansenjoyhockey. iii)False.e.g.,SomeAmericansenjoyhockey. iv) False.e.g.,SomeCanadiansdonotenjoyhockey.13. a) e.g.,Thecontrapositiveassumesasitshypothesisthattheoriginal

conclusionisfalse,whichmeansthattheoriginalhypothesismustalsonotbetrue.Iftheoriginalhypothesisisnottrue,thentheconditionalstatementmustbefalse.

b) e.g.,Theinverseofastatementisthecontrapositiveofthestatement’sconverse.

14. a) e.g.,Ifyouaretall,thenyoulikechocolate. contrapositive:Ifyoudonotlikechocolate,thenyouarenottall.

Thisisfalse:Iamtallanddonotlikechocolate. b) e.g.,Ifatrafficlightisgreen,itisnotred. contrapositive:Ifatrafficlightisred,itisnotgreen.Thisistrue:A

trafficlightcannotbetwocolours.15. a) e.g.,IfitisSaturday,thenitistheweekend. inverse:IfitisnotSaturday,thenitisnottheweekend. converse:Ifitistheweekend,thenitisSaturday. b) e.g.,Ifapolygonhassixsides,thenitisahexagon. Inverse:Ifapolygondoesnothavesixsides,thenitisnota

hexagon. converse:Ifapolygonisahexagon,thenithassixsides.


1. e.g.,

U

N

P Louise HalfeRita Mestokosho

Lee Maracle

F

Armand RuffoRichard Van Camp


NEL 609Answers

An

swers

2. a) e.g.,

b) AcB 5 51,2,3,4,5,6,7,8,9,10,11,126; n 1AcB2 5 12;A d C 5 51,2,3,4,5,66;n 1A d C 2 5 6 c) 57,86 d) 513,14,15,16,17,18,19,20,21,22,23,246 3. 8% 4. a) Ifyouwinanelection,thenyougotthemostvotes. inverse:Ifyoudonotwinanelection,thenyoudidnotgetthe

mostvotes. Thestatementisnotbiconditional;e.g.,insomeelectoralsystems,

youneedamajoritytowin. b) IftheplanetisEarth,thenitisthethirdplanetfromtheSun. inverse:IftheplanetisnotEarth,thenitisnotthethirdplanet

fromtheSun. biconditional:TheplanetisEarthifandonlyifitisthethird

planetfromtheSun. c) Ifanumberisbetween1and2,thenitisnotawholenumber. inverse:Ifanumberisnotbetween1and2,thenitisawholenumber. Thestatementisnotbiconditional.e.g.,3.5isnotbetween1and2

andisnotawholenumber. 5. a) i) False.e.g.,TheageofmajorityinBritishColumbiais19. ii) True iii)True iv) False.e.g.,TheageofmajorityinBritishColumbiais19. b) i) False.e.g.,A44-year-oldmayknowhowtodrive. ii) False.e.g.,Youmightbeolder. iii)False.e.g.,Youmightbeolder. iv) False.e.g.,A16-year-oldmayknowhowtodrive.


1. a) e.g.,

b)FandS c)F ( E d)S r 5 {naturalnumbersfrom1to30notdivisibleby3};Itis

differentfromE’,whichisthesetofnaturalnumbersthatarenotmultiplesof2.

e) e.g.,H 5 5multiplesof506

U

C

A 9 10 11 12

13 14 15 16 17 18 19 20 21 22 23 24

1 2

7 8

34 5 6

B

2. a) 8;e.g.,Ofthe19studentswithblackhair,8haveblueeyes. b) 11 c) 0 3. a) AcB 5 5212,211,210,29,28,27,26,25,24, 23,22,21,0,1,2,3,4,5,6,7,8,9,10,11,126; n 1AcB 2 5 25;A d B 5 5212,29,26,23,0,3,6,9,126; n 1A d B 2 5 9 b)

4. 1 5.

6. a) biconditional;xispositiveifandonlyif10x . x. b) notbiconditional;e.g.,YoumightliveinPortHardy. c) biconditional;xyisanoddnumberifandonlyifbothxandyare

oddnumbers. d) notbiconditional;e.g.,Twooddnumbershaveanevensum. 7. a) $443.26 b) 11months 8. a) conditionalstatement:true converse:false,e.g.,Thenumbercouldbezero. inverse:false,e.g.,Thenumbercouldbezero. contrapositive:true b) conditionalstatement:true converse:false,e.g.,Fridaycouldbeaholiday. inverse:false,e.g.,Fridaycouldbeaholiday. contrapositive:true

U

I

�11, �10, �8, �7, �5, �4, �2, �1,1, 2, 4, 5, 7, 8, 10, 11

A�12, �9, �6,�3, 0, 3, 6, 9,

12

Set 1:

Set 2:

Set 3:

Set 4:

Set 5:

Set 6:


NEL610 Answers

Chapter 4 – Counting MethodsLesson 4.1, page 235

1. a)Therearesixoutfitvariations.

khaki black

red red/khaki red/black

blue blue/khaki blue/black

green green/khaki green/black

b)O 5 Numberofdifferentoutfits O 5 1Numberofshirts2 # 1Numberofshorts2 O 5 3 # 2 O 5 6 2. a)

Thereareeightdifferentchoicesofupholsteryandcolour.

b)C 5 Numberofdifferentupholstery-colourchoices C 5 1Numberofupholsteryoptions2 # 1Numberofcolours2 C 5 2 # 4 C 5 8 3. a)No.e.g.,ThepossibilitiesarerelatedbythewordOR. b) Yes.e.g.,Theoutfitconsistsofashirt,atie,ANDshoes. c)No.e.g.,ThepossibilitiesarerelatedbythewordOR. d) Yes.e.g.,Thepossibilitiesincludetypeoftransmission,air

conditioningoption,typeofwindow,ANDGPSoption. 4. a)

b)Therearetwowaystowintheseriesdespitehavingoneloss.

black 6

silverwhite

87

red 5

cloth

Upholstery Colour

black 2

silverwhite

43

red 1

leather

loss

win

loss

win

Game 2 Series Result

2

1

win

loss

loss

loss

win

win

Game 3

win

loss

loss

win

loss

Game 1

win

5. 20 6. 360 7. 120 8. 18 9. a) 59049 b) 1512010. 25611. a) 17576000 b) 926100012. 20000 13. 1968314. 6515. a) 320 b) 416. a) 13824000 b) 12441600017. e.g.,IfmultipletasksarerelatedbyAND,itmeanstheFundamental

CountingPrinciplecanbeusedandthetotalnumberofsolutionsistheproductofthesolutionstoeachtask.Forexample:A4-digitPINinvolveschoosingthe1stdigitANDthe2nddigitANDthe3rddigitANDthe4thdigit.Sothenumberofsolutionsis10 # 10 # 10 # 10 5 10000.ORmeansthesolutionmustmeetatleastoneconditionsoyoumustaddthenumberofsolutionstoeachcondition,andthensubtractthenumberofsolutionsthatmeetmorethanonecondition.Forexample:Calculatingthenumberof4-digitPINsthatstartwith3ORendwith3.ThesolutionisthenumberofPINsthatstartwith3,plusthenumberofPINsthatendwith3,minusthenumberofPINsthatbothstartandendwith3:1000 1 1000 2 100 5 1900.

18. a) i) 8in52or2in13 ii) 26in52or1in2 iii) 16in52or4in13 b)No,e.g.,becausetheFundamentalCountingPrincipleonlyapplies

whentasksarerelatedbythewordAND.19. 3620. 1in102421. 359


1. a) 720 b) 362880 c) 20 d) 8 e) 12 f ) 2520 2. a) 3 # 2 # 1 5 6 b) 3!

3. a) 5! b)9!

6! c)

15!

12! # 4! d)

100!

98! 4. a),c),andd);e.g.,Factorialnotationisonlydefinedfornatural

numbers. 5. a) 40320 c) 28 e) 720 b) 132 d) 42 f ) 33 6. a)n b) 1n 1 42! c)n 1 1 d)n 1n 2 12 1n 2 22 e) 1n 1 52 1n 1 42 f)

11n 2 12

7. 9! 5 362880 8. 5! 5 120 9. 6! 5 72010. 28!orabout3.05 3 1029

11. a)n 5 9 b)n 5 1 c)n 5 9 d)n 5 612. 40320 13. 7!55040,e.g.,Thereare7numbersandeachonecanbeusedonly

once.14. 120


NEL 611Answers

An

swers

18. a) e.g.,TheformulasforbothnPnandnPrhaveanumeratorofn!.

However,theformulafornPnhasadenominatorof1andtheformulafornPrhasadenominatorof 1n 2 r2!.

b) e.g.,Agroupoffriendseachorderadifferentflavouroficecreamfromashopwith12flavours.Howmanypossibilitiesarethereifthegroupis12people?Ifthegroupis7people?

19. a) 311875200 b) 7893600in311875200orabout2.53% c) 154400in311875200orabout0.05%20. e.g.,

n11P2 2 nP151n 1 12!

1n 1 1 2 22! 2n!

1n 2 12! 5

1n 1 12!1n 2 12! 2

n!1n 2 12!

51n 1 12! 2 n!

1n 2 12! 5

n 1 1 # n # n 2 1 # n 2 2... 2 n # n 2 1 # n 2 2...n 2 1 # n 2 2...

5n # n 2 1 # n 2 2... 1n 1 1 2 12

n 2 1 # n 2 2... 5 n 1n2 5 n 2

21. e.g.,nPr115n!

1n 2 1r 1 12 2! 5

n!1n 2 r 2 12!

5n!

1n 2 r 2 12!# n 2 rn 2 r

51n 2 r2n!

1n 2 r2! 5 1n 2 r2 n!

1n 2 r2! 5 1n 2 r2nPr


1. 1620 2. 54756 3. 4 4. 720 5. a) 40320 b) 4320 c) 504 d) 18 6. 362880 7. a) 1n 1 52! c) n 2 4 b) 1n 1 42 1n 1 32 d) 1n 1 22 1n 1 12 8. a)n 5 9 b) n 5 7 9. a) 72 c) 120 b) 19958400 d) 23950080010. a) a:n $ 24,b:n $ 22,c:n $ 5,d:n $ 0 b) a:n $ 2,b:n $ 311. 2790720012. 18213. Agree.e.g.,Thenumberofwaystochooseapresidentandavice-

presidentfromagroupoffivestudentsis5!

15 2 22! 5 20.Icould

alsousetheFundamentalCountingPrinciplebecausetherearefivechoicesforpresidentandfourchoicesremainingforvice-president:5 # 4 5 20.

15. 504016. a) e.g.,YKONU,YUKNO,YKNOU b) 5!,e.g.,Eachlettercanbeusedonlyonce.17. a)n $ 4

b)51,2,3618. 725760


1. a) 20 b) 20160 c) 30240 d) 1 e) 5040 f ) 360360 2. a) e.g.,

President Vice-President

1 Katrina Jess

2 Katrina Nazir

3 Katrina Mohamad

4 Jess Katrina

5 Jess Nazir

6 Jess Mohamad

7 Nazir Jess

8 Nazir Katrina

9 Nazir Mohamad

10 Mohamad Nazir

11 Mohamad Jess

12 Mohamad Katrina

b) 4P2 5 12 3. a) 360 b) 6 4. e.g.,10P8isgreaterthan10P2;therearemorewaystoarrange8ofthe

10objectsthan2ofthe10objects. 5. 504 6. 32760 7. 40320 8. 124925010000 9. 100000000ineachgroup10. a) 95040 b)7920 c)144011. a) n $ 1 b)n $ 22 c)n $ 0 d)n $ 2312. a) 360 b) 1296 c) e.g.,Yes;ifyoureplacethemarble,therearemorepossibilitiesfor

thenextdraw.13. a) 1860480 b) 320000014. a) 5040 b) 496015. a)n 5 5 b)n 5 816. a) r 5 2 b) r 5 3

17. Forn [ N,nPn 5n!

1n 2 n2! 5n!

0!5

n!

15 n!and

nPn21 5n!

1n 2 1n 2 12 2! 5n!

1!5

n!

15 n!.


NEL612 Answers


1.a)Flavour 1 Flavour 2

vanilla strawberry

vanilla chocolate

vanilla butterscotch

strawberry vanilla

strawberry chocolate

strawberry butterscotch

chocolate vanilla

chocolate strawberry

chocolate butterscotch

butterscotch vanilla

butterscotch strawberry

butterscotch chocolate

b)vanilla strawberry

vanilla chocolate

vanilla butterscotch

strawberry chocolate

strawberry butterscotch

chocolate butterscotch

c)Thenumberoftwo-flavourpermutationsisdoublethenumberoftwo-flavourcombinationsbecauseeachtwo-flavourcombinationcanbewrittenintwodifferentways.

2. a) 10 b) 10 c) e.g.,Thenumbersarethesamebecausebychoosing3outof

5peopleforacommittee,youarealsochoosing2outof5peoplenottobeonthecommittee.Therefore,thenumberofwaysofchoosing3outof5isthesameasthenumberofwaysofchoosing2outof5.

3. 924 4. a) 10 c) 15 e) 924 b) 9 d) 1 f ) 8 5. 210 6. 3478761 7. 752538150 8. a) combinations;e.g.,Theorderwithinthestartinglineupisnot

important. b) 3003


1. a) 420 b) 5040 c) 12600 d) 83160 2. 90 3. 20 4. 2450448 5. 1260 6. a) 120 c) 20160 b) 2520 d) 39916800 7. a) 756756 b) 6 8. e.g.,Ashishkabobskewerhas4piecesofbeef,2piecesofgreen

pepper,and1pieceeachofmushroomandonion.Howmanydifferentcombinationsarepossible?

9. a) 126 b) 171610. 128711. a) 560 b) 18012. 5613. a) 5040 b) 126014. e.g.,nPnwillbetoohigh;itgivesthenumberofarrangementsofalln

items,butsomeofthearrangementswillbeidenticalbecauseoftheaidenticalitemsinthegroup.

15. a) 1260ways,assumingeachgroupconsistsofidenticalcoins. b) 35ways,assumingeachgroupconsistsofidenticalcoins.16. 16817. a) 560 b) 10080 18. e.g.,BANDITShas7differentletters,sothenumberofpermutations

is7!BANANASalsohas7letters,butthereare3Asand2Nssoyoumustdivide7!by3! # 2! 5 12.

