3CDMAS 2010 Sem2 Calculator Assumed Exam MLC

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    Student Name:

    Methodist Ladies College Semester 2, 2010

    3CD MATHEMATICS: SPECIALIST

    Question/Anse! "oo#$et % Se&tion 2 % C'$&u$'to!-'ssu(e)

    Teachers Name: __________________________________________________

    Time allowed for this paper

    Section Reading Woring

    C'$&u$'to!-*!ee ! minutes !0 minutes

    C'$&u$'to!-'ssu(e) 10 minutes 100 minutes

    M'te!i'$s !e+ui!e)/!e&o((en)e) *o! t,is 'e!

    Se&tion .ne C'$&u$'to!-'ssu(e)0: 8 ('!#s

    To e !oi)e) t,e sue!iso!Section T"o #uestion$%ns"er &oolet 'ormula sheet

    To e !oi)e) t,e &'n)i)'teStandard items: (ens, (encils, (encil shar(ener, eraser, correction )luid, ruler, highlighters

    S(ecial items: dra"ing instruments, tem(lates, notes on t"o un)olded sheets o) %* (a(er,and u( to three calculators satis)+ing the conditions set &+ the CurriculumCouncil )or this course

    Important Note to candidatesNo other items ma+ &e taen into the e-amination room .t is ou!res(onsi&ilit+ to ensure that+ou do not ha/e an+ unauthorised notes or other items o) a non(ersonal nature in thee-amination room .) +ou ha/e an+ unauthorised material "ith +ou, hand it to the su(er/isore*o!ereading an+ )urther

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    SEMESTE T. EAMIATI. 2 MATHEMATICS: SPECIALIST 3C/3DSECTI. T. CALC9LAT. ASS9MED

    Instructions to candidates1 A$$5uestions should &e attem(ted

    2 Write +our ans"ers in the s(aces (ro/ided in this #uestion$%ns"er 6oolet S(are ans"er(ages ma+ &e )ound at the end o) this &oolet .) +ou need to use them, indicate in the

    original ans"er s(ace "here the ans"er is continued 7ie gi/e the (age num&er8

    9 S,o '$$ ou! o!#in &$e'!$; our "oring should &e in su))icient detail to allo" +ourans"ers to &e checed readil+ and )or mars to &e a"arded )or reasoning .ncorrectans"ers gi/en "ithout su((orting reasoning cannot &e allocated an+ mars 'or an+5uestion or (art 5uestion "orth more than t"o mars, /alid "oring or ;usti)ication isre5uired .) +ou re(eat an ans"er to an+ 5uestion, ensure that +ou cancel the ans"er +oudo not "ish to ha/e mared

    * .t is recommended that +ou )o not use en&i$e-ce(t in diagrams

    See ne

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    SEMESTE T. EAMIATI. 3 MATHEMATICS: SPECIALIST 3C/3DSECTI. T. CALC9LAT. ASS9MED

    Se&tion To: C'$&u$'to!-'ssu(e) 8 M'!#s0

    This section hase$een 110 5uestions %ns"er'$$ 5uestions Write +our ans"ers in the s(ace(ro/ided

    Suggested "oring time )or this section is 100 minutes

    Question 8 6 ('!#s0

    7a8 3-(ress in (olar )orm the cu&e roots o)2

    2

    2

    2i

    7&8 %n e5uilateral triangle is to ha/e its /ertices on an %rgand diagram on a circle,centre 70,08, radius 2 ne /erte- re(resents a com(le- num&er "ith argument

    6 'ind, in (olar )orm, the num&ers re(resented &+ the /ertices, and the

    Cartesian e5uation "hich has these three num&ers )or roots

    See ne

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    MATHEMATICS: SPECIALIST 3C/3D 4 SEMESTE T. EAMIATI.CALC9LAT.-ASS9MED

    Question = 8 ('!#s0

    7a8 Let A=[4 20 23 15 3

    7 17 1] and B=[2 3 5

    1 1 1

    3 4 0] etermine C=A B

    7&8 Ticets to a concert cost ?se +our ans"er to 7a8 to determine ho" man+ children, teenagers and adultsattended the concert

    See ne

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    SEMESTE T. EAMIATI. 5 MATHEMATICS: SPECIALIST 3C/3DSECTI. T. CALC9LAT. ASS9MED

    Question 1 = ('!#s0

    Water )lo"s into and leas out o) a container such thatdx

    dt=k(2x1) , "here the

    de(th o) the "ater is x metres at time t seconds %t t=0 , the de(th is 0=! m

    and is decreasing at a rate o) 001 ms1

    7a8 Sho" that k=0.02

    7&8 etermine the time at "hich the de(th "ill &e 0!! m

    See ne

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    MATHEMATICS: SPECIALIST 3C/3D 6 SEMESTE T. EAMIATI.CALC9LAT.-ASS9MED

