Year9MathematicsExamination

SEMESTER22019

QUESTIONANDANSWERBOOKLET

STUDENTNAME:

TEACHER:

DATE:

TIMEALLOWEDFORTHISPAPERReadingtimebeforecommencingwork:10minutesWorkingtimeforthispaper:105minutesMATERIALTOBEPROVIDEDBYTHESUPERVISOR• ThisQuestion/AnswerBooklet

MATERIALTOBEPROVIDEDBYTHECANDIDATE• Pen/pencilforansweringquestions.• Erasingstationery.• Uptotwoscientificcalculators.• WrittennotesononeunfoldedA4sizedpaper;canbedouble-sided.

TOTALQUESTIONS:37+3(extension)

TOTALMARKS:120+13Section1:Noncalculator

45minutes,51marks

Section2:Calculatorallowed

55minutes,67marks+13

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KinrossCollegeYear9MathematicsExam,Semester220191

Section1:Noncalculator(Multiplechoice-10marks)1.[1mark]Heleninvests$20000inasimpleinterestbankaccountthatpays4%annually.Howmuchwillbeinherbankaccountafter5years?

(A) $3200 (B) $12000 (C) $4000 (D)$24000

2.[1mark] Whichside(AB,ACorBC)isadjacenttoθ inthistriangle?

(A)AC(C)AB

(B)BC(D)Opposite

3.[1mark]

Circlethecorrectanswerforthefollowingstatement.(3𝑥)!inexpandedformis:

(A)3 × 𝑥 × 𝑥 × 𝑥 × 𝑥(C)3𝑥!× 3𝑥! × 3𝑥! ×3𝑥!

(B)(3𝑥)!×( 3𝑥)! × (3𝑥)! × (3𝑥)! (D)3𝑥×3𝑥×3𝑥×3𝑥×3𝑥

KinrossCollegeYear9MathematicsExam,Semester220192

4.[1mark]

Theexpression!!×!!!

simplifiesto:

(A) ℎ! (B)!!!

(C) !!!

(D)!!!

5.[1mark]Whichratiorepresentscosforangle(∠Y)

(A) 56.2

(B) 3.626.2

(C) 3.625

(D) 53.62

6.[1mark]

Whatisthesolutiontotheequation3𝑚 − 1 = 4+𝑚?

(A)𝑚=!!(A)𝑚=

!!

(B)𝑚=!!(D)𝑚=

!!

KinrossCollegeYear9MathematicsExam,Semester220193

7.[1mark]Thelengthofthehypotenuseinthetriangleshownisclosestto:

(A) 36 (B) 9

(C) 16 (D) 258.[1mark]

750000000whenwritteninscientificnotationis:

(A) 75 × 10!

(B) 7.5 × 10!

(C) 7.5 × 10!

(D) 0.75 × 10!"

9.[1mark]

Thegradientofthefollowinglineis:

(A) −43 (B)-3 (C) 3

4 (D) −

34

KinrossCollegeYear9MathematicsExam,Semester220194

10.[1mark]

Alinearrelationgivesthefollowingtableofvalues:

The𝑥 −and𝑦 −interceptsofthegraphofthislinearrelationare:

(A) (4,0)and(0,4 )

(B) (4, 0)and(0,−8)

(C) −4,0 and 0,8

(D) −2,0 and 0,4

(E) (0,−2)and(4,0)

x −3 −2 −1 0 1 2 3

y −14 -12 -10 -8 -6 -4 -2

KinrossCollegeYear9MathematicsExam,Semester220195

Section2:Noncalculator(Shortanswer-41marks)1.[3marks]

Mikeput$1500intoasimpleinterestaccountforayear.Hedidnottakeanymoneyoutoraddanymoney to theaccount.At theendof theyearhehad$1650on theaccount.Whatwas theannualinterestrate?

2.[3marks]Findtheequationofthelinethathasagradientof-2andpassesthroughthepoint(3, 4).

3.[3marks]Findthemidpoint𝑀 (𝑥,𝑦)ofthesegmentjoining𝐶(3, 2)and𝐷(−4, 5).

4.[3marks]

Themidpoint𝑀 (𝑥,𝑦)ofthelinesegmentjoiningthepoints(2,9)and(-7,3)is:

KinrossCollegeYear9MathematicsExam,Semester220196

5.[4marks]

Writethefollowingnumbersinscientificnotation:

a)957000000

b)0.00064

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

Foreachofthelinesshownbelowcalculatethegradientandstatetheequationoftheline.

a)

Gradient =

y – intercept =

Equation of the line (y = mx + c):

b)

Gradient =

y – intercept =

Equation of the line (y = mx + c):

KinrossCollegeYear9MathematicsExam,Semester220197

7.[2marks]

Calculatethelengthofthesidexinthefigurebelow.(Pleaseleaveyouranswerinexactvalueorroundtothenearestcm)

8.[8marks]

Expresseachofthefollowinginsimplestform.

a) 𝑝×𝑝×𝑝×𝑝×𝑝

b) 6𝑛 × 7

c) 8𝑠𝑡 × 5𝑡𝑢

d) 3ℎ × 5ℎ

e) 7𝑞𝑟×(−2𝑞)

f) (−2𝑎)×(−3𝑐)×(−5𝑏)

g) 20𝑐 ÷ 4𝑐

h) 35÷ 5𝑏

KinrossCollegeYear9MathematicsExam,Semester220198

9.[3marks]Placetheangleθ inthesetrianglestomatchthelabels:

a)b)c)

10.[3,1,1,1=6marks]Drawatreediagramforanexperimentshowingallpossibleoutcomesandprobabilitiesoftossing2coins.(a)WhatistheprobabilityoftwoTails?(b)WhatistheprobabilitythatonecoinshowsTailsandonecoinshowsHeads?(c)Whatistheprobabilityofatleastonetail?