19. 168020. a) about2.38 3 1015

b) about3.06 3 1011

21. a) 14

b)1

14


1. a) 6b)

Canned Goods

Dry Goods

Fruits and Vegetables

Brian Rachelle Linh

Brian Linh Rachelle

Rachelle Brian Linh

Rachelle Linh Brian

Linh Rachelle Brian

Linh Brian Rachelle

c) 1 d) Partsa)andb)involvepermutationsbecausetheordermatters;

partc)involvescombinationsbecausetheorderdoesnotmatter. 2. e.g.,Ordermattersforthepermutationsbutnotforthe

combinations.Onegroupof4objectsisonecombination,butthe4objectscanbeputin4!=24differentorderstomake24differentpermutations.

3. 210 4. 220


NEL 613Answers

An

swers

b)DividenPr byr!togetnCr.Forexample,6C4 5 15and

6P4 5 360;3604!

5 15

20. a) 65780in13019909orabout0.51% b) 544320in13019909orabout4.18% c) 1in13019909

21. n 3 1 5n

6

22. n11Cr 51n 1 12!

r! 1n 1 1 2 r2!nCr 1 nCr21 5

n!

r! 1n 2 r2! 1n!

1r 2 12! 1n 2 1r 2 12 2!5

n!

r! 1n 2 r2! 1n!

1r 2 12! 1n 2 r 1 12!5

n! 1n 2 r 1 12!r! 1n 2 r2! 1n 2 r 1 12! 1

n!r!r! 1r 2 12! 1n 2 r 1 12!

5n! 1n 2 r 1 12r! 1n 2 r 1 12! 1

r # n!

r! 1n 2 r 1 12!5

n! 1n 2 r 1 1 1 r2r! 1n 2 r 1 12!

5n! 1n 1 12

r! 1n 1 1 2 r2!5

1n 1 12!r! 1n 1 1 2 r2!


1. a) combinations;e.g.,Itdoesn’tmatterwhatorderyouchoosethetoppings.

b) permutations;e.g.,Changingtheorderchangestheroleofeachcandidate.

c) permutations;e.g.,Eachdieisdifferent. d) permutations;e.g.,Changingtheorderchangestheposition

played. 2. SituationA:combinations;e.g.,Orderdoesnotmatter. SituationB:permutations;e.g.,Changingtheorderchangeswho

holdswhichposition. 3. a) 1 b) 56 4. 28561 5. a) 304278004800 b) 320000000000 6. 180 7. 113400 8. 300 9. 24010. 3628800,assumingeveryplayeriswillingtositinanyseat11. a) 60 b) 612. 12500013. 46214. 144144015. 24 16. 2569788

9. a)Agree.e.g.,Icalculatedthevaluesandbothare15. b) Ineachcase,theyareequal.

c) anrb 5 a n

n 2 rb

10. 56011. a) 252 b) 120 c) 6 d) 6 e) 6612. 2772013. a) i) 5objects,3ineachcombination ii) 10objects,2ineachcombination iii) 5objects,3ineachcombination b) e.g.,i)Howmanywayscanyouchoose3coinsfromabag

containingapenny,anickel,adime,aquarter,andaloonie?14. a) i) 1 ii) 1,1 iii) 1,2,1 iv) 1,3,3,1 v) 1,4,6,4,1 b)

c) e.g.,Thenumbersontheleftandrightsidesareall1s;everyothernumberisthesumofthetwonumbersaboveit.

d) 1,5,10,10,5,1;1,6,15,20,15,6,1 e) e.g.,ThenumberineachsquareofPascal’sTriangleisequaltothe

numberofpathwaystoitfromthetopsquare.15. a) n 5 6,n $ 2 b)n 5 7,n $ 4 c)n 5 7orn 5 2,n $ 2 d) r 5 2orr 5 4,0 # r # 616. a) 1 b) 90858767 c) e.g.,No.Evenifeveryoneinthecityplays,itisveryunlikelythat

anyonewillwinsinceeachplayeronlyhasa1in90858767chanceofwinning.

17. ThenumberofdiagonalsisgivenbynC2 2 n.18. a) 2boys,3girls: 17C22 # 113C32 5 6006 3boys,2girls: 17C32 # 113C22 5 2730 4boys,1girl: 17C42 # 113C12 5 455 5boys:7C5 5 21 6006 1 2730 1 455 1 21 5 9212 b) 1boy,4girls: 17C12 # 113C42 5 5005 5girls:13C5 5 1287 20C5 2 5005 2 1287 5 9212 c) e.g.,indirectreasoning;fewercalculationsareneeded.19. a) e.g.,Combinationsandpermutationsbothinvolvechoosing

objectsfromagroup.Forpermutations,ordermatters.Forcombinations,orderdoesnotmatter.Forexample,abcandbacaredifferentpermutations,butthesamecombination.

1

4 1641

1331

121

11


NEL614 Answers

Add the numberof ways each

task can occur

Use Fundamental CountingPrinciple: multiply the number

of ways each task can occur

ORAND

Doesorder

matter?

OD

Lookfor

conditions

Aresome itemsidentical?

Use combinations, nCr

yes

Use permutations, nPr

noyes

no

Divide by r!, where ris the number ofidentical items


1. e.g.,TheFundamentalCountingPrincipleisusedwhenacountingproblemhasdifferenttasksrelatedbythewordAND.Forexample,youcanuseittofigureouthowmanywaysyoucanrolla3withadieanddrawaredcardfromadeckofcards.

2.

3. 1048576 4. a)n 5 3,n $ 0 b)n 5 11,n $ 1 5. 6P6;e.g.,6P6isthenumberofwaystoarrange6differentobjects,

while8!

6!isthenumberofwaystoarrangeonly2of8objects.

6. 479001600 7. 13800 8. a) 11861676288000 b) 19769460480 9. 31187520010. a) 4989600 b) 45360011. a) 2522520 b) 2772012. 11C713. 484514. No.e.g.,Eachcombinationcanbearrangedinmanydifferent

waystomakeapermutation,sotherearemorepermutationsthancombinations.

15. a) 3876 b) 1620 c) 21016. 75675617. 66 18. a) 195955200 b) 3991680019. 844272

tails

heads

tails

heads

Toonie Loonie

tails

heads

tails

heads

tails

heads

tails

heads

tails

Quarter

heads

17. e.g.,

18. 700in1716orabout40.8%19. 7220. 33


1. a) 2028000 b) 1296000 2. 26 3. a) 1n 1 102!,n $ 210

b)1

n 2 2 n,n $ 2

4. a) 120 b) 48 5. a) 126 b) 3024 c)Ordermattersinpartb).e.g.,Eachofthe126groupsoffour

bookscanbeputin4! 5 24differentorders. 6. n 5 9sincen $ 2 7. a) 840 c) 220 b) 1526 d) 1316 8. 30 9. 2880


NEL 615Answers

An

swers

Chapter 5 – ProbabilityLesson 5.1, page 303

1. e.g.,Reversetherulesforplayers1and2oneachturn. 2. a) fair b) notfair;Gina;e.g.,Shehasa6in8chanceofwinning. c) fair 3. No.e.g.,Acertainchanceis100%. 4. No;Player2;e.g.,Player2hasmoreopportunitiestowin.


1. a) 3:5b) 0.625 2. a) 0.3 b) 7:3

3. a) 0.5 b) 1:1c)3:1 d)3

13orabout0.231

4. a) 2:3b)3:2 5. 0.7 6. a) 0.5 b) 1:1 c) e.g.,Theoddsagainstandtheoddsinfavourareboth1:1. 7. 2:3 8. 2:23 9. No.e.g.,Theoddsare1:4,buttheprobabilityis

15

,or20%.10. a) 1:1 b) 1:4 c) e.g.,Jason’sdatareflectshisrecordagainstallgoalies,notjust

Gilles.Gilles’datasuggeststhatheisbetterthanaverageatblockingpenaltyshots.

11. 0.6212. Yes.e.g.,Theprobabilityofawinis3in5(60%),theprobabilityofa

lossis1in5(20%),andtheprobabilityofatieis1in5(20%).Theprobabilitiesaddupto100%.

13. a) 13:7 b)2:314. a) 7:3 b) 29:21 c) 49:21,29:21 d) e.g.,Yes,becauseyourchancesofnotgettingsickaremuchbetter

ifyouarevaccinated. 15. a) touchdown:5:7;fieldgoal:5:1 b) fieldgoal16. a)Eduard:9:11;Julie:7:13;Bill:1:4 b) 11:917. a) e.g.,Yes.Ifhepaysthe$65,hecanreducethe45%chanceof

havingtopaytheadditional$235. b) No.e.g.,Withoddsof17:4,Granthasabouta19%chanceof

failingevenwithoutthepracticeexams,soheshouldprobablynotbuythem.

Yes.e.g.,Withoddsof3:7,hischanceoffailingis70%withoutthepracticeexams,soheshouldbuythem.

18. a) e.g.,Iftheoddsforaneventarem:n,thenP 1A2 5m

m 1 nand

P 1A r2 5n

m 1 n,soP 1A r2 : P 1A2 5

nm 1 n

:

mm 1 n

.Thisratiois

equalton:m.

b) e.g.,Theprobabilityoftheeventhappeningisa

a 1 b.Iftheodds

infavourofraintomorroware2:3,thentheprobabilityis2

2 1 35

25

,or40%.

c) e.g.,Theoddsagainsttheeventhappeningarec 2 a:a.Ifthe

probabilityofwinningthelotteryis1

1000000,theoddsagainst

are999999:1.

19. e.g.,IpreferusingprobabilitybecauseifIexpresstheprobabilityasapercent,ittellsmehowmanytimesoutofahundredIcouldexpecttheeventtooccur.e.g.,Ipreferusingoddsbecauseitcomparesthechancesforandagainsttheeventoccurring.

20. a) 0.149 b) about105:895


1.120

10000or0.012

2.1287

752538150orabout0.00000171

3.1

66orabout0.0152

4. a)1

66orabout0.0152

b)5

11orabout0.455

c)2366

orabout0.348

5. a)1

325orabout0.00308

b)1

338orabout0.00296

6. a)1

126orabout0.0079

b) e.g.,newprobability:1

70orabout0.0143

7. 1:5

8. a)1

2730orabout0.000366 b)

1455

orabout0.0022

9. a)49949990

orabout0.4999

b)99

9990orabout0.00991

c)25009990

orabout0.250

10. 1680:3127

11.1516

or0.9375

12. a)48

120or0.4

b)72

120or0.6

13. a)5

70orabout0.0714

b)1056

orabout0.179

14. a)4

752538150orabout0.00000000532

b)3124550

752538150orabout0.00415

c)45238050

752538150orabout0.0601

8085_Ch01-08_West_ANS.indd 615 2/29/12 5:37 PM

NEL616 Answers


1. a) A 5 {1,1},B 5 {4,4}

U

A B

b)mutuallyexclusive c) 0.125 d) 0.375 2. a)

b)No

c)2252

orabout0.423

3. a)

b)No c) 0.8 4. a)No.e.g.,2isbothanevennumberandaprimenumber. b)Yes.e.g.,Youcannotrollasumof10andasumof7atthesame

time. c)Yes.e.g.,Youcannotwalkandridetoschoolatthesametime.

5. a)144945389045

orabout0.373

b)119920389045

orabout0.308

c)Yes d)264865:124180 6. 12:28or3:7 7. a)28:8or7:2 b)25:11

15.1235

orabout0.343

16.1008040320

or0.25

17.6

35orabout0.171

18. e.g.,Iwouldusepermutationsinaproblemwheretheorderoftheitemswasimportant,andusecombinationsinaproblemwhereorderwasnotimportant.Permutations:Determinetheprobabilitythattwoitemsarenexttoeachotherinalineupofsevendifferentitemsthathasbeenplacedinarandomorder.Combinations:Determinetheprobabilitythat,giveneightbooks,fourofwhichareaboutmath,ifIchoosefiveoftheeightbooks,Ichoosethreemathbooks.

19.60

126orabout0.476

20. 35


1. a) notfair;Ethan;e.g.,Therearemoreproductsthataregreaterthanthesums.

b)fair 2. a)

Sums on Spinners

1 2 3 4 5

1 2 3 4 5 6

2 3 4 5 6 7

3 4 5 6 7 8

4 5 6 7 8 9

b)i) 0.2 ii) 0.15 iii) 0.15 3. a)0.5 b)1:1 c) 3:1

d)4052

orabout0.769

4. 5

28orabout0.179

5. a) slightlylessthan1:1 b) slightlymorethan1:1 c) Yes

6.1

364orabout0.00275

7. a)80

42504orabout0.001882

b)1584

42504orabout0.037267

c)120

42504orabout0.002823

8. about0.0000421

9.90

220orabout0.409


NEL 617Answers

An

swers

6.5674

orabout0.757

7.12

132orabout0.091

8.12.439

orabout0.317

9. 71.5%

10.3070

orabout0.429

11. e.g.,Astudentselectedatrandomgoestoafast-foodoutletthatparticularday.Whatistheprobabilitythatthestudenthadmorethan1hforlunch?

12. e.g., a) Surveyquestionsforagroupofclassmatesoveronemonth

(weekdaysonly):

How often do you cycle to school? 140

How often do you get to school other than by cycling? 60

How often do you cycle when the weather is fine? 80

How often do you cycle when it is raining or snowing? 60

b)Arandomlyselectedstudentcycledtoschoolonaparticularday.Whatistheprobabilitythattheweatherwasfinethatday?

13.58

or0.625

14. 67

orabout0.857

15.29

orabout0.222

16. a)27

orabout0.286

b)27

orabout0.286

17. a)LetX 5 {1stchipisdefective}andY 5 {2ndchipisdefective}.

First Chip Second Chip

P(X) �3

100

P(Y) �2

99

P(Y′) � 9799

P(Y′) � 9699

P(Y) �3

99

P(X′) � 97100

b)582

9900orabout0.0588;e.g.,Multiplytheprobabilityofthe

firstchipbeingdefectivebythatofthesecondchipbeingnon-defective,thenmultiplytheprobabilityofthefirstchipbeingnon-defectivebythatofthesecondchipbeingdefective,andthenaddtheproducts.

8. a) 0.2 b)No 9. a) No.e.g.,OneathletewontwoormoremedalsattheSummerand

WinterOlympics. b) 21:286 c) 68:23910. e.g.,Triciahasaprobabilityof0.3ofcyclingtoschoolonanygiven

day,andaprobabilityof0.2ofgettingaridefromherolderbrother,Steve.Otherwise,shewalkstoschool.Whatistheprobabilitythatshedoesnotwalktoschoolonanygivenday?

11. e.g.,Thereare67Grade10studentsthattakeartand37thattakephotography.Ifthereare84students,howmanytakeboth?

