Spm Mathematics 2005 K2

SPM 2005 MATHEMATICS PAPER 2 ian B. J ,cttt hend

di : h dibena

Masa:2 -l hours 2

:tions: zhs questionpaper cetnststs ol 2 "-e.llons.section A ond section B. Ansroerall : . i rr Section A n nd fo'or questionsit Section B. Writeyou.ranswersin the space pntt,icled :... stlort._paperWorking steps must be written clearly. Non_progro^^Lbb '""i"";;i;, :. ' ts allorued.

Section A 1.52ntorhs) Ansrcer all cluestiortsin. this section.

S:-r'e the quadratic equation 2h2 5 - Bk. 3 -r-:.:t cf.

:rikut:

[4 m(l

14 marhsl

---'"culatelht: value ofp and ofq that satisfy the fblowing srmurtaneous li.ear equatio's: 2p-Jq 4p+q

= 73 = 5

14 nrcrrltsj

_.r-,.t{,(f,,

97

aksamaar I marhah

ih kerata:

On the graph in the answer space, shade the region which satisfres the three i n e q u a l i t i e s r > -2r + 10,.r< 5 andy < 10. 13 nrarl:.

Answer:

Diagram 1 shows a right prism. Right angled triangle PQR is the uniform crosssection of the prism. 1 2c m

?

Diagram norkai.

I

f-'alculate the angle between the plane 8?U and the plane PQZLI. -{nsr,uer.'

99

[3 mcr'&.sl

..rletak p .clariden

D:1q"- 2, O is the origin, point g lies on thc, r_axis and point p lies on the I: 1,,axis.Straishr line Pl" is parallel to the r-axis and straight line pI? is pa..liJl io straight li ne s?.. Thc equatru. oi straight line PB is )i + 2y = 7q.

Diagram 2 a) State the equation of the straight line l'tl. garis l -:

b) Find the cquation of the straight line SZ and hence.state its jr-intercept. [5 nnrlts]

:) Dlara

-{asarer-'

0l

101

f.l:=:r'arn 3 shows a solid cone rvith radius 9 cm a n d h e i g h r l 4 c r r r .A c ) l i n r l , , r\ \ i r l j r : r d , r. 3 ::: antl height Z cm is taken out of the solid.

Diagrarn 3 Ca.:ulate the volumc, in cmrr, of the rcmaining solid.

22) f r..n= 7/

1 4m a

.r berpusa: )LiZ ialah

@ marhsl

D:=ram 4 shows two sectorsORS? and OLfV with the same centre O. RWO isa semicircle r:::: drar.nelcr.EOand RO = 2OV. ROV and OLIT are straisht lines.

= 7 cm and -L|OV = 60 . t':.rg n = ??, calculate ri

[6 ma

rhc perimeter, in cnr, of the wholc diagram,

rL the area, in cmr, of the shaded region.

103

[6 nrarAs]

r

LI tcntan: :llg mun:

i

:rvediaka:

I

, iua orar-:

tb) t\vo boys do write thc report on the first da1,.Thev are then exemptedfrom writing the reporl on the second day.

1

nvediaka:

c-alculatethe probability that both pupils chosento rvrite the report on the secondday are of thc same gender.

L

-'

9 A group of 5 boys and 4 girls takc part in a study on the type ol plgnts founclin a reser\r.r:l 1b1"1, Each da1'.two pupils arc chosenat random lo wrrte a report. 3*.u (a) Calculate the probability that both pupils chosento rvrite lhe report on the first d.r. arr bo.rs.

marha..)

I5 rrrurh'l -\rtstter: a)

b)

l0 Diagram 5 shows thc speed-time gtaph of a particle for a periocl of I seconds. Speed m s r)

T r m et s t

Diagyam 5 State the length of time, in s, that the particle moves with unilbrm speed. .rerrama. r 148 met 16 marhc

bl

Calculate the rate ol change ol spced,in m s 2, in the firsl 5 seconds. calculate the value of r, if the total distance travelled for the period of 1 secondsis 148 metrcs. [6 lrarA.s]

Anstuer: lal

rb)

r

keada

IIlr

siventhat matrixp = (?

IS

PQ a,

-3)

(; ?)

a n d m a t r i xa = u

(f

!)

*.rl 1,"t

Find the value of A and of ft.

b t Using matrices,find the varue ofr and ofy that satisfy the following simultaneouslinear equations: 2x 5y = -t7 ,r+3,y=8

l7 mark-

l7 nto rh sl

.\rtsuer:

br

Section B \48 ntarhs) Ansruer four questions fiom this section. l2 marL:

13 rrI Complete Table 1 in the answer space for the equation = 2r, - r _ 3. J 12 ntarhsl

. \ n.str'er.

r

-2

v

7

l

- 0.5 -2

I

2

3

-2

J

t2

Table I 109

4

4.5

5

.la

42

Graph for Question 12

: n 1 1 0 .A n c =

lt: F-ctrtlti" port of tht,quastirn, us( t lu,gtvph paper prot'iclt,clon page 111.\itu //?.r\ &sr .r -', i

Lir unrt pac

Bv using a scalc o12 cnr to I unit 0n thc.\ axis ancl 2 graph of .r' - 2rr r ;l f b r - 2 , : . . r . : 5 .

[4 marha:

( ln L, ;

Ulttl.

n \'-at\t-.,l'i,.\ .

l+ /l?arr.l:.

. \rrstt,er': b) R(li'r gt(1plt ott pugt, 111. c

12markc

nilai r r

From yonr graph. find (i ) the value ol I $'hen .r iii ) the ,,aluc o1 .r. u hcn y

3.ti. 37.

