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MATHEMATICAL METHODS (CAS)Written examination 2
Thursday 6 November 2014 Reading time: 3.00 pm to 3.15 pm (15 minutes) Writing time: 3.15 pm to 5.15 pm (2 hours)
SUPERVISOR TO ATTACH PROCESSING LABEL HEREVictorian Certificate of Education 2014
STUDENT NUMBER
Letter
2014MATHMETH(CAS)EXAM2 2
SECTION 1–continued
Question 1ThepointP(4,–3)liesonthegraphofafunction f. Thegraphof f istranslatedfourunitsverticallyupandthenreflectedinthey-axis.ThecoordinatesofthefinalimageofPareA. (–4,1)B. (–4,3)C. (0,–3)D. (4,–6)E. (–4,–1)
Question 2Thelinearfunction f D R f x x: ,→ ( ) = −4 hasrange[–2,6).ThedomainDofthefunctionisA. [–2,6)B. (–2,2]C. RD. (–2,6]E. [–6,2]
Question 3Theareaoftheregionenclosedbythegraphof y x x x= +( ) −( )2 4 andthex-axisis
A. 1283
B. 203
C. 2363
D. 1483
E. 36
SECTION 1
Instructions for Section 1Answerallquestionsinpencilontheanswersheetprovidedformultiple-choicequestions.Choosetheresponsethatiscorrect forthequestion.Acorrectanswerscores1,anincorrectanswerscores0.Markswillnotbedeductedforincorrectanswers.Nomarkswillbegivenifmorethanoneansweriscompletedforanyquestion.
3 2014MATHMETH(CAS)EXAM2
SECTION 1–continuedTURN OVER
Question 4Let f beafunctionwithdomainRsuchthat ′( ) = ′( ) < ≠f f x x5 0 0 5 and when .At x=5,thegraphof f hasaA. localminimum.B. localmaximum.C. gradientof5.D. gradientof–5.E. stationarypointofinflection.
mapsthelinewithequation x y− =2 3 ontothelinewithequationA. x + y = 0B. x+4y = 0C. –x – y=4D. x+4y=–6E. x – 2y = 1
Question 13Thedomainofthefunctionh,where h x xa( ) = ( )cos log ( ) andaisarealnumbergreaterthan1,ischosensothat h isaone-to-onefunction.Whichoneofthefollowingcouldbethedomain?
A. a a−
π π2 2,
B. (0,p)
C. 1 2, aπ
D. a a−
π π2 2,
E. a a−
π π2 2,
Question 14IfXisarandomvariablesuchthatPr Pr ,X a X b>( ) = >( ) =5 8 and then Pr X X< <( )5 8 is
Question 17Thesimultaneouslinearequations ax–3y=5 and 3x – ay = 8 – a haveno solution forA. a=3B. a=–3C. botha=3anda=–3D. a ∈ R\{3}E. a ∈ R\[–3,3]
2014MATHMETH(CAS)EXAM2 8
SECTION 1–continued
Question 18Thegraphof y = kx–4 intersectsthegraphof y = x2 + 2x attwodistinctpointsforA. k=6B. k>6ork < –2C. –2≤k≤6D. 6 2 3 6 2 3− ≤ ≤ +kE. k = –2
Question 19
JakeandAnitaarecalculatingtheareabetweenthegraphof y x= andthey-axisbetweeny=0andy=4.Jakeusesapartitioning,showninthediagrambelow,whileAnitausesadefiniteintegraltofindtheexactarea.
a. Findtheperiodandamplitudeofthefunctionn. 2marks
b. Findthemaximumandminimumpopulationsofwombatsinthislocation. 2marks
c. Findn(10). 1mark
d. Overthe12monthsfrom1March2013,findthefractionoftimewhenthepopulationofwombatsinthislocationwaslessthann(10). 2marks
SECTION 2
Instructions for Section 2Answerallquestionsinthespacesprovided.Inallquestionswhereanumericalanswerisrequired,anexactvaluemustbegivenunlessotherwisespecified.Inquestionswheremorethanonemarkisavailable,appropriateworkingmust beshown.Unlessotherwiseindicated,thediagramsinthisbookarenotdrawntoscale.
a. WhatwasthemaximumvalueoftheconcentrationofmedicineinJuan’sblood,inmilligramsperlitre,correcttotwodecimalplaces? 1mark
b. i. Findthevalueoft,inhours,correcttotwodecimalplaces,whentheconcentrationofmedicineinJuan’sbloodfirstreached0.5milligramsperlitre. 1mark
ii. FindthelengthoftimethattheconcentrationofmedicineinJuan’sbloodwasabove0.5milligramsperlitre.Expresstheanswerinhours,correcttotwodecimalplaces. 2marks
17 2014MATHMETH(CAS)EXAM2
SECTION 2–continuedTURN OVER
c. i. Whatwasthevalueoftheaveragerateofchangeoftheconcentrationofmedicinein
Juan’sbloodovertheinterval 23
3,
?Expresstheanswerinmilligramsperlitre
perhour,correcttotwodecimalplaces. 2marks
ii. Attimest1andt2 ,theinstantaneousrateofchangeoftheconcentrationofmedicinein
Aliciatookpartinasimilarcontrolledexperiment.However,sheusedadifferentmedicine.Theconcentrationofthisdifferentmedicinewasmodelledbythefunction n t Ate kt( ) = − ,t ≥0, whereAandk ∈ R+.
d. IfthemaximumconcentrationofmedicineinAlicia’sbloodwas0.74milligramsperlitreatt=0.5hours,findthevalueofA,correcttothenearestinteger. 3marks