12. a) 14.8% b)17.2%

13. a)8

52orabout0.154

b)3252

orabout0.615

14. a) 53% b)16% c)22%15. 80%16. No17. a) i) 45% ii) 16% iii) 51% b) 44% c) 16%18. e.g.,Todeterminetheprobabilityoftwoeventsthatarenotmutually

exclusive,youmustsubtracttheprobabilityofbotheventsoccurringafteraddingtheprobabilitiesofeachevent.Example:Femalestudentsatahighschoolmayplayhockeyorsoccer.Iftheprobabilityofafemalestudentplayingsocceris62%,theprobabilityofherplayingingoalis4%,andtheprobabilityofhereitherplayingsocceroringoalis64%,thentheprobabilityofherplayingingoalatsocceris62% 1 4% 2 64% 5 2%.

19. 13%20. a)P 1AcBcC 2 5 P 1A2 1 P 1B2 1 P 1C 2 b)P 1AcBcC 2 5

P 1A2 1 P 1B2 1 P 1C 2 2 P 1A d B2 2 P 1A d C 2 2 P 1B d C 2 1

P 1A d B d C 2


1. a) dependent

b)1

12orabout0.0833

2. a) dependent

b)12

204orabout0.0588

3. a) independent

b)1

16or0.0625

4. a) i)30

182orabout0.165

ii)56

182orabout0.308

iii)86

182orabout0.473

b)No

5. a)80

190orabout0.421

b)58

or0.625


NEL618 Answers

6. a)

P(boy) � 0.5

First Child Second Child

P(boy) � 0.5

P(girl) � 0.5

P(girl) � 0.5

P(girl) � 0.5

P(boy) � 0.5

b) 0.25 c) 0.5

7.100

1560orabout0.0641;dependent

8. a)1

36 b)

14

c)2536

9. a) 0.6 b)0.05 c)0.3510. a) e.g.,Spinnerhas6equalareas,numbered1to6. b) e.g.,Spinnerhas10equalareas,numbered1to10.

11. a) No.e.g.,Annehasa1590

orabout0.167probabilityofdrawingtwo

bluemarbles,whileAbbyhasa56

342orabout0.164probabilityof

drawingtwobluemarbles.

b)8272

30780orabout0.269

c) No.e.g.,Annehasa25

100or0.25probabilityofdrawingtwored

marbles,whileAbbyhasa90

380orabout0.237probabilityof

drawingtworedmarbles.12. a) 0.25

b)158400

or0.395

c)242400

or0.605

13. a) 0.0025 b) 0.902514. a) e.g.,Problem:Whatistheprobabilityofdrawingacardfroma

shuffledstandarddeckandgettingaredcard,thenreplacingit,shufflingthedeckagain,drawingasecondcard,andgettinga

heart?Answer:18

or0.125

b) e.g.,Problem:Whatistheprobabilityofdrawingacardfromashuffledstandarddeckandgettingaredcard,thendrawingasecondcardwithoutreplacingthefirstone,andgettingaspade?

Answer:13

102orabout0.127

15. 0.09

18. a)6

22350orabout0.000268

b)2146222350

orabout0.960

c)882

22350orabout0.0395

19. a)0.57 b)0.4320. e.g.,Problem1:OnweekdaysIhavecerealforbreakfast70%ofthe

time.OntheweekendsIhavecerealforbreakfast40%ofthetime.Onarandomday,whatistheprobabilitythatIdonothavecereal?

Answer:2.77

orabout0.386.

Problem2:Idrawwithoutlookingtwocardsfromawellshuffledstandarddeck,drawingthesecondcardwithoutreplacingthefirstone.Ifmysecondcardisaredcard,whatistheprobabilitythatmyfirstcardisblack?

Answer:2651

orabout0.510

21. e.g.,TheprobabilityofeventAandeventBbothoccurringistheprobabilitythatAoccurs,multipliedbytheprobabilitythatBoccursgiventhatAoccurs.Example:Ifa6-sideddieisrolledtwice,P(rollinga4thefirsttimeandgettingatotalgreaterthan7) 5

P(rollinga4thefirsttime) # P(gettingatotalgreaterthan7 0 rollinga

4thefirsttime),or1

125

16

# 12

.

22. a)24

970200orabout0.0000247

b)857280970200

orabout0.884

c)3480

970200orabout0.0036


1. a) independent b) independent c) dependent d) independent 2. a) independent

b)16

orabout0.167

3. a) dependent

b)1

12orabout0.0833

4. a)1

24orabout0.0417

b)1

36orabout0.0278

c)16

2652orabout0.00603

d)1

15orabout0.0667

5. a)No b)Yes


NEL 619Answers

An

swers

12. a) A 5 {facecards},B 5 {spades}

b) notmutuallyexclusive

c)3048

or0.625

13. a) G 5 {probabilityMyawillexerciseonSunday}S 5 {probabilityMyawillshoponSunday}

b) notmutuallyexclusive c) 0.614. e.g.,Suppose6studentscanbothskiandswim.Whatisthe

probabilitythatarandomlyselectedstudentcannotskiorswim? LetW 5 {studentswhoswim}andK 5 {studentswhoski}.

Answer:3

24or0.125

16. a) TheformulaisP 1A d B2 5 P 1A2 # P 1B2 onlywhenAandBareindependentevents.

b) e.g.,Drawingtworedmarblesfromabagcontaining5redand15bluemarbles,withreplacement:A 5 {redon1stdraw}andB 5 {redon2nddraw}areindependentevents,so

P 1A d B2 5 P 1A2 # P 1B2 514

# 14

51

16.

c) e.g.,Drawingtworedmarblesfromabagcontaining5redand15bluemarbles,withoutreplacement:A 5 {redon1stdraw}andB 5 {redon1stdraw}aredependentevents,so

P 1A d B2 5 P 1A2 # P 1B 0 A2 514

# 419

51

19.

17. a) about0.366 b) about0.606 c) about99.9%18. a) about0.179 b) about0.863;assumedthatthechanceofwinninganyofthefour

gameswasequal

19.1632

or0.5;106

1024orabout0.1035


1. Yes.e.g.,Theprobabilitiesofwinningareequal. 2. 0.7 3. 0.06 4. about0.000679 5. 0.2

6.4

104orabout0.0385

7. a)0.49 b)0.09 c)0.42 d)0.91

8.30

552orabout0.0543

9.0.0720.268

orabout0.269


1. a)notfair;e.g.,Camilahasabetterchanceofwinning. b)fair;e.g.,CooperandAlyssahaveanequalchanceofwinning. 2. 0;e.g.,Themaximumtensionis100%. 3. a)3:2 b)2:3 4. 3:7 5. a)2:5 b)5:2 6. No.e.g.,Tocalculatetheodds,itshouldbeoddsagainst:oddsfor,

whichis4:1. 7. secondcourse

8.1

36orabout0.0278

9.36

330orabout0.109

10. a)1

2600orabout0.000385

b)6

17576orabout0.000341

11. a) notmutuallyexclusive;e.g.,Thereareprimenumbersthatarealsooddnumbers.

b) mutuallyexclusive;e.g.,Youcannotrollasumof6andasumof8atthesametime.

c) mutuallyexclusive;e.g.,Youcannoteatapeachandanappleatthesametime.


NEL620 Answers

3. a)

b) 27 c) 14 4. a) e.g.,oddwholenumberslessthan100andevenwholenumbers

lessthan100 b) e.g.,oddwholenumberslessthan100andprimenumbersless

than100 5. 12 6. a) Yes b) Ifanumberislessthanzero,thenitisnegative.Yes.e.g.,All

numberslessthanzeromustbenegative. c) Ifanumberisnotnegative,thenitisnotlessthanzero.Yes.

e.g.,Allnumbersthatarenotnegativeareeitherzeroorpositive,andallofthesenumbersarenotlessthanzero.

d) Ifanumberisnotlessthanzero,thenitisnotnegative.Yes.e.g.,Allnumbersnotlessthanzeroareeitherzeroorpositive,sotheyareallnotnegative.

e) Yes.e.g.,Anumberisnegativeif,andonlyif,itislessthanzero. 7. a)

heads1

tails

Die Coin

heads2

tails

heads3

tails

heads4

tails

heads5

tails

heads6

tails

b) 6outcomesfromrollingadieand2outcomesfromtossingacoin;6 # 2 5 12combinedoutcomes

8. a)1757600 b)1579500 9. a)479001600 c)840 e)126 b)40320 d)15120 f)49510. a)1307674368000 b)2730 c)9111. 856812. a)120 b)40013. n 5 27

15. e.g.,Outof50retailoutlets,19areholdingsalesthismonth.15outletssellonlysustainablymanufactureditems,and6oftheseareholdingsalesthismonth.Whatistheprobabilitythataretailoutletsellssomenon-sustainablymanufactureditemsandishavingasale?

M 5 {outletssellingsustainablymanufactureditems}S 5 {outletshavingsales}

Answer:0.26

16.160306

orabout0.523

17. 0.8

18.400

1560orabout0.256

19.16

orabout0.167

20. Yes.e.g.,P 1A d B2 5 P 1A2 # P 1B2 5 0.5 # 0.6 5 0.321. a)0.42 b)0.28 c)0.12

Cumulative Review, Chapters 3–5, page 373

1. a)e.g.,Manitoba,Québec,PEI,NewBrunswick,NovaScotia b)e.g.,10,20,30,40,50 2. a)

U

A

C

MondayWednesday

TuesdayThursday

Saturday

SundayFriday

B

b)AandB c) i) False;e.g.,AandBaredisjointsets. ii) True;e.g.,CisasubsetofA. iii) True;e.g.,AistheinverseofB. iv) False;e.g.,AincludesC.


NEL 621Answers

An

swers

14. a)2940 b)8001 c)145615. 80016. Yes.e.g.,Bothplayershaveanequalchanceofwinning.17. a) 25:1

b)2526

orabout0.962

18. 0.5

19. a)1

635013559600orabout0.00000000000157

b)1677106640

635013559600orabout0.00264

20. a) e.g.,choosinganappleorapearfromabowloffruit b) e.g.,choosing2bluemarblesfromabagcontaining7blueand

3redmarbles,withoutreplacement c) e.g.,rollingastandarddieandgetting4,tossingacoinandgetting

heads

21. a)3

36orabout0.0833

b)2736

or0.75

c)36

or0.5

d)2

36orabout0.0556

22. a)1016

or0.625 b)38

or0.375

23. a)1

36orabout0.0278

b)12

552orabout0.0217

Chapter 6 – Polynomial FunctionsLesson 6.1, page 383

1. b),c),d) 2.

x-Intercepts y-InterceptEnd Behaviour Domain Range

Number of Turning Points

b) 25, 21 2 QII to QI 5x [ R6 5 y 0 y $ 22.5,y [ R6

1

c) 22, 21, 1 25 QIII to QI 5x [ R6 5 y [ R6 2

d) 0.5 2 QII to QIV 5x [ R6 5 y [ R6 0

3. a)

-3 -2 1 2

2

1

-2

3

-1

-3

-10 3-4

4

5y

-4

-5

4

x

Number of x-Intercepts y-Intercept

End Behaviour Domain Range


1 21 QIII to QI 5x [ R6 5 y [ R6 0

b)

-3 -2 1 2

2

1

3

-1-1

0 3-4

4

5

6

7

8

9

10y

4

x




0 4 QII to QI 5x [ R6 5y 0 y $ 4, y [ R6

1


NEL622 Answers

c)

-3 -2 1 2

4

2

-4

6

-1

-6

-20 3-4

8

10y

-8

-10

4

x




1 3 QII to QIV 5x [ R6 5 y [ R6 0

d)

-3 -2 1 2

2

1

-2

3

-1

-3

-10 3-4

4

5y

-4

-5

4

x




1 0 QIII to QI 5x [ R6 5 y [ R6 0

e)

-6 -4 2 4

4

2

-4

6

-2

-6

-20 6-8

8

10y

-8

-10

8

x




0 23 QIII to QIV 5x [ R6 5 y 0 y 5 23, y [ R6

0

f)

-3 -2

2

1

-2

3

-1

-3

-10-4-5-6-7

4

5y

-4

-5

x




2 27 QIII to QIV 5x [ R6 5 y 0 y # 2, y [ R6 1

4. a) 1x-intercept

x

y

b) 0,1,or2x-intercepts

x

y

x

y

x

y


NEL 623Answers

An

swers

c) 1,2,or3x-intercepts

x

y

x

y

x

y


1. Degree Leading Coefficient Constant

a) 2 6 22

b) 1 2

23

10

c) 3 21 6

d) 3 4 210

2. a) i) minimumx-intercepts:0,maximumx-intercepts:2 ii) endbehaviour:QIItoQI,domain:5x [ R6,

range:5 y [ R 0 y $ minimum6 iii) minimumturningpoints:1,maximumturningpoints:1 b) i) minimumx-intercepts:1,maximumx-intercepts:1 ii) endbehaviour:QIItoQIV,domain:5x [ R6,

range:5 y [ R6 iii) minimumturningpoints:0,maximumturningpoints:0 c) i) minimumx-intercepts:1,maximumx-intercepts:3 ii) endbehaviour:QIItoQIV,domain:5x [ R6,

range:5 y [ R6 iii) minimumturningpoints:0,maximumturningpoints:2 d) i) minimumx-intercepts:1,maximumx-intercepts:3 ii) endbehaviour:QIIItoQI,domain:5x [ R6,range:5 y [ R6 iii) minimumturningpoints:0,maximumturningpoints:2

3. Degree Sign of Leading Coefficient Constant Term

a) 2 2 2

b) 1 1 2

c) 3 1 21

d) 3 2 6

4. a) e.g.,y 5 5 b) e.g.,y 5 3x 1 5 c) e.g.,y 5 4x2 1 3x 1 5 d) e.g.,y 5 25x3 1 x2 2 x 1 5

5. a)QIIItoQI c)QIItoQI e)QIItoQIV b)QIIItoQIV d)QIItoQIV f)QIIItoQI 6. a)v) b) i) c) ii) d) vi) e) iii) f) iv) 7.




a) 1 5 QII to QIV 5x [ R6 5 y [ R6 0

b) 0, 1, or 2 26 QII to QI 5x [ R6 5 y 0 y $

minimum,y [ R6

1

c) 1, 2, or 3 21 QIII to QI 5x [ R6 5 y [ R6 0 or 2

d) 1, 2, or 3 0 QII to QIV 5x [ R6 5 y [ R6 0 or 2

8. a)e.g.,y 5 2x2 1 2 b)e.g.,y 5 x3 1 2x2 2 x 2 2 c)e.g.,y 5 x 2 3 d)e.g.,y 5 x3 1 2x2 2 x 1 5 e)e.g.,y 5 2x2 1 2 9. e.g.,Lukasmadeanerrorwhenhestated,“Thereisnoconstantterm,

sothereisnoy-intercept.”Sincethereisnoconstantterm,thereisay-interceptaty 5 0.