    Question 11 1 ('!#s0

    7a8 Setch in the com(le- (lane the gra(h o) arg ( 1z )= 34

    7&8 7i8 Setch the locus re(resented &+ |z2 i|4

    See ne

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    SEMESTE T. EAMIATI. 7 MATHEMATICS: SPECIALIST 3C/3DSECTI. T. CALC9LAT. ASS9MED

    7ii8 4ence, )ind the e-act greatest and least /alues o) z3+4 i gi/en that|z2 i|4

    7c8 The com(le- num&er x+ iy is such that arg (x+iy )= , "here x>0,y>0 'ind, in terms o) and , the /alues o)

    7i8 arg(x+ iy)

    7ii8 arg(y+ix)

    See ne

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    MATHEMATICS: SPECIALIST 3C/3D 8 SEMESTE T. EAMIATI.CALC9LAT.-ASS9MED

    Question 12 6 ('!#s0

    The ta&le &elo" sho"s the details o) a (o(ulation o) angaroos in a region o) Western%ustralia in 2000

    %ge 7+ears8 0 @ 2 2 @ * * @ A A B B 10

    .nitial (o(ulation 1200 1*00 1A00 B10 *2!

    6reeding Rate 0 01 9! 2! 0!

    Sur/i/al Rate 0* 0! 0= 02 0

    7a8 Write do"n the Leslie matri-, L , )or this (o(ulation

    7&8 What is the total (o(ulation in 200A

    7c8 'ind the (ercentage gro"th rate &et"een the 9rdand *thgeneration

    See ne

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    SEMESTE T. EAMIATI. = MATHEMATICS: SPECIALIST 3C/3DSECTI. T. CALC9LAT. ASS9MED

    ue to com(laints )rom local (ro(ert+ o"ners, it is decided that culling is necessar+

    7d8 To reduce the (o(ulation gro"th, 10 D o) angaroos aged &et"een * and B +earsare culled at the start o) e/er+ second +ear What "ill the (o(ulation &e in 201A

    See ne

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    MATHEMATICS: SPECIALIST 3C/3D 1 SEMESTE T. EAMIATI.CALC9LAT.-ASS9MED

    Question 13 7 ('!#s0

    The lines l1 and l2 ha/e e5uations

    r=

    (3

    1

    0

    )+

    (1

    2

    4

    )

    and r=

    ( 1

    11

    )+

    ( 2

    1

    1

    )res(ecti/el+, "here and are (arameters7a8 'ind the acute angle &et"een l2 and the line ;oining the (oints E (1,1, 1)

    and # (2,1,4 ) , gi/ing +our ans"er correct to the nearest degree

    7&8 etermine the (osition /ector o) the (oint R that lies on the line ;oining E

    (1,1,1) and # (2,1,4) such that ER : R# F 1 : 2

    7c8 'ind an e5uation o) the (lane through # (2,1,4) and (er(endicular tol1 , in the )orm r n=

    See ne

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    SEMESTE T. EAMIATI. 11 MATHEMATICS: SPECIALIST 3C/3DSECTI. T. CALC9LAT. ASS9MED

    See ne

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    MATHEMATICS: SPECIALIST 3C/3D 12 SEMESTE T. EAMIATI.CALC9LAT.-ASS9MED

    Question 14 7 ('!#s0

    The (ath o) a (article is de)ined &+ the (arametric e5uations

    x=120 t4 t2 , y=60 t6 t2

    The (ath crosses the x a-is at t=a and at t=b

    7a8 etermine the /alue o) a and b

    7&8 etermine the /alue o)dy

    dxat t=a and at t=b

    See ne

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    SEMESTE T. EAMIATI. 13 MATHEMATICS: SPECIALIST 3C/3DSECTI. T. CALC9LAT. ASS9MED

    Question 15 6 ('!#s0

    7a8 ?se de Moi/res Theorem to sho" that cosn=1

    2(zn+zn ) and

    sinn=1

    2 i(znzn ) , "here z=cos+i sin G9H

    7&8 ?se 7a8 to (ro/e the identit+, sin3 cos2=1

    2(sin 5+sin )

    See ne

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    SEMESTE T. EAMIATI. 14 MATHEMATICS: SPECIALIST 3C/3DSECTI. T. CALC9LAT. ASS9MED

    Question 16 5 ('!#s0

    ?se mathematical induction to sho" that

    n!>2n

    )or all (ositi/e integers n 4

    Note: n !=1 23 n

    See ne

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    SEMESTE T. EAMIATI. 15 MATHEMATICS: SPECIALIST 3C/3DSECTI. T. CALC9LAT. ASS9MED

    Question 17 1 ('!#s0

    % rocet shi( lea/es s(ace station % "hich is located at (204020

    ) m at > am "ith aconstant /elocit+ o) (

    60

    120

    360) m h1 .t is su((osed to reach the neigh&ouring s(acestation 6, "hich is located at ( 80160

    2020) m

    7a8 etermine "hether or not this rocet shi( reaches s(ace station 6 .) not, )ind theclosest distance &et"een the rocet shi( and s(ace station 6 and "hen this occursto the nearest minute

    See ne

  • 7/25/2019 3CDMAS 2010 Sem2