Year10MathematicsExaminationSEMESTER22019

QUESTIONANDANSWERBOOKLETSTUDENTNAME:

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TOTALQUESTIONS:28 TOTALMARKS:

Year10Mainstream(115TotalMarks)Year10AcademicExtension(135TotalMarks)Section1:Non-Calculator-assumed45minutes

(50marks)

Section2:Calculator

55minutes(65marks)

(Additional20marksAE)

KinrossCollegeYear10MathematicsExam,Semester220191

ATTHEENDOFTHEEXAMINATIONAttachanyextrasheetsusedtothisQuestion/Answerbooklet.IMPORTANTNOTETOCANDIDATESNootheritemsmaybetakenintotheexaminationroom.Itisyourresponsibilitytoensurethatyoudonothaveanyunauthorisednotesorotheritemsofanon-personalnatureintheexaminationroom.Ifyouhaveanyunauthorisedmaterialwithyou,handittothesupervisorBEFOREreadinganyfurther.

..…DONOTTURNTHISPAGEUNTILASKEDTODOSO…..

KinrossCollegeYear10MathematicsExam,Semester220192

1.Expandandsimplify: (𝑥 − 3)(𝑥 + 3)

(A) 𝑥 + 3! (B) 𝑥! + 3! (C) 𝑥! − 9 (D)Noneofthese 2. Whichofthefollowingtriangleshasitssideslabelledcorrectly?

(A) (B) (C) (D) 3.Whichofthefollowingmathematicalstatementsisfalse?

(A) a2=b2+c2(B) 2 2b a c= − (C) 2 2c a b= + (D)c2=a2–b2 4. Completethefactorisation:𝑥! + 9𝑥 + 20 = (𝑥 + 5)(𝑥+? )

(A)8 (B)2 (C)4 (D)-2

Section1:MultiplechoiceNON-CALCULATOR(Total10marks,onemarkperquestion)

KinrossCollegeYear10MathematicsExam,Semester220193

5.

Quartile3ofthedatadisplayedintheboxplotaboveis:(A) 15 (B)25 (C)20 (D)35 6.Whichexpressionistheexpandedsimplifiedformof:(2𝑥 − 1)(3𝑥 + 5) (A) 6𝑥! + 10𝑥 − 3𝑥 − 5 (B) 6𝑥! + 7𝑥 − 5 (C)6𝑥! + 7𝑥 − 5 (D) 6𝑥! + 7𝑥 − 6 7.Forthegiventriangle:

(A)sin = aθb(B)sin = bθ

a(C)sin = cθ

b(D) sin = bθ

c

8.Themedianofthesetofdatais:(10,16,28,13,25,17,19,21,16,14,17)

(A) 15 (B) 16.5 (C)16 (D)17

KinrossCollegeYear10MathematicsExam,Semester220194

9.Isabelainvests$15000inasimpleinterestbankaccountthatpays5%annually.Howmuchwillbeinherbankaccountafter3years?(A) $17250 (B) $11500 (C) $12000 (D) $12500 10.Whatisthetotalnumberofpeoplewhoparticipatedinthisdataset?

(A) 25 (B) 30 (C) 34 (D) 15

KinrossCollegeYear10MathematicsExam,Semester220195

Section1:NonCalculator–assumed(Total40marks)11.[2,1,1,1,1,1,1,1,1=10marks]Considerthegivendataset:

3,6,17,8,4,13,12,24,8,11,5,13

a) Listthedatainorder,fromsmallesttolargest.

________________________________________________________________

b) Forthedata,find:

i theminimumandmaximumvalues ___________________________ ii therange ___________________________ iii themode ___________________________ iv themean,correcttoonedecimalplace ___________________________ v themedian(Q2) ___________________________ vi thelowerandupperquartiles ___________________________

(Q1andQ3) vii theinterquartilerange(IQR) ___________________________ viiianyoutliers ___________________________

KinrossCollegeYear10MathematicsExam,Semester220196

12.[1,2,3,4=10marks]Expandandsimplifythefollowing. a) 2 3𝑥 − 8 + 2 b)(𝑥 + 3)(𝑥 + 4) c)(9𝑥 − 3)(4𝑥 + 5) d) 4(𝑥 + 7)(𝑥 + 4)13.[2,2,3=7marks]Factorisethesequadratictrinomials:a) 𝑥! + 8𝑥 + 16 b) 𝑥! − 𝑥 − 20 c)−2𝑥! + 16𝑥 − 14

KinrossCollegeYear10MathematicsExam,Semester220197

14.[1.5,1.5=3marks]LabelthesidesofeachtrianglebyusingthelettersH(hypotenuse),O(opposite)andA(adjacent):

a)b)

15.[2,2=4marks]

Placetheangle𝜃inthefollowingtrianglestomatchthelabels:a)b)

KinrossCollegeYear10MathematicsExam,Semester220198

16.[4,1,1=6marks]Considerthevariablesxandyandthecorrespondingbivariatedata.

x 1 2 3 4 5 6 7 8

y 8 5 2 4 5 4 2 1 a) Drawascatterplotforthedata.(4marks)

b) Istherepositive,negativeornocorrelationbetweenxandy? c) Isthecorrelationbetweenxandystrongorweak?