10. a) e.g.,

-3 -2 1 2

-2

-1

-3

-10 3-4

y

-4

-5

-6

-7

-8

-9

-10

4

x

b) e.g.,

-4 2 4

4

2

-4

-2

-6

-20

y

-8

-10

x

c) e.g.,

2 4

4

2

6

0 6

8

10y

x

8 10


NEL624 Answers

d) e.g.,

-4 2 4

4

2

-4

6

-2

-6

-20

8

10y

-8

-10

x

11. e.g.,Acubicfunctionmayhavezeroortwoturningpoints.Iftherearenoturningpoints,thefunctionhasonlyonex-intercept.Iftherearetwoturningpoints,thefunctionmayhaveone,twoorthreex-intercepts,dependingonthevaluesofa,b,c,anddinthefunctiony 5 ax3 1 bx2 1 cx 1 d(seefiguresshown).

x

y

x

y

x

y

12. e.g.,Cubicfunctionsmayhaveturningpoints,buttheydonothaveanymaximumsorminimums.Quadraticfunctionshaveoneturningpoint.Thepointatwhichtheyturn(thevertex)definesthefunction’smaximumorminimum.

13. a) i) b) iii) c) iv) d) ii) 14. a) Thedegreeis3,soitisacubicfunction.Theleadingcoefficient

ispositive,sothefunctionisincreasingfromlefttoright.ThegraphextendsfromquadrantIIItoquadrantI.Ithasay-interceptof25.720andmayhave1,2,or3x-intercepts.

b) thepriceofgasin197915. a) 4.243m;Itisveryclose. b) extendsfromQIIItoQI c) No.e.g.,thetidesrepeateveryday,asshowninthetablefor

Jan.10,butacubicfunctionwillcontinuetoincrease.16. e.g.,Askforthedegreeofthefunctiontodeterminetheend

behaviour.Askforthevalueoftheleadingcoefficienttodeterminewhichquadrantstheendbehaviourextendstoandwhetherthefunctionisincreasingordecreasingfromlefttoright.Askforthenumberofx-interceptstodeterminehowmanytimesthefunctioncrossesthex-axis.Thesequestionswillenableyoutodrawaroughsketchofthegraphanddetermineaplausibleequation.

17. a) i) 10.85,3.082 , 13.15,23.082 ii) 10.31,12.602 , 14.36,220.752 iii) 121.27,10.392 , 124.73,210.392 b) i)

-4 2 4

4

2

-4

-2-2

0

y

x

ii)

-8 4 8

10

5

-10

15

-4

-15

-50

20y

-20

x

iii)

-4 2 4

10

5

-10

15

-2-8 -6-10

-15

-50

20y

-20

x

c) e.g.,Thex-coordinateoccursapproximatelyatthemidpointbetweenthex-intercepts.Oncethismidpointisfound,substitutethisx-valueintotheequationtodeterminethey-coordinate.e.g.,iii)thex-interceptsare26,23,and0.Themidpointbetween26and23is24.5;findthey-valuewhenxis24.5.Themidpointbetween23and0is21.5;findthey-valuewhenxis21.5.

18. a) e.g.,P 102 5 0,P 10.52 5 0.375,P 112 5 0;Thefunctionseemsreasonable.

b)D:5x 0 0 # x # 1,x [ R6;R: e y 0 y #49

,y [ R f

c) a23

,49b ;e.g.,Atthispoint,theprobabilityofsinkingtwooutof

threefreethrowsbeginstodecrease. d) x 5 0,1;e.g.,Theprobabilityofsinkingtwooutofthreefree

throwsiszeroiftheprobabilityofsinkingonethrowis0.Theprobabilityofsinkingexactlytwooutofthreefreethrowsis0iftheprobabilityofsinkingonethrowis1.(Thatis,iftheprobabilityofsinkingafreethrowis1,youarecertaintomakeallshots,soyouwouldsink3outof3.)

y

x

2 turning points, 1 x-intercept

2 turning points, 2 x-intercepts

2 turning points, 3 x-intercepts

0 turning points, 1 x-intercept


NEL 625Answers

An

swers


1. a),c),d)2. Degree Domain Range Constant

a) 2 5x [ R6 5 y 0 y # 6, y [ R6 5

c) 0 5x [ R6 5 y 0 y 5 4, y [ R6 4

d) 3 5x [ R6 5 y [ R6 –2

b) i) d) ii) c) iii) a)

3. a)QIItoQIV b) QIIItoQI c) QIIItoQI d) QIIItoQIV 4. a)

Degree x-Intercepts y-InterceptEnd Behaviour Domain Range


i) 3 5 4 QII to QIV 5x [ R6 5 y [ R6 2

ii)2 21.5, 2 26 QII to QI 5x [ R6 5 y 0 y $ 26.25,

y [ R61

iii) 1 6.5 2 QII to QIV 5x [ R6 5 y [ R6 0

iv) 3 21, 3 9 QIII to QI 5x [ R6 5 y [ R6 2

b) i) leadingcoefficient:2,constant:4 ii) leadingcoefficient:1,constant:26 iii) leadingcoefficient:2,constant:2 iv) leadingcoefficient:1,constant:9 5.




a) 0, 1, or 2 6 QIII to QIV 5x [ R6 5 y 0 y # maximum,y [ R6

0

b) 1, 2, or 3 6 QIII to QI 5x [ R6 5 y [ R6 1

c) 0, 1, or 2 21 QII to QI 5x [ R6 5 y 0 y $ minimum,y [ R6

0 or 2

d) 1, 2, or 3 0 QIII to QI 5x [ R6 5 y [ R6 0 or 2

6. a) e.g.,y 5 1x 1 1.587423 2 x 2 4 b) e.g.,y 5 1x 2 32 1x 1 42 c) e.g.,y 5 2x 2 3 d) e.g.,y 5 1.5 1x 2 222 e) e.g.,y 5 1.5 1x 2 422 2 6


1. a) e.g.,slope:21,y-intercept:7.5 b) e.g.,slope:0.1,y-intercept:3 2. a) e.g.,y 5 2x 1 7.5 b) e.g.,y 5 0.1x 1 2

3. Independent Dependent

a) speed distance

b) size of family number of cellphones

c) time of day number of people

d) time of year hours of daylight

4. a) e.g.,Thelineofbestfithasanegativeslopeandhasaboutthesamenumberofpointsaboveandbelowit.Thepointsareveryclosetothelineofbestfit,soitshouldgiveastrongrepresentationofthedata.

b) e.g.,about75;interpolation,becausethepointisbetweenknownvalues

c) e.g.,about52;interpolation,becausethepointisbetweenknownvalues

d) e.g.,about105;extrapolation,becausethepointisoutsideknownvalues

5. a)

40 8

240

230

220

250

Tim

e (s

)

12Years after 1980

260

270

280

16 20 24 28

Women’s 3000 mSpeed Skating

y

x

b)Astheyearsincrease,theworld-recordtimesdecrease. c) y 5 21.147...x 1 264.178...(whereyistimeinsecondsandxis

theyear);Thesloperepresentstherateatwhichtheworld-recordtimedecreaseseachyear,inseconds;they-interceptrepresentstheworld-recordtimein1980(year0).

d) e.g.,235.489...sor3:55.49min e) 3:55.75min;Myestimatewasveryclose. 6. a)

100 20

9.75

9.65

9.55

9.85

Tim

e (s

)

30Years after 1960

9.95

10.05

40 50 60

Men’s 100 m Sprinty

x

b)Astheyearsincrease,theworld-recordtimesdecrease. c) y 5 20.006...x 1 10.032...;Thesloperepresentstherateat

whichtheworld-recordtimeinsecondsdecreaseseachyear;they-interceptrepresentstheworld-recordtimein1960(year0).

d) e.g.,9.75s e) 9.74s;Myestimatewasveryclose. 7. a) e.g.,Aslatitudeincreases(i.e.,yougofurthernorth),themean

temperatureswoulddecrease.Myplotverifiesthatmypredictioniscorrect.

b) y 5 20.637...x 1 49.730... c) 16.6° C d) 49.8° N


NEL626 Answers

8. a)Asfamilysizeincreases,thenumberofcellphonesincreases. b)

1 2

2

1

0

3

Cel

lpho

nes

3Family size

4

5

6

4 5 6 7 8

Family Size vs.Number of Cellphones

y

x

y 5 0.614...x 2 0.260... c) e.g.,1.58cellphones;Iwouldexpectafamilyof3tohave

2cellphones. 9. 2events,toensurehedoesn’tgooverbudget10. 109bikes11. a)

10 20

20

10

0

30

Life

exp

ecta

ncy

(yea

rs)

30Years after 1920–1922

40

50

60

70

80

90

40 50 60 70 80 90

Life Expectancy of Malesy

x

10 20

20

10

0

30

Life

exp

ecta

ncy

(yea

rs)

30Years after 1920–1922

40

50

60

70

80

90

40 50 60 70 80 90

Life Expectancy of Femalesy

x

b) males:y 5 0.23x 1 58.466...;females:y 5 0.286...x 1 60.977...

c)males:79years;females:87years

12.

0.2 0.4

8

4

0

12

Num

ber o

f tou

rs

0.6Value of the dollar ($US)

16

0.8 1.0 1.2

Dollar Value vs.Number of Tours

y

x

y 5 224.879...x 1 33.314... e.g.,Usingextrapolation,theexpectednumberoftoursis8.There

isastronglinearrelationshipbetweenthevalueofthedollarandthenumberoftours.

13. a) e.g.,Createascatterplotofthedataandperformalinearregression.Inserttheknownindependentvalueforxandsolvefory.Iftheregressionyieldsy 5 0.5x 1 2,andyouwanttoestimatethevalueofthedependentvariablewhentheindependentvariableis4,input4forxandsolvefory;thisgivesusay-valueof4.

b) e.g.,Fromthelinearregression,substitutetheknownvalueofthedependentvariablefory,andsolveforx(theindependentvariable).

14. a) y 5 2.445...x 2 23.118... b) 210.9boardfeet;e.g.,Thisanswerdoesnotmakesense,because

areacannotbenegative.Extrapolatingdoesnotalwaysmakesense,becausethetrenddoesnotalwayscontinueoutsidethegivendatarange.

c) e.g.,Basedonthescatterplot,thedatadoesnotseemtobelinear. d) e.g.,Quadraticregressionmaybebetterbecausethedatafita

quadraticfunction.


1. a) e.g.,Thenumberofbirthsincreasesfrom1947toabout1960;afterthatitdecreasesataboutthesamerateuntil1971.

b) about1960 c) about425000 d) between1953and1965 2. a) 149bpm b) about244W 3. a) Theballrisestoamaximumheightatabout3sandthenitsheight

decreases. b) y 5 210.071...x2 1 51.408...x 1 11 c) i) 11m ii) 76.6m iii) 38.4m d) about5.3s 4. a),b)

1 2

400

200

0

600

Volu

me

(cm

3 )

3Time (s)

800

1000

4 5

Balloon Volume

y 5 4.189...x3 1 25.130...x2 1 50.267x 1 33.510...

y

x

e.g.,Astimeincreases,volumeincreasesatafasterrate. c) 8181.47cm3


NEL 627Answers

An

swers

5. a) 4.0° C b) 1006.55cm3

6. 1.41m 7. a) e.g.,2yearsafter1977,fertilityrateisabout3.42per1000females;

7yearsafter1977,fertilityrateisabout3.43per1000females b) e.g.,Thevaluewhenx 5 2isclose;thevaluewhenx 5 7isnotas

close. 8. a)

10 20

100

50

0

150

Volu

me

(L)

30Time (min)

200

250

40 50

Hot-water TankVolume

V

t

e.g.,Astimeincreases,thevolumedecreases. b) V 5 0.064...t 2 2 7.650...t 1 224.885... c) 17.2min d) 56.2min 9. a) y 5 0.004 ... x3 2 0.294 ... x

2 1 4.548 ... x 1 74.659 ... ; 65.342... b) Never.Theminimumof65.3per100000isreachedbetween

2009and2010.10. a)

10 20

200

100

0

300y

30x

400

500

40 50 60

x versus yy

x

b) y 5 0.010...x3 2 0.557...x2 1 11.078...x 1 1.409... c) 87.7;theresultfromtheregressionequationisoffby4.7.11. a) e.g.,Linear:y 5 115.83x 1 6999.96for0 # x # 9,Quadratic:

y 5 29.783...x2 1 311.404...x 1 6023.16for10 # x # 22,Linear:y 5 2115.917x 1 10689.9for23 # x # 30

b) e.g.,about14s


1. a) i) e.g.,y 5 2x 1 3 ii) e.g.,y 5 14x 2 6 b) i) e.g.,y 5 2x3 1 3 ii) e.g.,y 5 x3 2 6 2.

Possible Number of x-Intercepts y-Intercept


Possible Number of Turning Points

a) 0, 1, or 2 21 QIII to QIV 5x [ R6 5 y 0 y # 3, y [ R6 1

b) 1 1.5 QIII to QI 5x [ R6 5 y [ R6 0

c) 1, 2, or 3 242 QIII to QI 5x [ R6 5 y [ R6 0 or 2

d) 1, 2, or 3 2 QII to QIV 5x [ R6 5 y [ R6 0 or 2

3. a) e.g.,y 5 2x3 1 2x 2 6 b) e.g.,y 5 2x2 1 2x 1 8 4.

5. e.g.,Thelineofbestfitwouldhaveanegativeslopeofabout21andaboutthesamenumberofpointsaboveandbelowtheline.They-interceptwouldbeabout125.

6. a)

10 20

20

10

0

30

Dis

tanc

e (k

m)

30Time (min)

40

40 50

Distance vs. Timey

x

b) y 5 0.844...x 2 0.308... c) i) about30min ii) about38km iii) about50.6km/h 7. a)

1 2

40

20

0

60

Surf

ace

area

(m2 )

3Time (min)

80

100

120

4 5

Balloon Surface AreaA

t

b) A 5 3.214...t 2 1 12.242...t 1 12.828... c) e.g.,interpolate:at1.5min,surfaceareawouldbeabout38.4m2;

extrapolate:at5min,surfaceareawouldbeabout154.4m2


1. a),d),ande) 2.