KinrossCollegeYear9MathematicsExam,Semester220199

Section2:Calculatorallowed(Multiplechoice-5marks)1.[1mark]

HowlongdoesKimneedtoinvest$5000at4%p.a.simpleinterestinordertoproduce$1000interest?

(A)5years(B)1year(C)9months(D)6months

2.[1mark]

Whatisthesimpleinterestearnedaftersixyearswhen$1450isinvestedintoanaccountthatpays3%perannum?

(A) $81.00(C)$87.32

(B)$531.00(D)$261.00

3.[1mark]

Thenumber17−2 isequivalentto:

(A) 34-1(C)-172

(B) !!"#

(D) !!!"

4.[1mark]

Useyourcalculatortoevaluate 17 −34

correctto2decimalplaces.

(A)1.33(C)0.56

(B)2.73(D)2.74

5.[1mark]

Thevalueoftan 29°,correcttofourdecimalplaces,is:

(A)0.4848(B)0.8746(C)0.1307(D)0.5543(E)0.2591

KinrossCollegeYear9MathematicsExam,Semester2201910

Section2:Calculatorallowed(Shortanswer-62marks)

1.[2,2,3=7marks]Janelleinvests$18500at5.2%perannumfor3yearsintoasavingsaccountofferingaflatrateofsimpleinterest.

a)Howmuchsimpleinterestwillsheearn?

b)Howmuchwilltheaccountbeworthattheendofthe5years?

c)Howmuchextrainterestwouldsheearnifshekeepsthisnewbalanceinthebankforafurther6months?

2.[2marks]

Marywishestopurchaseaveryexpensivepairofdressshoes.Theycost$135butsheonlyhas$30tospend.Thestoreagreestoalay-bywhereshemustpayanequalamounteachweekfor7weeksaftersheputsdownthedepositof$30.Howmuchisherweeklypayment?

KinrossCollegeYear9MathematicsExam,Semester2201911

3.[1,1,2,3=7marks]

Simplifythefollowing:

a) 9𝑏!×7𝑏! b) x12

x

c) 3x6y2( )4

d) !!!×!"!!×!!!

!!×!!!×!!

4.[4marks]UsePythagorastheoremtofindtheunknownlengthsonthetrianglesbelow.Roundyouranswersto1decimalplace.

a) x

b)

8cm

10cm

𝑥

11m 12.9m

𝑥

KinrossCollegeYear9MathematicsExam,Semester2201912

5.[2,2,2=6marks]

Write down the gradient and the y-intercept of the following linear graphs

a) y = 2x + 5

Gradient =

y- intercept =

b) y = 32x −11

Gradient =

y- intercept =

c) −5y = 2−10x

Gradient =

y- intercept =

6.[2marks]Theinternationalmobilephonecallrate,in$C,isgivenbytheequation:C=2+1.7t,wheretisthetimeofthecallinminutes.Findthelengthofacallforwhichthecostwas$5.4.

KinrossCollegeYear9MathematicsExam,Semester2201913

7.[3,3,3=9marks]Fortheequationy=2x–5

a.Completethetableforthexvaluesgiven.

b.Graphtheequationoftheliney=2x–5.Plottheinformationontheaxesbelow.

c.Whatistheexactxvaluewheny=33?(usealgebra!)

KinrossCollegeYear9MathematicsExam,Semester2201914

8.[3,2=5marks]Apilotflyingaplaneatanaltitudeof11790mseesamountainpeak2900mawayfromhiminthehorizontaldirection.Thedirectdistancebetweentheplaneandthepeakis3000m.

a)Findtheheightofthemountain,correcttothenearestmeter.

b)Findthepilot’sangleofelevationtothemountainpeaktothenearestdegree.

KinrossCollegeYear9MathematicsExam,Semester2201915

9.[8marks]

Foreachofthefollowing,findthevalueoftheunknownvariablecorrecttotwodecimalplaces.

a) b)

c) d)

KinrossCollegeYear9MathematicsExam,Semester2201916

10.[4marks]

Findthevalueofθtothenearestdegree. a) b)

11.[3marks]

Theelevationanglefromapointonthegroundtothetopoftheflagpoleis38∘andthedistancetothebaseofthepoleis30maway.Findtheheightoftheflagpoletothenearestmeter.

KinrossCollegeYear9MathematicsExam,Semester2201917

12.[3,2=5marks]Abagcontains2pink(P)and4yellow(Y)marbles,andtwomarblesareselectedwithoutreplacement.

a)Drawatreediagramshowingalloutcomesandprobabilities.

b)Findtheprobabilityofselecting:

i)apinkmarbleandthenayellowmarble(P,Y)

ii)2pinkmarbles

iii)exactly1pinkmarble

KinrossCollegeYear9MathematicsExam,Semester2201918

Section3:Calculatorallowed(Extension)

1.[5marks]Andreawon$4500.Shedecidedtoinvestintoanaccountatarateof7.5%compoundingannuallyfor4

years.Compoundinterestcanbefoundbyusingtheformula 1100

trA P ⎛ ⎞= +⎜ ⎟⎝ ⎠

,

wherePistheprincipal,ristheyearlyrateandtrepresentsthenumberofyears.Aisthetotalamountaccumulatedaftertyears.(a) HowmuchmoneydidAndreahaveattheendofthe4years?(b) Howmuchinterestwasearnedoverthistime?

2.[3marks]

Whatdoes ( ) ( )3 44 2

9 9

a b aba b

−

−equal?

KinrossCollegeYear9MathematicsExam,Semester2201919

3.[5marks]Fromthetopofabuilding202mhigh,theangleofdepressiontoanotherbuilding120mawayis25°.Howhighisthissecondbuilding?