…STOP…

KinrossCollegeYear10MathematicsExam,Semester220199

Section2:CALCULATOR(Total65marks)1.[1,1,1,2,1,1,3=10marks]HerearethenamesofthelasttenprimeministersofAustraliatogetherwiththeagesatwhichtheywereprimeminister. (Hint:placeagesinnumericalorder)

WilliamMcMahon 64GoughWhitlam 57MalcolmFraser 46BobHawke 54PaulKeating 48JohnHoward 57KevinRudd 51

JuliaGillard 50 TonyAbbott 56 MalcomTurnbull 61

a) Calculate:

i)theMedian. ii)thelowerquartile. iii)theupperquartile. b) Determinetheinterquartilerange.c) Determinetherange.d) Determinethemeanage.

e) Drawamedianboxplottorepresenttheabovedataabovethescalebelow.

40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70

KinrossCollegeYear10MathematicsExam,Semester2201910

2.[2,2,2=6marks]Joshuabuysa$9000caronthefollowingterms:

• 30%deposit• monthlyrepaymentsof$210for2years.

Find: a) thedepositpaid.

____________________________________________________________________________________________________________________________________________

b) thetotalamountpaidforthecar.

____________________________________________________________________________________________________________________________________________

c) theinterestcharged.

____________________________________________________________________________________________________________________________________________

3.[2,2=4marks]Useeachdiagramtohelpexpandtheexpressions.

a) (x +3)(x +1) b) (x + 4)2

KinrossCollegeYear10MathematicsExam,Semester2201911

4.[3,3=6marks]Findthelengthsofthemissingsides,roundingtheanswersto1decimalplaces:

a)b)

5.3Solveforx,correcttoonedecimalplacewherenecessary.

KinrossCollegeYear10MathematicsExam,Semester2201912

6.[2,1,1=4marks]Determinethefollowingkeyfeaturesofthegivengraph.

a)Coordinatesoftheturningpointandwhetheritisamaximumorminimum.b)Coordinatesofthex-intercepts.c)Coordinatesofthey-intercept.

7.[2,2=4marks]

a)Factoriseandsolveusingthenullfactor:𝑥! + 20𝑥 + 100 = 0

b)Factoriseandsolveusingthenullfactor:−7𝑥! + 49𝑥 − 42 = 0

KinrossCollegeYear10MathematicsExam,Semester2201913

8.[2,2,3=7marks]Findtheinterestpaidona$7000loanunderthefollowingconditions.

a) 8%p.a.simpleinterestover4years

b) 7%p.a.simpleinterestover3yearsand4months

Findtheinterestpaidona$9000loanfor4%p.a.compoundedbi-annuallyover3years

9.[3,2=5marks]Gavin has an outstanding balance of $4620 on his credit card at the beginning of May. The interest rate charged on the credit card is 21% p.a. (a) Calculate the interest that Gavin is charged on the card for the month of May if he makes no

further payment on the amount outstanding. (b) In May Gavin repays $1900 and makes purchases of $385. Calculate the outstanding balance on

Gavin’s credit card at the end of May. (c) Calculate the interest that is payable for May.

KinrossCollegeYear10MathematicsExam,Semester2201914

10.[3,3=6marks]Findthelengthsofthesidesmarkedx,forthesetrianglescorrectto2decimalplaces:

a)b)

11.[3,3=6marks]Findtheunknownanglescorrectto2decimalplaces:

a)b)12.4

KinrossCollegeYear10MathematicsExam,Semester2201915

ACADEMICEXTENSION(20Marks)

1.5The flight of an aeroplane from Sydney to Adelaide can be modelled by the equation h = –2.5t2 + 225t where h is the height of the plane (in metres) above the ground, and t is the flight time in minutes. (a) How long does it take to fly from Sydney to Adelaide? (b) What is the height of the aeroplane after 10 minutes? (c) At what time will the aeroplane return to this height? Explain without actually solving the

equation. (d) At what time does it reach its maximum height? (e) What is the maximum height the aeroplane reaches?

KinrossCollegeYear10MathematicsExam,Semester2201916

2.6Andrew and James set out from a fire tower. Andrew walks 200 metres south, stops and calculates the angle of elevation to the top of the tower as 22°. James walks due west, stops and calculates the angle of elevation to be 28°. Determine: (a) the height of the tower (rounding your answer to 1 decimal place) (b) the horizontal distance of the tower from James, to the nearest metre (c) the distance between Andrew and James (d) the bearing from Andrew to James, to the nearest degree.

KinrossCollegeYear10MathematicsExam,Semester2201917

3.9A loan of $25 000 is to be repaid over 3 years with interest charged at 9% p.a. on the outstanding balance. (a) Find the amount of interest that is paid if the annual repayment made is $10 000. (b) Calculate the saving made if the annual repayment is increased to $12 500.