Number of x-Intercepts y-Intercept Domain Range


b) 1, 2, or 3 24 5x [ R6 5 y [ R6 0 or 2

c) 0, 1, or 2 232 5x [ R6 5 y 0 y # 0, y [ R6 1

3. y-Intercept End Behaviour Domain Range

a) –1 QIII to QIV 5x [ R6 5 y 0 y # maximum, y [ R6

b) 5 QIII to QI 5x [ R6 5 y [ R6c) 0 QII to QI 5x [ R6 5 y 0 y $ 29, y [ R6d) 5 QIII to QI 5x [ R6 5 y [ R6




a) 0 12 QII to QI 5x [ R6 5 y 0 y $ 4, y [ R6

1

b) 1 21 QII to QIV 5x [ R6 5 y [ R6 0


NEL628 Answers

4.




a) 0 24.5 QIII to QIV 5x [ R6 5 y 0 y # 24,

y [ R61

b) 3 0 QIII to QI 5x [ R6 5 y [ R6 2

5. a) e.g.,slope:15

,y-intercept:0.5

b) e.g.,slope:22,y-intercept:6 6. a)

20 40

80

40

0

120

Cos

t ($

)

60Distance (km)

160

200

80 100

Cost of Taxi Ridey

x

Asthedistanceincreases,thecostincreasesinalinearrelationship.

b) y 5 1.711...x 1 4.956... c) i) $90.51 ii) $4.96 7. a) 22m b) 1.06s 8. a)

2 4

100 000

50 000

0

150 000

Num

ber o

f mal

es

6Years after 1990

200 000

250 000

8 10 12

Males in Trade Programy

x

b) y 5 1471.495...x 2 2 16363.017...x 1 198121.986...

c) Years After 1990 Number of Males

2 171 280

4 156 210

6 152 912

8 161 386

10 181 631

12 213 649

9. a) y 5 7.062...x3 2 77.357...x2 1 1069.99x 1 7208.23 b) 200110. a) y 5 25x2 1 20 b) about1.4s

Chapter 7 – Exponential and Logarithmic FunctionsLesson 7.1, page 439

1. a)No.linear d) No.cubic b) Yes e) Yes c)No.quadratic f) No.quadratic 2. b) nox-intercept,y-intercept:y 5 1,endbehaviour:extendsfrom

QIItoQI,domain:5x|x [ R6,range:5 y|y . 0,y [ R6 f)nox-intercept,y-intercept:y 5 1,endbehaviour:extendsfrom

QIItoQI,domain:5x|x [ R6,range:5 y|y . 0,y [ R63. a)

12

10

4

6

8

14

2

16

18

20y

-6 -4 2 4-2 0 6-8 8

x

b)

-6 -4 2 4

4

2

-2

6

-2 0 6-8

8y

8

x

c)

30

25

10

15

20

35

5

40y

-6 -4 2 4-2 0 6-8 8

x

d)

-6 -4 2 4

4

2

-2

6

-2 0 6-8

8y

8

x


NEL 629Answers

An

swers

Exponential Function y 5 10 122x y 5 6 122x y 5 27a13b

x y 5 4a1

2b

x

Number of x-Intercepts 0 0 0 0

y-Intercept y 5 10 y 5 6 y 5 27 y 5 4

End Behaviour extends from QII to QI extends from QII to QI extends from QII to QI extends from QII to QI

Domain 5x | x [ R6 5x | x [ R6 5x | x [ R6 5x | x [ R6Range 5 y | y . 0, y [ R6 5 y | y . 0, y [ R6 5 y | y . 0, y [ R6 5 y | y . 0, y [ R6


1. a) Yes.Foreachunitincreaseinx,thevalueofydoubles. b)Yes.Foreachunitincreaseinx,thevalueofyisdividedby4.

2.Number of x-Intercepts y-Intercept Domain Range

End Behaviour

a) 0 4 5x | x [ R6 5 y | y . 0,y [ R6

QII to QI

b) 0 2 5x | x [ R6 5 y | y . 0,y [ R6

QII to QI

c) 0 7 5x | x [ R6 5 y | y . 0,y [ R6

QII to QI

d) 0 3 5x | x [ R6 5 y | y . 0,y [ R6

QII to QI

3. e.g.,Increasingexponentialfunctionsincreaseasxincreases,whereasdecreasingexponentialfunctionsdecreaseasxincreases.

30

25

10

15

20

35

5

40y

-6 -4 2 4-2 0 6-8 8

x

Increasing

30

25

10

15

20

35

5

40y

-6 -4 2 4-2 0 6-8 8

x

Decreasing

4. a) 5,increasing c) 10,increasing b) 2,decreasing d) 1,decreasing

5. a) i) Yes.y 5 2x;ydoublesasxincreasesby1 ii)1,increasing b) i) No.yincreasesby2asxincreasesby1 ii)3,increasing

c)i) Yes.y 5 64 a14b

x;ydecreasesby

14

asxincreasesby1

ii)64,decreasing d)i) No.e.g.,ydecreases,thenincreases,thendecreasesagain ii)1,both

6.Number of x-Intercepts y-Intercept


a) 0 3 QII to QI 5x | x [ R6 5 y | y . 0,y [ R6

b) 0 4 QII to QI 5x | x [ R6 5 y | y . 0,y [ R6

c) 0 2 QII to QI 5x | x [ R6 5 y | y . 0,y [ R6

d) 0 3.5 QII to QI 5x | x [ R6 5 y | y . 0,y [ R6

e) 0 25 QII to QI 5x | x [ R6 5 y | y . 0,y [ R6

f) 0 12 QII to QI 5x | x [ R6 5 y | y . 0,y [ R6

a)

12

10

4

6

8

14

2

16

18

20y

-6 -4 2 4-2 0 6-8 8

x

b)

-6 -4 2 4

4

2

-2

6

-2 0 6-8

8y

8

x


NEL630 Answers

c)

-6 -4 2 4

4

2

-2

6

-2 0 6-8

8y

8

x

d)

12

10

4

6

8

14

2

16

18

20y

-6 -4 2 4-2 0 6-8 8

x

e)

30

25

10

15

20

35

5

40y

-6 -4 2 4-2 0 6-8 8

x

f)

-6 -4 2 4

8

4

12

-2 0 6-8

16y

8

x

7. a) e.g.,Sincethebaseisgreaterthan1,thefunctionisincreasing. b)e.g.,Sincethebaseisbetween0and1,thefunctionisdecreasing. c) e.g.,Sincethebaseisgreaterthan1,thefunctionisincreasing.



a) 0 4 QII to QI 5x | x [ R6 5 y | y . 0,y [ R6

b) 0 8 QII to QI 5x | x [ R6 5 y | y . 0,y [ R6

c) 0 3 QII to QI 5x | x [ R6 5 y | y . 0,y [ R6

d) 0 10 QII to QI 5x | x [ R6 5 y | y . 0,y [ R6

e) 0 30 QII to QI 5x | x [ R6 5 y | y . 0,y [ R6

f) 0 1 QII to QI 5x | x [ R6 5 y | y . 0,y [ R6

g) 0 3 QII to QI 5x | x [ R6 5 y | y . 0,y [ R6

h) 0 45 QII to QI 5x | x [ R6 5 y | y . 0,y [ R6

9. a) Yes.a . 0and0 , b , 1 b)No.a . 0andb . 1 c)Yes.a . 0and0 , b , 1 d)No.a . 0andb . 110. a) increasing

12

10

4

6

8

14

2

16

18

20y

-6 -4 2 4-2 0 6-8 8

x

b)decreasing

30

25

10

15

20

35

5

40y

-6 -4 2 4-2 0 6-8 8

x


NEL 631Answers

An

swers

c)increasing

-6 -4 2 4

4

2

-2

6

-2 0 6-8

8y

8

x

d)decreasing

-6 -4 2 4

8

4

12

-2 0 6-8

16y

8

x

11. a) increasing;iii) c) decreasing;ii) b) decreasing;i) d) increasing;iv)12.

Function y-Inter cept Base Domain Range

Increasing or Decreasing

a) y 5 9 172x 9 7 5x | x [ R6 5 y | y . 0,y [ R6

increasing

b) y 5 7 142x 7 4 5x | x [ R6 5 y | y . 0,y [ R6

increasing

c)y 5 6a1

7b

x 6 17

5x | x [ R6 5 y | y . 0,y [ R6

decreasing

d) y 5 2 10.352x 2 0.35 5x | x [ R6 5 y | y . 0,y [ R6

decreasing

e) y 5 2 1e2x 2 e 5x | x [ R6 5 y | y . 0,y [ R6

increasing

a)

12

10

4

6

8

14

2

16

18

20y

-6 -4 2 4-2 0 6-8 8

x

b)

-6 -4 2 4

4

2

-2

6

-2 0 6-8

8y

8

x

c)

-6 -4 2 4

4

2

-2

6

-2 0 6-8

8y

8

x

d)

12

10

4

6

8

14

2

16

18

20y

-6 -4 2 4-2 0 6-8 8

x

e)

-6 -4 2 4

4

2

-2

6

-2 0 6-8

8y

8

x

13. a) i) range:5 y|y . 0,y [ R6,a 5 2,b 5 0.5;decreases ii) range:5 y|y . 0,y [ R6,a 5 1,b 5 3;increases iii) range:5 y|y . 0,y [ R6,a 5 3,b 5 0.5;decreases iv) range:5 y|y . 0,y [ R6,a 5 2,b 5 4;increases b) i) B.e.g.,Theiry-interceptsmatch. ii) D.e.g.,Theiry-interceptsmatch. iii) A.e.g.,Theiry-interceptsmatch. iv) C.e.g.,Theiry-interceptsmatch.

14. a) e.g.,increasing:y 5 5 122 x,decreasing:y 5 5a14b

x

b)e.g.,Same:numberofx-intercepts,y-intercepts,endbehaviour,domain,andrange

Different:rateofchange(increasingvs.decreasingfunction)15. Yes.e.g.,Allexponentialfunctionsareoftheform f 1x2 5 a 1b2 x.16.

f 1x2 5 ax 1 b f 1x2 5 a 1b2xNumber of x-Intercepts

1 0

y-Intercept b a

End Behaviour QIII to QI OR QII to QIV QII to QI

Domain 5x | x [ R6 5x | x [ R6Range 5 y | y [ R6 5y 0 y . 0, y [ R6Increasing or Decreasing

either increasing (a . 0) or decreasing (a , 0)

either increasing (b . 1) or decreasing (0 , b , 1)


NEL632 Answers

17. Thenumberofx-intercepts,theendbehaviour,thedomain,andtherangearecommontoallexponentialfunctions.They-interceptandwhetherthefunctionincreasesordecreasesisuniquetothefunction.

18. a) studentA:y-intercept:80,domain:5x|x . 0,x [ R6,range:5 y|0 , y , 80,y [ R6

studentB:y-intercept:100,domain:5x|x . 0,x [ R6,range:5 y|0 , y , 100,y [ R6

b)e.g.,Concentrationofcaffeineinbloodnaturallydecreasesovertimeasthekidneysfilteritfromthebloodintotheurine.

c)StudentBconsumedmorecaffeine.StudentBprocessedthecaffeinemorequickly.

d)studentA:20mg,studentB:20mg e)Itdescribestheinitialamountofcaffeineconsumed.Theyare

differentbecausetheenergydrinkscouldcontaindifferentamountsofcaffeine.

19. a) Hour Students Who Are Told

0 3

1 6

2 12

3 24

4 48

5 96

b) Yes.e.g.,Aftereachhour,thenumberofstudentswhoaretoldinthathouraboutthepresentationdoubles.

c) y 5 3 122 x;domain:5x|x $ 0,x [ W6,range:5 y|y $ 3,y [ W6

d)

12

10

4

6

8

14

2

16

18

20y

-6 -4 2 4-2 0 6-8 8

x

;768students

20. a) Yes.e.g.,Anydatawithaconstantdoublingtimecanbeexpressedwithanexponentialfunction.

b)y 5 122 x3;a representstheinitialnumberofrequests,b representsthe

rateofgrowthofthenumberofrequests,x representstheamountoftimeinhourssincethenewsbroke,yrepresentsthetotalnumberofinterviewrequests.

c)domain:5x|x $ 0,x [ W6,range:5 y|y $ 4,y [ W6

d)Time x y

9:00 a.m. 0 4.0

10:00 a.m. 1 5.0

11:00 a.m. 2 6.4

12:00 p.m. 3 8.0

1:00 p.m. 4 10.1

2:00 p.m. 5 12.7

3:00 p.m. 6 16.0

4:00 p.m. 7 20.2

At4:00p.m.,Philippehadreceivedabout20requests.


1. a) linear,notexponential;e.g.,differencesareconstant b) exponentialgrowth;y 5 12.52 x,e.g.,constantratios

6

20

10

0

30

40

50

60

70

80

90

100y

1 2 3 4 5

x

c) quadratic,notexponential;e.g.,differencesarenotconstantoraconstantratio

d) cubic,notexponential;e.g.,differencesarenotconstantoraconstantratio

2. a) y 5 10.097... 10.200...2 x,decayfunction,domain:5x|x [ R6,range:5y|y . 0,y [ R6,y-intercept:10.1,endbehaviour:extendsfromQIItoQI,decreasing

b)y 5 2.780... 11.054...2 x,growthfunction,domain:5x|x [ R6,range:5y|y . 0,y [ R6,y-intercept:2.78,endbehaviour:extendsfromQIItoQI,increasing

3. a) e.g.,Yes,theratiosofconsecutivepairsofy-valuesareclose. b)e.g.,Wecancreatetheformulabysettingatothefirstrentvalue

andbtotheaverageratioofconsecutivepairsofy-values. c)$14000


NEL 633Answers

An

swers

4. a)

350

200

100

0

300

400

500

600

Mas

s (g

)

Length (mm)

Rainbow Trout: Length vs. Mass

700

800

900

1000y

45050 150 250

x

b) e.g.,y 5 26.934... 11.008...2 x c) e.g.,690g;Iidentifiedthepointonthecurvethathadanx-valueof400. d) 446mm;e.g.,Iidentifiedthepointonthecurvethathaday-valueof1000. 5. a)

2

1

0

3

4

5

6

Popu

lati

on (b

illio

ns)

Years since 1970

Population by Year

7

8y

10 20 30 40 50

x

b) e.g.,y 5 3.911... 11.014...2 x,wherexisthenumberofyearssince1970andyisthepopulationinbillions

c) e.g.,8.05billion d) e.g.,61.5yearsafter1970,thatis,during2031 6. a) y 5 14.429... 11.065...2 x b)27.1cm c)95.8cm;e.g.,no,sinceitwas98.0cmonday28 d)day20 7. a) y 5 122 x b)domain:5x|x . 0,x [ N6,range:5 y|y . 0,y [ N6 c)7 8. a)

12

200

100

0

300

400

500

600

Air

pres

sure

(mb)

Altitude (km)

