2017 Further Mathematics-nht Written examination 2 · PDF fileFURTHER MATHEMATICS Written examination 2 Monday 5 June 2017 Reading time: ... 2017 FURMATH EXAM 2 (NHT) 16 SECTION B
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FURTHER MATHEMATICSWritten examination 2
Monday 5 June 2017 Reading time: 2.00 pm to 2.15 pm (15 minutes) Writing time: 2.15 pm to 3.45 pm (1 hour 30 minutes)
SUPERVISOR TO ATTACH PROCESSING LABEL HEREVictorian Certificate of Education 2017
STUDENT NUMBER
Letter
2017FURMATHEXAM2(NHT) 2
THIS pAgE IS BlANK
3 2017FURMATHEXAM2(NHT)
TURN OVER
THIS pAgE IS BlANK
2017FURMATHEXAM2(NHT) 4
SECTION A – Question 1 – continued
SECTION A – Core
Instructions for Section AAnswerallquestionsinthespacesprovided.Youneednotgivenumericalanswersasdecimalsunlessinstructedtodoso.Alternativeformsmayinclude,forexample,π,surdsorfractions.In‘Recursionandfinancialmodelling’,allanswersshouldberoundedtothenearestcentunlessotherwiseinstructed.Unlessotherwiseindicated,thediagramsinthisbookarenotdrawntoscale.
b. Usethedataabovetodeterminetheequationoftheleastsquaresline.Writethevaluesoftheinterceptandslopeintheboxesbelow.Roundyouranswerstothreesignificantfigures. 3marks
number of rainy days = + ×month number
c. Drawtheleastsquareslineonthetime series plot above. 1mark
Question 7 (3 marks)The community centre has received a donation of $5000. The donation is deposited into another savings account. This savings account pays interest compounding monthly.Immediately after the interest has been added each month, the community centre deposits a further $100 into the savings account.After five years, the community centre would like to have a total of $14 000 in the savings account.
a. What is the annual interest rate, compounding monthly, that is required to achieve this goal? Write your answer correct to two decimal places. 1 mark
b. The interest rate for this savings account is actually 6.2% per annum, compounding monthly. After 36 deposits, the community centre stopped making the additional monthly deposits of
$100.
How much money will be in the savings account five years after it was opened? 2 marks
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SECTION B – continuedTURN OVER
SECTION B – Modules
Instructions for Section BSelect twomodulesandanswerallquestionswithintheselectedmodules.Youneednotgivenumericalanswersasdecimalsunlessinstructedtodoso.Alternativeformsmayinclude,forexample,π,surdsorfractions.Unlessotherwiseindicated,thediagramsinthisbookarenotdrawntoscale.
Question 1 (4marks)PeoplepaytoattendconcertsattheWhiteoakTheatre.Theycanchoosetheirseatsforeachconcertfromthreeclasses,A,B or C.Thetablebelowshowsthenumberofseatsavailableineachclassandthecostperseat.
Class Number of seats available
Cost per seat($)
A 100 45
B 340 35
C 160 30
a. ThecolumnmatrixNcontainsthenumberofseatsineachclass.
NABC
=
100340160
WhatistheorderofmatrixN? 1mark
b. MatrixWcontainsthecostofeachclassofseatinthetheatre.
W = 45 35 30A B C
i. DeterminethematrixproductWN. 1mark
ii. ExplainwhatthematrixproductWNrepresents. 1mark
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SECTION B – Module 1 – continuedTURN OVER
c. Thenumberofseatsthatweresoldforthefirstconcertthisyearisshowninthetablebelow.
Question 2 (8marks)TheWhiteoakTheatreClubhas200memberswhobuyticketsforeveryconcert.Thememberscanchooseseatsfromthreedifferentclasses,A,B or C.Foreachconcert,thechoiceofseatclassforthesememberscanbedeterminedusingthetransitionmatrixT,shownbelow.
this concertA B C
T =
0 70 0 25 0 050 30 0 65 0 650 00 0 10 0 30
. . .
. . .
. . .
ABC
next concert
a. AnincompletetransitiondiagramformatrixTisshownbelow.
a. WritedownthetwoactivitiesthatareimmediatepredecessorsofactivityG. 1mark
b. ForactivityD,theearlieststartingtimeandthelateststartingtimearethesame.
WhatdoesthistellusaboutactivityD? 1mark
c. Determinetheminimumcompletiontime,inweeks,forthisproject. 1mark
d. Determinethelateststartingtime,inweeks,foractivityC. 1mark
e. Whichactivitycouldbedelayedforthelongesttimewithoutaffectingtheminimumcompletiontimeoftheproject? 1mark
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SECTION B – Module 2 – Question 2 – continued
Question 2 (4marks)Theholidayhomehasfourrooms,A,B,C and D.Thefloorplan,belowleft,showstheseroomsandtheoutsidearea.Thereare12doors,asshownonthefloorplan.OnlyroomCandtheoutsidearelabelled.Agraphisshowntotherightofthefloorplan.Onthisgraph,verticesrepresenttheroomsandtheoutsidearea,andedgesrepresentthedoors.
outsideoutside
outside
outside
Floor plan
outside
A
BC D
Graph
C
a. Onthefloorplanabove,roomChasalreadybeenlabelled.
UsethelettersA,B and Dtolabeltheotherthreeroomsonthefloor plan above. 1mark
(Answer on the floor plan above.)
b. SimonisinroomCandhisdaughterZofiaisoutside. SimoncallsZofiatoseehiminroomC. ZofiavisitseveryotherroomonceonherwaytoroomC.
b. Findthemaximumnumberoftrucksthatcouldtravelfromtheentrancetotheexitperday. 1mark
c. Acompanywouldliketosendonegroupoftrucksfromtheentrancetotheexit. Alltrucksinthisgroupmustfolloweachotherandtravelalongthesameroute. Thetrucksinthisgroupwillbetheonlytruckstousethesestreetsonthatday.
a. ThecowsaremilkedearlyinthemorninginMilkdale. Oneday,thesunrisesinanothertown,Creamville(36°S,147°E),at6.42am. AssumeMilkdaleandCreamvilleareinthesametimezone.
Question 1 (4 marks)Anita often drives to a farmers’ market.The graph below shows the relationship between the average speed for the journey (in km/h) and the time (in hours) it takes her to reach the farmers’ market.
average speed (km/h)
time (hours)
120
100
80
60
40
20
O 1 2 3
a. One day, it took Anita two hours to reach the farmers’ market.
What was her average speed in kilometres per hour? 1 mark
b. In March, Anita travelled to the farmers’ market at an average speed of 80 km/h. In April, she travelled to the farmers’ market at an average speed of 40 km/h due to
roadworks.
How much longer did it take Anita to reach the farmers’ market in April compared to the time she took in March? 1 mark
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SECTION B – Module 4 – continuedTURN OVER
c. Theequationfortherelationshipbetweenaverage speed and timehastheform
average speed ktime
� � �=
i. Findthevalueofk. 1mark
ii. Ontheaxesprovidedbelow,drawagraphoftherelationshipbetweenaverage speed