[ 2 r n or h s ]

Drarv a suitable straight line on vour grilph to find all thc values ol r nhich satisl-v thc ecluation2-t: 3r = 10 fbr -2 ::..r .:: 5. Statc these valuc-qo1.r. [4 ntarlts]

[4 mark,

.lrr.-itr,r. .{

r-

.i) l)iagTant 6 shorvs trvo points, M and

on a (--artesial plane

Diagram 'ft

6

an,sflpnl3lien T is thc translatinn i ;j ). \. 1,,

'fi:rnsfcrrntation R i s a n a n t i c l o c k r v i s cr,o t a t i o r r o f 9 0 , ' a b o i r t t h e c c n t r e r 0 . 2 . (i) Statc the coordinltcs ofthe imrlgc ofpoini M un(lel tlanslormation R ( i i ) s t a t ( ' t h e c r r c r r l i n . t e so l t h c i n r i r g c o f p o i n t N r r n d c r t r r e { i r l o r v i n g r . r n : 1 i , r n . , r i i i. . ra) T!, L5 tnori

b' 'r'R.

11ts

Ansuer: 1 a ) ( i)

(i i ) ( a )

(b)

r D l Diagrlm

7 shols three quadrilaterals,ABCD, EFGH and P@RSon a Cartesian piane.

J

Diagram EFGH is the imagc of ABCD under transformation V. PQRS is thc image ttf EFCH under translbrmation W. (i) Describein full the translormation: (a) Y

(b)w.

ruoyai I Lr berloreL

(ii) Given that quadrilateral PQRS represents a region ol area,15.6 cm, , calculate thU irre it. in cm', of the region represented by the shaded region.

17 markc

[7 uior-lrsI -{ltstoer. 'b) (i) (a)

115

(b.)

( i i)

, )fang n1ua

H

The data in Diagram 8 shows the marks for an English Langrrage monthly tcst for 42 pupil. ltl

25 33 25

20 32 38 35 34 17

37 28 12 26 3l

31 47 it1 29 35 48

26 2139 38 1:) 11

,10 36 23

30 38 39

31 28 :14

2:l 22 lr4

Diagram 8 l en g k a p k l mart a

et Llsing data in Diagram 8 and a classinterval ofb marks, conplete Table 2 in the ansrver spacc.

14 tnorhsl

-{l sruer: al

Midpoint

Table 2

rn anda be: I1 ntorka,

bt Based on your tablc in (a), (i) state the modal class, (iil calculate the mean mark Ibr the Engtish Language monthly test and give your ans\\ (.: correct to dccin.ral places. 11 nort:, .\nsuter: b) (i) (ii)

' tt n 1 1 8 . 2 cm kepa itu. i4 morkc '.

c) For this part of tlu: cluestion, use th.e graph paper prouided otr poge llg. By using a scale of2 cm to 5 marks on the horizontal axis and 2 cnt to 1 pupil on rht r trljcr., axis, draw a histogram for the data.

117

(iraph for Question

.\|sr?r.'

ri!k segler-

!'ratan Ier-:

r I,HGM t

-

ttefir graph on pago 119.

,

D i a g r a n r g r i r s h o w s a s o l i d l i g h t prism l'itlr recl.irrrgular birsc PI,'IN on il horiz(rr::,.table. Thc surface 1'IFGHJ is the unilirnl cross,-sectionot tllr prism. RcctangleAJHI_ rs an inclint_'clplant'and r.cctanglc LHCIl ts a horizontal plane. .lE antI CF- are vertt(rt. cclgt:s.

Diagram 9(i) ,g yang s€

I)rrru full -scalc.t h c e l c v a t i o n o f t h e s o l i d o n a leltic[] 1iom X.

l3 m.ari.:

- vs=3

to _EF as vicrved l i l r i r a il i s l

1 / ts r u c f .

Rajah 9'::

plane palrllcl

A s o l i d . i g t r t p r i s n r w i t h r r n i { b . n rc r o s s - s c c t i o rLrr ! , 1 1 . {i s r c r r o v c c ll i . ' n r the.,,1,,i I)iagranr 9rir. Th. rcmaining soiid is as sho*.n i. Ditrgram g(iil. Rccl.anglo\,.(/li i horizontrrlplanc. a.ll'and,Yitr'ar.er.ertical cdges.l.'S = jl crl ancl ,>-C- 2 t,nr

12I

Diagrarn 9(ii) '+ tnerkc clengan f i mqrl:c

Draw full scale, (i) the plan of the rernaining solid. 14 narhsl (ii) the elevation of the remaining solid on a vertical plane parallel to P1,l as vicu'ed liom Y. 15 tnrtrhs)

,lirsa.'er'. b ) ( i ) .( i i )

kaan bu

Tirble 3 shorvs thc latitudes dan longitudes offour poinls J, K, L ztndXI, on the surfncc ol the eartlr.

Point

Latitude

Longitude

J K

20"LJ

25"T 25"T

L

20"u 30"s

.v"B

M

Table

r"B

3

P is a point on the surfirce of the earth such that JP is the diameter of thc t,arth. State the position of P. l2 nrcrli.r I

r23

: t lu nilu i t u d sepuri nl Qrl?a: r r l r ls e p uI : ingltan ni: il ntorl:c

(b) Calculate (i) the value ofr, if thc distancefrom J to K measuredalongthe nleridian is 1200 n:..::rc---miles, (ii) the value ofy, if the distancefrom J due west to -Lmcasuredalong the commonparalieof latitude is 3 270 nautical miles. Ii nrcrl:, (c) An aeroplanctook off from J ar.rdflcw due rvestto 1- along the commonparallel of latirude and then due south lo M. II the averagespeedfor the whole flight is 600 knots, caiculatcthc timc taken for the rvhole flight. 13rnarAsl Ansuer: :6 (a)

(b) (i)

(ii)

(c)

125