700

800

900

1000y

2 4 6 8 10

x

b)y 5 1050.311... 10.873...2 x c)137.3mb d)5km,22km 9. a) 20% b)y 5 575.228... 10.799...2 x c)e.g.,about3years;3.1years10. a) e.g.,No,therateofchangeofatmosphericCO2isincreasing. b)e.g.,y 5 315.61 11.012 x,wherexisthenumberofyearssince1960

andyistheatmosphericconcentrationofcarbondioxideinppm

c)y 5 315.609... 11.004...2 x d)387ppm,403ppm11. a) y 5 83.933... 10.9516...2 x b)14min c)29min12. a) y 5 40.798... 10.747...2 x b)9h c)2h13. a) y 5 4120.075... 11.499...2 x b)237553 c) y 5 4120.075 11.22 x14. a) 10% b)12.2weeks15. a)i) 137barrels ii)47barrels b)132ndweek c)256thweek16. a) y 5 3000 10.92 x b)365barrels c)61stweek17. a) e.g.,Calculatetherateofchangeinthedecrease(b)anduse

100fora.Usesoftwareoracalculatortoperformexponentialregressiontogetthosevalues.

b)80.80% c)3118. a)40 b)e.g.,No,theseconddifferencesareconstant,sothedatacanbe

modelledbyaquadraticfunction. c)11219. a)14

b)A 1t2 5 100a12b

t14

c) A 1t2 5 100.001... 10.95...2 t d)

40

20

0

60

80

100

120

Mas

s (g

)

Day

Mass of Tin-117y

10 20 30 40

x


1. a)No.e.g.,extendsfromQIItoQIV b)Yes.e.g.,decreasesfromQIItoQI c)Yes.e.g.,increasesfromQIItoQI


NEL634 Answers

2. a) i)

-6 -4 2 4

4

2

-2

6

-2 0 6-8

8y

8

x

ii)

12

10

4

6

8

14

2

16

18

20y

-6 -4 2 4-2 0 6-8 8

x

iii)

12

10

4

6

8

14

2

16

18

20y

-6 -4 2 4-2 0 6-8 8

x

iv)

-6 -4 2 4

4

2

-2

6

-2 0 6-8

8y

8

x

b)i) numberofx-intercepts:0,y-intercept:3,endbehaviour:QIItoQI,domain:5x|x [ R6,range:5 y|y . 0,y [ R6

ii) numberofx-intercepts:0,y-intercept:8,endbehaviour:QIItoQI,domain:5x|x [ R6,range:5 y|y . 0,y [ R6

iii) numberofx-intercepts:0,y-intercept:5,endbehaviour:QIItoQI,domain:5x|x [ R6,range:5 y|y . 0,y [ R6

iv) numberofx-intercepts:0,y-intercept:2,endbehaviour:QIItoQI,domain:5x|x [ R6,range:5 y|y . 0,y [ R6

3. a) numberofx-intercepts:0,y-intercept:5,endbehaviour:QIItoQI,domain:5x|x [ R6,range:5 y|y . 0,y [ R6;increasing

-6 -4 2 4

4

2

-2

6

-2 0 6-8

8y

8

x

b)numberofx-intercepts:0,y-intercept:90,endbehaviour:QIItoQI,domain:5x|x [ R6,range:5 y|y . 0,y [ R6;decreasing

60

50

20

30

40

70

10

80

90

100y

-6 -4 2 4-2 0 6-8 8

x

c)numberofx-intercepts:0,y-intercept:8,endbehaviour:QIItoQI,domain:5x|x [ R6,range:5 y|y . 0,y [ R6;increasing

-6 -4 2 4

4

2

-2

6

-2 0 6-8

8y

8

x

4. a)a 5 5 a 5 3 b) 0 , b , 1 b . 1 c) domain:5x|x [ R6,range:5 y|y . 0,y [ R6 domain:5x|x [ R6,range:5 y|y . 0,y [ R6


NEL 635Answers

An

swers

5. a) decreasing

12

10

4

6

8

14

2

16

18

20y

-6 -4 2 4-2 0 6-8 8

x

b)increasing

12

10

4

6

8

14

2

16

18

20y

-6 -4 2 4-2 0 6-8 8

x

c)decreasing

-6 -4 2 4

8

4

12

-2 0 6-8

16y

8

x

d)increasing

-6 -4 2 4

0.4

0.2

-0.2

0.6

-2 0 6-8

0.8

1y

8

x

6. a)

RoundNumber of Students

Who Receive Handouts

0 7

1 49

2 343

3 2401

4 16 807

b)Yes.y 5 7 172 x;e.g.,Therateofincreaseofthenumberofstudentspolledineachroundincreasesataconstantrate.

7. y 5 36.871... 10.663...2 x 8. a) y 5 7.628... 11.742... 2 x b) i) $10.07 ii) $17.55 iii) $30.58 iv) $53.28 9. a) e.g.,Firstdivideamountsinconsecutiverowstodetermine

thebase,thenusetheinitialamountandthebasetowriteanexponentialformula.

b) 4% c) $2220.3710. a) 140cm c) fourthbounce b) 37cm11. a) exponentialfunction,nox-intercept,y-intercept:90,end

behaviour:QIItoQ1,decreasing b) domain:5t 0 t $ 0,t [ R6,range:5C

1t2 0 21 # C 1t2 # 90,C 1t2 [ R6;Domainrepresentsthetimeperiodinwhichthecoffeecools.Rangerepresentsthetemperatureofthecoffee.

c) about71° C d) 17min,47min e) about63min


1. x-intercept:1,numberofy-intercepts:0,endbehaviour:QIVtoQI,domain:5x|x . 0,x [ R6,range:5 y|y [ R6

2. a)No.e.g.,nox-interceptandoney-intercept b)No.e.g.,twox-interceptsandoney-intercept c) Yes.e.g.,onex-interceptandnoy-intercept d)No.e.g.,onex-interceptandoney-intercept e) Yes.e.g.,onex-interceptandnoy-intercept f)No.e.g.,nox-interceptandoney-intercept 3. c:x-intercept:1,numberofy-intercepts:0,endbehaviour:QIVto

QI,domain:5x|x . 0,x [ R6,range:5 y|y [ R6,a . 0,e.g.,graphisincreasing

e:x-intercept:1,numberofy-intercepts:0,endbehaviour:QItoQIV,domain:5x|x . 0,x [ R6,range:5 y|y [ R6,a , 0,e.g.,graphisdecreasing

4. y 5 logx:x-intercept:1,numberofy-intercepts:0,endbehaviour:QIVtoQI,domain:5x|x . 0,x [ R6,range:5 y|y [ R6,increasing

y 5 2logx:x-intercept:1,numberofy-intercepts:0,endbehaviour:QItoQIV,domain:5x|x . 0,x [ R6,range:5 y|y [ R6,decreasing


NEL636 Answers

5.

x-InterceptNumber of y-Intercepts


a) 1 0 QIV to QI 5x | x . 0,x [ R6

5y | y [ R6

b) 1 0 QI to QIV 5x | x . 0,x [ R6

5y | y [ R6

c) 1 0 QIV to QI 5x | x . 0,x [ R6

5y | y [ R6

d) 1 0 QIV to QI 5x | x . 0,x [ R6

5y | y [ R6

e) 1 0 QI to QIV 5x | x . 0,x [ R6

5y | y [ R6

f) 1 0 QIV to QI 5x | x . 0,x [ R6

5y | y [ R6

a)

1 2

2

1

-1

-2

3

0 3

y

4 5 6 7 8

x

b)

0.5 1.0

4

2

-2

-4

6

0 1.5

y

2.0 2.5 3.0 3.5 4.0

x

c)

5 10

20

10

-10

30

40

0 15

y

20 25 30 35 40

x

d)

1 2

2

1

-1

-2

3

0 3

y

4 5 6 7 8

x

e)

0.2 0.4

0.4

0.2

-0.2

-0.4

0.6

0 0.6

y

0.8 1.0 1.2 1.4 1.6

x

f )

100

200

100

-100

-200

300

500

400

600

0

y

200 300 400

x

6. e.g.,onex-intercept,noy-intercepts,domain:5x 0 x . 0,x [ R6 7. a)e.g.,y 5 5logx

1 2

2

1

-1

-2

3

0 3

y

4 5 6 7 8

x

b)e.g.,y 5 24logx

1 2

2

1

-1

-2

3

0 3

y

4 5 6 7 8

x

8. i) b,e.g.,x-interceptis1,noy-intercept,graphextendsfromQIVtoQI

ii) c,e.g.,x-interceptis1,noy-intercept,graphextendsfromQItoQIV

iii)d,e.g.,nox-intercept,y-interceptis1,graphextendsfromQIItoQI

iv)a,e.g.,nox-intercept,y-interceptis2,graphextendsfromQIItoQI

9. Yes.e.g.,Anexponentialfunctionhasnox-intercepts,andalogarithmicfunctionhasonex-intercept.

10. Ashydrogenionconcentrationincreases,pHdecreases.

1 2

2

1

-1

-2

3

0 3

y

4 5 6 7 8

x


NEL 637Answers

An

swers

11. Astheenergyofthesoundincreases,thenumberofdecibelsincreases.

10 20

200

100

-100

300

400

0 30

y

40 50 60 70 80

x

12. a) P-intercept:1,t-intercept:none,domain:5P 0 0 , P # 1,P [ R6,range:5t 0 t $ 0,t [ R6,function:decreasing,P 5 1:t 5 0

b) about131years c) about30years13. a)a , 0 b)Thedomainisrestricted,x . 0,asthefunctionsarelogarithmic. c)Therangeisunrestricted,asallvaluesofyarepossible.

14. a)

T-intercept:0.000 003 16 ...,M-intercept:none,domain:5T 0 T . 0,T [ R6,range:5M 0 M $ 0,M [ R6,function:increasing,T 5 1:M 5 5.5

b) about7.2 c) about3000timesasintense15. a) A-intercept:3000,t-intercept:none,domain:

5A 0 A $ 3000,A [ R6,range:5t 0 t . 0,t [ R6,function:increasing

b) about31years c) about18years

Lesson7.5,page494

1. a) e.g.,Graphislogarithmicbecausegraphisincreasing,x-interceptis1,thereisnoy-intercept,endbehaviourisQIVtoQI,domainis5x 0 x . 0,x [ R6,andrangeis5 y 0 y [ R6.

b) factorof10 c) increasesbyafactorof3 2. y 5 26.653... 1 108.49... ln x;x-intercept:1.063,y-intercept:

none,endbehaviour:QIVtoQI,domain:5x 0 x . 0,x [ R6,range:5 y 0 y [ R6,function:increasing

0.1 0.2

1

0.5

1.5

0 0.3

2

2.5

3

3.5

4

4.5

5

5.5

6 M

0.4 0.5 0.6 0.7 0.8 0.9 1.0

T

3. a)

b) t 5 2346.090... 1 28.957... ln P;P-intercept:155110,t-intercept:none,endbehaviourisQIVtoQI,domain:5 P 0 P [ N6,range:5t 0 t $ 0,t [ W6,function:increasing

c) about1974 4. a)independent:seismographicreading(r),dependent:Richterscale

magnitude(M) b)

c) M 5 20.006... 1 0.434... ln r d) about15.8timesasintense 5. a) independent:pressure(P);dependent:altitude(h) b)h 5 30665.960... 2 6640.436... ln P c) P-intercept:101.3,h-intercept:none,endbehaviour:QItoQIV,

domain:5P 0 P . 0,P [ R6,range:5h 0 h [ R6,function:decreasing

d) 99.2kPa e) 26.7kPa

60

70

Population

80

90

100

120

P10

20

30

40

50

Yea

rs s

ince

1900

Population of Albertat

0

500 000

1 000 000

1 500 000

2 000 000

2 500 000

3 000 000

3 500 000

2

1

0

3

Rich

ter s

cale

mag

nitu

de

4

5

6

7

8 M

10 000 000

20 000 000

30 000 000

40 000 000

50 000 000

60 000 000

70 000 000

80 000 000

Seismographic reading (microns)

Earthquakes

r


NEL638 Answers

6. a)

t 5 38070.332 ... 2 8266.961... ln P b)268years c)5730years 7. a)A 5 14999.826... 11.045... 2 t b)t 5 2218.44... 1 22.717... ln A c)about12years;e.g.,Ipreferthelogarithmicequation,becauseit

makesthecalculationssimpler.

8. a) independent:distancefromEarth(d ),dependent:distancemodulus(m)

b)

c)m 5 25.086 ... 1 2.174... lnd d)23.19 e) 4.8pc

9. a)

100

20

10

30

0

40

50

60

70

80

90

100 t

200 300

Facebook Users

Registered users (millions)

Mon

ths

sinc

e la

unch

400 500 600

n

b) t 5 5.888... 1 10.833... lnn c)August2009

60 70

4 000

2 000

0

6 000

Age

(yea

rs)

80 90 100

8 000

10 000

12 000

14 000

16 000

18 000

20 000 t

10 20 30 40 50Percent of carbon-14 (%)

Carbon-14

P

Star Brightness

Distance from Earth (pc)

Dis

tanc

e m

odul

us

300

20

10

0

-20

-30

-10400

m

-40

500100 200

d

10. e.g.,Enterthedatainmycalculator,performalogarithmicregression,graphthedatapointsinascatterplotandthelogarithmicfunctiononthesameaxes,andidentifythepointwiththeknownx-valueandtheunknowny-value.

11. a) i) n 5 ln A 2 ln 5000

ln 1.05

ii) n 5 ln A 2 ln 5000

2 ln 1.025

iii) n 5 ln A 2 ln 5000

4 ln 1.0125

iv) n 5 ln A 2 ln 5000

365 ln 1.000 136 ...

b) e.g.,Thedenominatorapproachesln1 5 0asthenumberofcompoundingperiodsincreases.


1. a) ii) e.g.,decreasingexponentialfunctionwithy . 0 b) iv) e.g.,increasinglogarithmicfunctionwithx . 0 c) iii)e.g.,increasingexponentialfunctionwithy . 0 d) i) e.g.,decreasinglogarithmicfunctionwithx . 0 2. a) y 5 12.620... 11.094... 2 x,whereyisthedebtinbillionsofdollars

andxisthenumberofyearsafter1955.

b) $247.28billion c) 1998 3. numberofx-intercepts:0,y-intercept:6,endbehaviour:QIItoQI,

domain:5x 0 x [ R6,range:5 y 0 y . 0,y [ R6

-6 -4 2 4

4

2

-2

6

-2 0 6-8

8y

8

x

4. x-intercept:1,y-intercept:none,endbehaviour:QItoQIV,domain:5x 0 x . 0,x [ R6,range:5y 0 y [ R6,function:decreasing

5. a) 21.199... 1 0.289...lnx b)9.5magnitude

30 35

100

50

0

150

40

200

250

300

Net

fede

ral d

ebt

($ b

illio

ns)

Years since 1955

Net Federal Debt

350

400

450

500

550

600y

455 10 15 20 25

x


NEL 639Answers

An

swers


1. a) e.g.,ExponentialfunctionsextendfromQIItoQI.PolynomialscanextendfromeitherQIIIorQIItoQIorQIV.

b) e.g.,Thedomainisalways5x 0 x [ R6,therangeisalways5y 0 y . 0,y [ R6,andtheyallextendfromQIItoQI.aisthey-intercept.

