7/25/2019 3CDMAS 2010 Sem2 Calculator Assumed Exam MLC
1/21
1234567-8
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
7/25/2019 3CDMAS 2010 Sem2 Calculator Assumed Exam MLC
2/21
NTWR
T3
NT4
S%R3%
1234567-8
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$e-ce(t in diagrams
See ne
7/25/2019 3CDMAS 2010 Sem2 Calculator Assumed Exam MLC
3/21
NTWR
T3
NT4
S%R3%
1234567-8
SEMESTE T. EAMIATI. 3 MATHEMATICS: SPECIALIST 3C/3DSECTI. T. CALC9LAT. ASS9MED
Se&tion To: C'$&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
7/25/2019 3CDMAS 2010 Sem2 Calculator Assumed Exam MLC
4/21
12
N2T
W
R.T3
.N
T4.
S
%R3%
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
7/25/2019 3CDMAS 2010 Sem2 Calculator Assumed Exam MLC
5/21
NTWR
T3
NT4
S%R3%
1234567-8
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
7/25/2019 3CDMAS 2010 Sem2 Calculator Assumed Exam MLC
6/21
12
N2T
W
R.T3
.N
T4.
S
%R3%
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
7/25/2019 3CDMAS 2010 Sem2 Calculator Assumed Exam MLC
7/21
NTWR
T3
NT4
S%R3%
1234567-8
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
7/25/2019 3CDMAS 2010 Sem2 Calculator Assumed Exam MLC
8/21
12
N2T
W
R.T3
.N
T4.
S
%R3%
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
7/25/2019 3CDMAS 2010 Sem2 Calculator Assumed Exam MLC
9/21
NTWR
T3
NT4
S%R3%
1234567-8
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
7/25/2019 3CDMAS 2010 Sem2 Calculator Assumed Exam MLC
10/21
12
N2T
W
R.T3
.N
T4.
S
%R3%
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
7/25/2019 3CDMAS 2010 Sem2 Calculator Assumed Exam MLC
11/21
NTWR
T3
NT4
S%R3%
1234567-8
SEMESTE T. EAMIATI. 11 MATHEMATICS: SPECIALIST 3C/3DSECTI. T. CALC9LAT. ASS9MED
See ne
7/25/2019 3CDMAS 2010 Sem2 Calculator Assumed Exam MLC
12/21
12
N2T
W
R.T3
.N
T4.
S
%R3%
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
7/25/2019 3CDMAS 2010 Sem2 Calculator Assumed Exam MLC
13/21
NTWR
T3
NT4
S%R3%
1234567-8
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
7/25/2019 3CDMAS 2010 Sem2 Calculator Assumed Exam MLC
14/21
NTWR
T3
NT4
S%R3%
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
7/25/2019 3CDMAS 2010 Sem2 Calculator Assumed Exam MLC
15/21
1234567-8
NTWR
T3
NT4
S%R3%
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 Calculator Assumed Exam MLC
16/21
NTWR
T3
NT4
S%R3%
SEMESTE T. EAMIATI. 16 MATHEMATICS: SPECIALIST 3C/3DSECTI. T. CALC9LAT. ASS9MED
% second rocet shi( is also launched )rom s(ace station 6 at > am "ith constant /elocit+and is aimed to collide "ith the )irst rocet at e-actl+ 1 (m
7&8 etermine the /elocit+ o) the second rocet shi( that "ill ensure collision taes(lace at the re5uired time
See ne
7/25/2019 3CDMAS 2010 Sem2 Calculator Assumed Exam MLC
17/21
1 m
A m
1234567-8
NTWR
T3
NT4
S%R3%
SEMESTE T. EAMIATI. 17 MATHEMATICS: SPECIALIST 3C/3DSECTI. T. CALC9LAT. ASS9MED
Question 18 6 ('!#s0
% "eight W is attached to a ro(e 1A m long that (asses o/er a (ulle+ at (oint P , Am a&o/e the ground The other end o) the ro(e is attached to a truc at a (oint A , 1m a&o/e the ground, as sho"n in the diagram
7a8 Sho" that y=25+x211 re(resents the distance in metres the "eight is a&o/e (oint6, gi/en x m re(resents the horiIontal distance )rom (oint 6 to the truc G2H
7&8 .) the truc mo/es a"a+ at the rate o) 9 ms1, ho" )ast is the "eight rising "hen it is 2 ma&o/e the ground G*H
7/25/2019 3CDMAS 2010 Sem2 Calculator Assumed Exam MLC
18/21
NTWR
T3
NT4
S%R3%
SEMESTE T. EAMIATI. 18 MATHEMATICS: SPECIALIST 3C/3DSECTI. T. CALC9LAT. ASS9MED
A))ition'$ o!#in s'&e
#uestion num&er7s8:_______________________________________________
7/25/2019 3CDMAS 2010 Sem2 Calculator Assumed Exam MLC
19/21
7/25/2019 3CDMAS 2010 Sem2 Calculator Assumed Exam MLC
20/21
12
N2TW
R.T3
.N
T4.S
%R3%
A))ition'$ o!#in s'&e
#uestion num&er7s8:_______________________________________________
7/25/2019 3CDMAS 2010 Sem2 Calculator Assumed Exam MLC
21/21