2. a) domain:5x 0 x [ R6,range:5y 0 y . 0,y [ R6,y-intercept:9,endbehaviour:QIItoQI

b) e.g.,Changebtoavaluegreaterthan1. 3. a) i) x-intercept:none ii) y-intercept:125 iii)QIItoQI iv) domain:5x 0 x [ R6,range:5 y 0 y . 0,y [ R6 v) decreasing b) i) x-intercept:none ii) y-intercept:0.12 iii)QIItoQI iv) domain:5x 0 x [ R6,range:5 y 0 y . 0,y [ R6 v) decreasing c) i) x-intercept:none ii) y-intercept:1 iii)QIItoQI iv) domain:5x 0 x [ R6,range:5 y 0 y . 0,y [ R6 v) increasing d) i) x-intercept:none ii) y-intercept:0.85 iii) QIItoQI iv)domain:5x 0 x [ R6,range:5 y 0 y . 0,y [ R6 v) increasing 4. a) ii,e.g.,Graphisincreasing. b) i,e.g.,Graphisdecreasing. 5. a) e.g.,y 5 1000 132 x,whereyisthepopulationandxisthe

numberofquartersafterApril1,1896 b) e.g.,domain:5x 0 0 # x # 3,x [ W6(quarters),range:

5 y 0 1000 # y # 27000,y [ W 6(population) c) e.g.,1732,5196;e.g.,thesetwopointsaremidpointsofthefirst

twoquarters,andsocorrespondtox 5 0.5andx 5 1.5.

6. a)

b) y 5 200.798... 11.088... 2 x c) 468 d) 2014 7. a) 38% b) 7400years 8. x-intercept:1,numberofy-intercepts:none,endbehaviour:QIVto

QI,domain:5x 0 x . 0,x [ R6,range:5y 0 y [ R6

100

50

0

150

200

250

300

Dee

r pop

ulat

ion

Years after 2005

Deer Population

350

400y

1 2 3 4 5 6 7

x

9.

x-InterceptNumber of y-Intercepts


a) 1 0 QIV to QI 5x | x . 0,x [ R6

5y | y [ R6

b) 1 0 QI to QIV 5x | x . 0,x [ R6

5y | y [ R6

c) 1 0 QIV to QI 5x | x . 0,x [ R6

5y | y [ R6

d) 1 0 QI to QIV 5x | x . 0,x [ R6

5y | y [ R6

a)

1 2

4

2

-2

6

8

0 3

y

4 5 6 7 8

x

b)

1 2

4

2

-2

6

8

0 3

y

4 5 6 7 8

x

c)

4 8

8

4

12

16

20

24

28

0 12

y

16 20 24 28 32

x

d)

1 2

1

2

0.5

-0.5

-1

1.5

0 3

y

4 5 6 7 8

x

10. i) d,e.g.,x-interceptis1,noy-intercept,extendsfromQItoQIV ii) b,e.g.,nox-intercept,y-interceptis1,increasingfunction iii)a,e.g.,x-interceptis1,noy-intercept,extendsfromQIVtoQI iv) c,e.g.,nox-intercept,y-interceptis6,decreasingfunction11. 0.23%


NEL640 Answers

Chapter 8 – Sinusoidal FunctionsLesson 8.1, page 519

1. a)

0.8

b)

2.5

c)

3.0 2. a) 90°

b) 30°

c) 135°

d) 270°

3. a) 60°

b) 235°

c) 390°

4. a)

7.0

BA

C

45°

BA

C

150°

BAC

180°

BA

C

400°

b)

11.0 5. a) 450°

b) 600°

6. a) i) 9:20a.m. ii) 9:55a.m. iii)10:55a.m. b) i) 2.1 ii) 5.8 iii)12 7. a) about6.28m b) 2,120°

8. a) 2 b) 45°

c) 5 d) 400°

9. Disagree,e.g.,Forthecirclewithradius5m,thearcofananglewillbehalfaslongasthearcoftheequivalentangleinthecircleofradius10m,buttheratioofarclengthtoradius,whichgivestheradiananglemeasure,willbethesame.

10. e.g.,Usebenchmarkstoestimatetheradianmeasureequivalentofanglesgreaterthan360° ,where1radianisabout60° .Forexample,determinetheradianmeasureof

i)480° ii)525° iii)650°

i) 480° 5 8 # 60°,and8 # 1 5 8

OR480° 5 360° 1 90° 1 30° ,and2p 1p

21

p

65

13p

6 ii) 525° , 540°

540° 5 9 # 60° ,and9 # 1 5 9 OR540° 5 360° 1 180° ,and2p 1 p 5 3p

iii) 650° , 660° 660° 5 11 # 60°,and11 # 1 5 11

OR660° 5 360° 1 180° 1 120°,and2p 1 p 1p

35

10p

3

B A

C

640°


NEL 641Answers

An

swers

4. e.g.,Thegraphissymmetricalalongthex-axis,withtheaxisofsymmetrybeingat180°and360°,respectively.Thegraphisrotationallysymmetricalaroundthepoint 1270°,02 .

5. a) 0 b) 1 6. a) 0° ,180° ,360° ,540° ,720°

b) 90° ,270° ,450° ,630°

7. e.g.,Theup-and-downpatterninthegraphofy 5 sinxlooksliketherepeatingpatternofwavesinalake.

8. e.g.,Yes,becauseeachpointonthesinegraphcorrespondstoapointonthecosinegraphwiththesamey-coordinatebutwithanx-coordinateof90°less.

9. e.g.,Itwouldlooklikethegraphofcosx,asitwouldstartat1,decreaseto0afterspinning90° ,thendecreaseto21afterspinning180°,andsoon.


1. a) 5 y 0 23.5 # y # 3.5,y [ R6,3.5 b) 5 y 0 23 # y # 1,y [ R6,2 2. a) y 5 2,1.5 b) y 5 21;4 3. a) 120°

b) 3 4. a) 5 y 0 27 # y # 3,y [ R6,5,y 5 22,180°

b) 5 y 0 20.5 # y # 6.5,y [ R6,3.5,y 5 3,5 5. 5 y 0 22 # y # 3,y [ R6,2.5,y 5 0.5,4.25 6. a)

b)

2

1

0

3

4

5

6

7

8y

45° 90° 135° 180°

x

2

1

-2

3

-3

-1

0

y

4 8 12 16

x

11. a)

b)

12. a) 4.0 b) 3.0 c) 5.9


1. a)

b) 0;180°and540°

c) 0;270°and630°

d)

2. e.g.,Thegraphofy 5 sinxrepeatsitselfafteritpassesthrough360°or2p.

3. e.g.,Thegraphissymmetricalalongthex-axis,withtheaxisofsymmetrybeingat90°and270°,respectively.Thegraphisrotationallysymmetricalaroundthepoint 1180°,02 .

BA

C

1200°

B A

C

29.3

1.0

0.5

-1.0

1.5

-1.5

-0.5

0

y

90° 180° 270°

sin x cos x

360° 450° 540° 630° 720°

Sin x vs. Cos x

x

1.0

0.5

-1.0

1.5

-1.5

-0.5

0

y

2 4 6 8 10 12

Sin x vs. Cos x

x

sin x cos x


NEL642 Answers

17. a) graph2,graph1,graph3 b) e.g.,EachApitchhasdoublethefrequencyofthepreviousone. c) graph2:110Hz,graph3:440Hz d) e.g.,Soundwavescanbeapproximatedbyasinusoidalfunction.

Thevolumeofthesoundisdictatedbytheamplitude.Theperiod,orfrequency,varieswiththesizeoftheinstrument(e.g.,atubacreateslow-frequency/long-periodwaveswhileapiccolocreateshigh-frequencywaves.)

18. a) about17ms b)


1. a) 2.4 b) 3.6 c) 7.0 d) 9.0 2. a) 60° b) 180° c) 360° d) 540° 3.0.1,20°,0.5,1.5,p,190°,200°,310°,400° 4. a) 5 y 0 21 # y # 1,y [ R6,1,360°or2p,y 5 0 b) e.g.,Theirrange,amplitude,periodandequationofmidlineare

thesame;theiry-interceptisdifferent. 5. a) 0°,180°,360°,540°,720°

b)maximum:90° ,450° ,minimum:270° ,630° 6. a) 5 y 0 25 # y # 1,y [ R6,3,180°,y 5 22 b) 5 y 0 23 # y # 1,y [ R6,2,360°,y 5 21 7. a) range:5 y 0 24 # y # 6,y [ R6,amplitude:5,

equationofmidline:y 5 1,period:7 b) range:5 y 0 0.5 # y # 3.5,y [ R6,amplitude:1.5,

equationofmidline:2,period:0.5

8. a)13

s

b) y 5 0amperes c) 4.5amperes

100

50

-100

150

200

-150

-200

-50

0

y

0.02 0.04

Alternating Current

Time (s)Volt

age

(V)

0.06 0.08 0.1

x

7. e.g.,Theperiodwouldbethesame,buttheamplitude(andtheminimaandmaxima)wouldbesmaller.

8. a) 1.6m b) 0.8m c) 2.5s d) about1m,1.6m 9. a) y 5 0;e.g.,velocityoftheairbetweenbreaths. b) 0.8L/s c) 5s;e.g.,timetobreatheinandoutcompletely 10. a) e.g.,Both:theincreasedamplitudemeansthatthebreathsare

deeperandthedecreasedperiodmeansmorebreathsperminute. b) e.g.,amplitudeandperiodhavechanged c) 1.2L/s 11. e.g.,Thegymnastcompletesajumpevery3seconds,goingfrom3

feetabovethegroundto30feet,withatotaljumpheightof27feet. 12. range:5 y 0 27 # y # 3,y [ R6;amplitude:5;midline:y 5 22;

period:0.5 13. a) A:period 5 1s,minimum 5 10cm,maximum 5 26cm,

amplitude 5 8cm; B:period 5 0.5s,minimum 5 10cm,maximum 5 18cm,

amplitude 5 4cm b) e.g.,A,becauseitsamplitudeisgreater. 14. a) e.g.,hoop’sradius b) hoop3 c) hoop1;hoop3orhoop2 d) e.g.,hoop3,becausethemidlineofthegraphislower 15. e.g.,Therangeisthedifferenceofthemaximumandminimum

y-values.Theamplitudeishalfthedifferenceofthemaximumandminimumvalues.Theequationofthemidlineisy 5 averageoftheminimumandmaximumvalues.

16. e.g.,Theperiodandmidlinestaythesame,whiletheamplitudedecreases.

2.0

1.0

-2.0

-1.0-1.5

-2.5

-0.50

0.5

1.5

2.5y

0.2 0.4

Flagpole Vibrations

Time (s)Dis

tanc

e (c

m)

0.6 0.8 1.0

x

2.0

1.0

-2.0

3.0

-3.0

-1.0

0

y

0.2 0.4

Flagpole Vibrations (20 km/h less)

Time (s)Dis

tanc

e (c

m)

0.6 0.8 1.0

x


NEL 643Answers

An

swers

12. a) 86ft b) about1.8min,or1min48s c) 4ft 13. a) iii b) i 14. a) v b) ii 15. a) e.g.,sinusoidalfunction,amplitude:3,midline:y 5 21,range:

5 y 0 24 # y # 2,y [ R6,period:72° ,horizontaltranslationfromy 5 cosx :30°left

b)

16. a)

Note Period (s) Frequency (Hz)

G 0.0051 196.0

D 0.0034 293.7

A 0.0023 440.0

E 0.0015 659.3

b) e.g.,Eachstringistunedtoalmost1.5timesthefrequencyofthepreviousstring.

c) e.g.,About2periodsofthelowernoteand3periodsofthehighernote.Thefrequencyofthehighernoteisapproximately1.5timesthefrequencyofthelowernote.

d) e.g.,4,6,and9periods 17. a) i)3,y 5 4,5 y 0 1 # y # 7,y [ R6,180°,60°totheright ii)3,y 5 4,5 y 0 1 # y # 7,y [ R6,180°,240°totheright iii)3,y 5 4,5 y 0 1 # y # 7,y [ R6,180°,120°totheleft b) e.g.,Thegraphsareallthesame. c)

e.g.,Itisalsothesamebecauseitisacosinegraphwiththesameattributesasthesinegraphs,exceptthatitistranslatedtotheleftby45° 190° dividedbyb).

18. a) 10.5cm,2.5cm b) 0.25s,e.g.,Theapplecompletes4bouncespersecond.

x

2

1

-2

3

-3

-4

-5

-1

0

y

60° 120° 180° 240° 300 360°

4

2

6

8

10

0

y

60° 120° 180° 240° 300° 360°

x


1. c),a),b);e.g.,Iorderedthefunctionsbasedonthevaluesofa. 2. c),a),b);e.g.,Therangeisdefinedbythefunction’samplitude,soI

orderedthefunctionsbasedonthevaluesofa. 3. a),b),c);e.g.,Themagnitudeoftheperiodisinverselyproportionaltob. 4. a) 45°left b) 180°right c) 45°right 5. a) 7,5 y 0 27 # y # 7,y [ R6 b) 13,5 y 0 213 # y # 13,y [ R6 6. a) y 5 5,8,5 y 0 23 # y # 13,y [ R6 b) y 5 27,6,5 y 0 213 # y # 21,y [ R6 7. a) y 5 2;7;23 b) y 5 23;0;26 8. a) 30°right b) 100°left c) 4.5right d) 3left 9. a) 90°;45°right b) 4p;1right 10. e.g., a)y 5 6sin2x b)

11. e.g., a)y 5 0.5cos4x b)

6

2

1

-2

3

-3

-1

4

5

6y

y � 3 sin 4x-4

-5

-6

7531 2 4

x0

y � 6 sin 2x

6

1.0

0.5

-1.0

1.5

-1.5

-0.5

2.0

-2.0

7531 2 4

x0

y � 2 cos x

y � 0.5 cos 4x

y


NEL644 Answers

3. a)

e.g.,about28days b) e.g.,Becausethedatafollowasinusoidalpattern. c) y 5 22.954 ... sin 10.230 ... x 2 0.208 ... 2 1 40.284 ... d) 63.2° e) 23.3° f)May14 4. a) e.g.,Becausethedatafollowsasinusoidalpattern. b)

y 5 2.726 ... sin 10.505 ... x 1 3.016 .. . 2 1 4.426 ... ;yes c) 7.2m,1.7m d) 12h25min e) 4.3m 5. 6h50min 6. a) y 5 19.581 ... sin 10.462 ... x 2 1.662 ... 2 1 6.238 ...

b) y 5 16.992 ... sin 10.470 ... x 2 1.751 ... 2 2 4.738 ...

c) y 5 18.388 ... sin 10.464 .. . x 2 1.694 ... 2 1 0.686 ...

d) e.g.,Theamplitudes,phaseshiftsandperiodsaresimilar;theequationsofthemidlinesaredifferent.

e) e.g.,Yes,butitismoredifficulttofitacurvetoit. f) 14.1° C

30 35

20

10

0

30

40

40

50

60

70y

5 10 15 20 25 50 55 6045

x

Day

Moon Angle

Ang

le (°

)

24 28

2

1

0

3

32 36 40

4

5

6

7

8y

4 8 12 16 20

x

Time (h)

Water Height

Hei

ght

(m)

19. a) 33m,3m b) 2pminorabout6.3min,e.g.,Thewheelcompletesarotation

every6.3min. 20. a) 0.75s b) e.g.,Aperson’sbloodpressuremakesacompletelow-to-highcycle

aboutevery0.75s. 21. e.g.,Iftheequationisintheformy 5 asinb 1x 2 c2 1 d ,the

amplitudeisa,themidlineisy 5 d ,itistranslatedtotherightbyc

degreesorradians,andtheperiodis360°

bor

2p

b.Forexample,the

equationy 5 2sin2 1x 2 45°2 1 3hasanamplitudeof2,amidlineofy 5 3,itistranslatedtotheright45°,andaperiodof180°.

22. a)

e.g.,Theperiod,amplitudeandequationofmidlinearethesame;theyarereflectedacrossthex-axis.

b) e.g.,Atranslationofpor180°. c) Yes,e.g.,graphsoffunctionsoftheformy 5 asinxand

y 5 2asinxarehorizontaltranslationsofeachotherby180°orp.


1. a)

b) y 5 1.5sin 13.141 ... x 2 1.570 ... 2 1 66.5 2. a)

Revolution 014

12

34

1 1 14

1 12

1 34

2

Time (s) 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Height (ft) 11 6 1 6 11 6 1 6 11

b) y 5 5sin 13.141 ... x 1 1.570 .. . 2 1 6 c) 1ft7in. d) 1ft11in.

2.0

1.0

-2.0

3.0y � 2 sin x y � �2 sin x

-3.0

-1.0

0

y

45° 90° 135° 180° 225° 270° 315°

x

360°

66.0

65.0

64.0

67.0

68.0

69.0

70.0

0.50 1.0 1.5 2.0 2.5Time (s)

Pendulum Swing

Hei

ght

(in.)

3.0 3.5 4.0 4.5 5.0

y

x


NEL 645Answers

An

swers


1. a) 3.2 b) 8.8 c) 0.3 d) 6.0 2. a) 315°

b) 270°

c) 330°

d) 540°

3. a) 0°,60°,120°,180°,240°,300°,360°,420°,480°,540°,600° ,660°,720°

b) 0,1.047,2.094,3.141,4.189,5.236,6.283,7.330,8.378,9.425,10.472,11.519,12.566

4. a) 5 y 0 21 # y # 7,y [ R6,4,120°,20°totheright,y 5 3 b) 5 y 0 26 # y # 22,y [ R6,2,180°,60°totheright,y 5 24 5. y 5 19.557 ... sin 10.476 ... x21.762 ... 2 1 6.141 ...

6. a)

y 5 1.751 ... sin 11.570 ... x2 b) 4s c) e.g.,Positiveandnegativevelocitiescorrespondtoexhalationsand

inhalations(orviceversa). d) 10s,12s,14s,16s,18s


1. a) 0.3 b) 2.0 c) 4.0 d) 9.6 2. a) 540°

b) 300°

c) 30°

d) 630°

3. a) 180° , x , 360°,540° , x , 720°

b) 0° # x , 90°,270° , x , 450°,and630° , x # 720°

4. a) 5 y 0 24 # y # 0,y [ R6,2,360°,y 5 22

b) 5 y 0 22.5 # y # 20.5,y [ R6,1,90°,y 5 21.5

5. a) y 5 8;e.g.,Shestartedat8mfromthesensor. b) 6m c) 4s;thisistheamountoftimetocompleteoneswing. d) 2m e) e.g.,Yes,sincesheisattheherfurthestdistancefromthedetector. 6. a)A:3m,2m,about12s;B:4m,3m,about16s b) e.g.,Theyaretravellingataboutthesamespeed(75min48s).

Velo

city

of a

ir (L

/s)

6

1.0

0.5

-1.0

1.5

2.0

-1.5

-2.0

-0.5

08

y

2 4 5 7 1091 3

Gymnast Breathing

x

Time (s)

7. a) y 5 20.341 ... sin 10.536 ... x 2 2.332 ... 2 2 2.706 ...

b) 17.6° C,223.0° C;e.g.,thefunctionisreasonablyaccurate. c) 16.1° C 8. a) y 5 4.207 ... sin 10.017 ... x 2 1.398 ... 2 1 12.411 ...

b) 8h12minto16h37min c) day171 d) 9h10min e) days119and224 9. a) 212.9° C,e.g.,Ideterminedasinusoidalregressionfunction

thatmodelsthedata,substitutingnumbersformonths,andextrapolatedthepredictedvalueforthe13thmonth.

b) 39mm,e.g.,Ideterminedasinusoidalregressionfunctionthatmodelsthedata,substitutingnumbersformonths,andextrapolatedthepredictedvalueforthe13thmonth.

c) e.g.,Temperature,sinceprecipitationismorelikelytovary. 10. a)

Time (s) 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3

Height (cm) 70 55 40 55 70 55 40 55 70 55 40 55 70

b) y 5 15sin 12px 1 1.570 ... 2 1 55 c) 55cm 11. a) y 5 6sin 1px21.570 ... 2 1 11 b) 15.2in.,14.5in. 12. e.g.,No,becausetheregressionfunctiontakesintoaccounttheeffects

ofothermonths. 13. a) HayRiver:y 5 20.681 ... sin 10.501 ... x22.018 ... 2 2

4.284 ... ,yes; MardelPlata:y 5 6.221 ... sin 10.504 ... x 1 1.059 ... 2 1

14.188 ... ,yes b)

e.g.,Thegraphshaveverysimilarperiods;theamplitudeismuchlessforMardelPlata,butthemidlineismuchgreater;themaximumisonlyslightlygreaterforMardelPlata;themaximumsandminimumsofthegraphsarealmostexactlyopposite.

c) e.g.,Theirlocations(northorsouthoftheequator)affectwhenthetemperatureishighorlow.Theirdistancefromtheequatoraffectthemagnitudeofthetemperaturechanges.

d) e.g.,LateMayandlateAugust,sincethatiswhenthegraphsintersect.

e) e.g.,south,asJanuaryandFebruarytemperaturesarewarmerthanJulyandAugusttemperatures.

14. a) e.g.BecausetheEarthismovingalongitsorbit,sotheMoonmust“catchup.”

b) e.g.,Theperiodofthetwographswillbedifferent(withthesynodicbeinglonger),butallotherattributeswillbethesame.

Tem

pera

ture

(°C

)

6

20

10

-20

30

-30

-10

08

y

2 4 5 7 10 11 1291 3

Monthly Temperatures: Hay River, NWTvs. Mar del Plata, Argentina

x

Month


NEL646 Answers

10. about2.4cyclespernanosecond;about5.0cyclespernanosecond11. about212.2° C12. about9.6° C

Cumulative Review, page 586

1. a) x-intercepts:23,22,2;y-intercept:212;endbehaviour:QIIItoQI;domain:5x 0 x [ R6;range:5 y 0 y [ R6

b) x-intercepts:23,1,3;y-intercept:29;endbehaviour:QIItoQIV;domain:5x 0 x [ R6;range:5 y 0 y [ R6

2. a) 3,positive,212 b) 3,negative,29 3. a) x-intercepts:1;y-intercept:22;endbehaviour:QIIItoQI;

turningpoints:0;domain:5x 0 x [ R6;range:5 y 0 y [ R6 b) x-intercepts:0,1or2;y-intercept:28;endbehaviour:QIII

toQIV;turningpoints:1;domain:5x 0 x [ R6;range:5 y 0 y # 24, y [ R6

c) x-intercepts:1,2or3;y-intercept:22;endbehaviour:QIIItoQI;turningpoints:2;domain:5x 0 x [ R6;range:5 y 0 y [ R6

d) x-intercepts:3;y-intercept:0;endbehaviour:QIItoQIV;turningpoints:2;domain:5x 0 x [ R6;range:5 y 0 y [ R6

4. a)

y 5 4.808 ... x 3 2 106.412 ... x

2 1 597.474 ... x 2 163.803 ...

b) e.g.,fromhalfwaythroughmonth8tothreequartersofthewaythroughmonth13

c) e.g.,274degreedays;thereare31daysintheseventhmonth,so

x 5 8 21

31

6 7

400

200

0

600

8

800

1000

1200y

9 10 11 12 13 14 151 2 3 4 5

x

Month

Energy Consumed to Heat a Building

Ener

gy c

onsu

med

(deg

ree

days

)

7. a)

e.g.,Whenit’sdrivingtowardyou. b) 877Hz,735Hz 8. a) iv b) ii 9. a) 4,y 5 3,5 y 0 21 # y # 7,y [ R6,p

3,2.5right

b)

Soun

d (d

B)

0.003

1.0

0.5

-1.0

1.5

-1.5

-0.5

0

y

0.001 0.002

Emergency VehicleApproaching

Time (s)

x

Time (s)

Soun

d (d

B)

0.003

1.0

0.5

-1.0

1.5

-1.5

-0.5

0

y

0.001 0.002

Emergency VehicleDeparting

x

65

2

1

-2

3

5

4

6

7

8

-1

087

y

21 43

x


NEL 647Answers

An

swers

d)

40 000

50 000

60 000

30 000

0

70 000

80 000

90 000

100 000

110 000

120 000y

4 8 12 16 20

x

Years since 1996

Population of WoodBuffalo, Alberta

Popu

lati

on

i)111026 ii)during2009

7. a)

b) 0.02g c) 276days 8. a)

b)P 1t2 5 161.581... 11.251...2 t c) e.g.,arepresentstheinitialpopulation,161.581...,brepresentsthe

growthfactor,1.251.... d) about8years 9. x-intercept:1,y-intercept:none,endbehaviour:QIVtoQI,domain5x 0 x . 0,x [ R6,range:5y 0 y [ R6

1200 1600

100

50

0

150

200

250M(t)

400 800

t

Time (days)

Polonium-210 Half-Life

Mas

s (g

)

6

200

100

0

300

400

500

600P(t)

1 2 3 4 5

t

Year

Insect Population

Popu

lati

on



Increasing or Decreasing?

0 5 QII to QI 5x 0 x [ R6 5 y 0 y . 0, y [ R6 increasing

0 30 QII to QI 5x 0 x [ R6 5 y 0 y . 0, y [ R6 decreasing

a)

b)

6. a)

Year Population

1996 35 000

1997 37 800

1998 40 824

1999 44 090

2000 47 617

2001 51 426

2002 55 541

2003 59 984

2004 64 783

2005 69 965

2006 75 562

b) e.g.,Therateofgrowthisconstant,andgrowthoccursrapidly. c) 35000;They-interceptrepresentstheinitialpopulation(in1996).

y

-2-3-4-5 1 2 3 4 5-1 0x

300

100

150

200

250

350

50

400

60 000

50 000

20 000

30 000

40 000

70 000

10 000

80 000

90 000

100 000y

-2-3-4-5 1 2 3 4 5-1 0x


NEL648 Answers

13. a) range:5 y 0 1 # y # 11,y [ R6,midline:y 5 6,amplitude:5m,period:90s

b) e.g.,TheFerriswheelstarts1moffthegroundandover90srotatesto11mandback.Theaxisofthewheelis6moffthegroundandthewheelhasaradiusof5m.

14.

Amplitude Period

Equation of the Midline Domain Range

Horizontal Translation

a) 3 90° y 5 2 5x 0 x [ R6 5 y 0 21 # y # 5, y [ R6 30° right

b) 5 6.28 y 5 22 5x 0 x [ R6 5 y 0 27 # y # 3, y [ R6 4.00 left

15. a)

e.g.,Theaveragemonthlytemperaturesshouldberelativelyconsistentfromyeartoyear.

b) y 5 13.983 ... sin 10.551 ... x 2 2.363 ... 2 1 56.676 ...

c) 70.6 ° F d) e.g.,fromearlyMaytoearlyOctober

6 7

20

10

0

30

8

40

50

60

70

80y

9 10 11 121 2 3 4 5

x

Month

Average High Temperature in Vancouver, BC

Ave

rage

hig

h te

mpe

ratu

re (°

F)

10. a) x-intercept:1,y-intercept:none,endbehaviour:QIVtoQI,domain:5x 0 x . 0,x [ R6,range:5 y 0 y [ R6,function:increasing

b) x-intercept:1,y-intercept:none,endbehaviour:QItoQIV,domain:5x 0 x . 0,x [ R6,range:5 y 0 y [ R6,function:decreasing

11. a)

b) y 5 6.357 ... lnx 1 5.561 ...

c) about22.8ft d) about2.8yearsold 12. a) numberofx-intercepts:multiple;y-intercept:sinx,0;cosx,1;

domain:5x 0 x [ R6;range:5 y 021 # y # 1,y [ R6,period:2p;amplitude:1;equationofthemidline:y 5 0

b)

12

8

4

16

-16

1

12

8

-4

-8

4

0

y

-12

2 3 4 5

x

12

8

4

16

-16

1

12

8

-4

-8

4

0

y

-12

2 3 4 5

x

12 14

10

5

0

15

20

25y

2 4 6 8 10

x

Age of tree (years)

Cherry Tree Height

Hei

ght

(ft)

1.0

0.5

-1.0

1.5

-1.5

-0.5

0

y

�

sin x cos x

2� 3� 4�

Sin x vs. Cos x

x


Documents

Answers - Ms Moon's Math Classes - Home€¦ · NEL Answers 595 Answers Chapter 1 ... The future value of option A is $7826.00 and the future value ... 13. e.g., In both cases, interest