ian B. J,ctt t hend

di: h dibena

:rikut:

[4 m(l

Masa: 2 -l hours2

:tions: zhs question paper cetnststs ol 2 "-e.llons. section A ond section B. Ansroer all: . i rr Section A n nd fo'or questions it Section B. Write you.r answers in the space pntt,icled:... stlort._paper Working steps must be written clearly. Non_pro gro^^Lbb

'""i"";;i;,

:. ' ts allorued.

Section A1.52 ntorhs)

Ansrcer all cluestiorts in. this section.

S:-r'e the quadratic equation 2h2 5 - Bk.3

-r-: . : t cf.14 marhsl

---'"culate lht: value ofp and ofq that satisfy the fblowing srmurtaneous li.ear equatio's:

2 p - J q = 7 34p+q = 5 14 nrcrr l ts j

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

97

SPM 2005 MATHEMATICS PAPER 2

aksamaar

I marhah

ih kerata:

norkai.

On the graph in the answer space, shade the region which satisfres the threer > - 2 r + 1 0 , . r < 5 a n d y < 1 0 .

Answer:

i nequa l i t ies

13 nrarl:.

Diagram 1 shows a right prism. Right angled triangle PQR is the uniform crosssection ofthe prism.

? 12 cm

f-'alculate the angle between the

-{nsr,uer.'

Diagram I

plane 8?U and the plane PQZLI. [3 mcr'&.sl

99

..rletak p.c lar i den

garis l -:

:) Dlara

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

a) State the equation

b) Find the cquation

-{asarer-'

of the straight

of the straight

Diagram 2

line l'tl.

l ine SZ and hence. state its jr- intercept.

[5 nnrlts]

0 l

1 0 1

14 ma

.r berpusa:)LiZ ialah

f.l:=:r'arn 3 shows a solid cone rvith radius 9 cm3 ::: antl height Z cm is taken out of the solid.

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 .

Diagrarn 3

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

f r . .n= 22)7 /

@ marhsl

D:=ram 4 shows two sectors ORS? and OLfV with the same centre O. RWO isa semicircler:::: drar.nelcr.EO and RO = 2OV. ROV and OLIT are straisht lines.

= 7 cm and -L|OV = 60 .

t ' : . rg n = ??, ca lcu late

r i

rL

rhc perimeter, in cnr, of the wholc diagram,

the area, in cmr, of the shaded region.

103

[6 nrarAs][6 ma

L LI tcntan:

r : l l g mun :

i :rvediaka:

9 A group of 5 boys and 4 girls takc part in a study on the type ol plgnts founcl in a reser\ r.r:l1b1"1, 3*.u Each da1'. two pupils arc chosen at random lo wrrte a report.(a) Calculate the probability that both pupils chosen to rvrite lhe report on the first d.r. arrbo.r s.

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

c-alculate the probability that both pupils chosen to rvrite the report on the second day areof thc same gender.

I , iua orar-:

1 nvediaka:

-' marha..)

.rerrama.

r 148 met

I5 rrrurh'l

-\rtstter:

a )

b )

l0 Diagram 5 shows thc speed-time gtaph of a particle for a periocl of I seconds.

Trme t s t

Diagyam 5

State the length of time, in s, that the particle moves with unilbrm speed.

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 seconds is148 metrcs.

[6 lrarA.s]

b l

Speed m s r)

16 marhc

Anstuer:

l a l

r b )

r k e a d a I SI I l r

PQ

a ,

b t

l7 mark -

s iven tha t mat r i x p = (? -3 )

and mat r i x a=u ( f ! ) * . r l 1 , " t

(; ?)Find the value of A and of ft.

Using matrices, find the varue ofr and ofy that satisfy the following simultaneous linearequations:

2x 5y = - t7, r + 3 , y = 8 nto rh sll7

l2 marL:

.\rtsuer:

b r

. \ n.str 'er.

13 rr I Complete Table 1

Section B\48 ntarhs)

Ansruer four questions fiom this section.

in the answer space for the equation J = 2r, - r _ 3.

Table I

109

12 n tarhs l

r - 2 l - 0.5 I 2 3 4 4.5 5

v 7 -2 -2 J t2 . l a 42

Graph for Question 12

:n 110. Anc= l t : F-ctr t lt i" port of tht,quastirn, us( t lu,gtvph paper prot' iclt,cl on page 111. \ itu //?.r\ &sr .r - ' , i

Bv us ing a sca lc o1 2 cnrgraph of .r' - 2rr r ;l

[4 marha:

L ir unrt pac to I un i t 0n thc . \ ax is anc l 2fb r -2 , : . . r . : 5 .

( l n L , ; U l t t l . n \ ' - a t \ t - . , l ' i , . \ .

l + / l ? a r r . l : .

12 markc

. \rr stt,er':

b) R(li 'r gt(1plt ott pugt, 111.

c From yonr graph. f ind(i ) the value ol I $'hen .r

i i i ) the ,, aluc o1 .r. u hcn y3. ti.3 7 .

Drarv a suitable straight line on vour grilphecluation 2-t: 3r = 10 fbr -2 ::..r .:: 5.Statc these valuc-q o1 .r.

[2 rno rh s ]

values ol r nhich satisl-v thc

[4 ntarlts]

to find all thc

[4 mark ,

nilai r r

. l rr .- i tr ,r .

. { r -

. i) l) iagTant 6 shorvs trvo points, M and on a (--artesial plane

Diagram 6

'ft an,sflpnl3lien T is thc translatinn i

; j ).\ . 1 , ,

' f i : rns fc r rn ta t ion R is an an t ic lockrv isc , ro ta t io r r o f 90 , 'abo i r t the ccn t re r0 .2 .

( i ) S ta tc the coord in l tcs o f the imr lgc o fpo in i M un( le l t lans lo rmat ion R( i i ) s ta t ( ' the c r rc r r l in . tes o l thc in r i rgc o f po in t N r rndcr t r re { i r lo rv ing r . rn :1 i , rn . , r i i i . .

r a ) T ! ,b ' ' r 'R .L5 tnori

11ts

ruoya i ILr berloreL17 markc

Ansuer:

1 a ) ( i )

( i i ) (a )

( b )

r D l Diagrlm 7 shols three ABCD, EFGH and P@RS on a Cartesian piane.

Diagram

J

EFGH is the imagc of ABCD under transformation V.PQRS is thc image ttf EFCH under translbrmation W.

(i) Describe in full the translormation:( a ) Y(b) w.

(i i) Given that quadrilateral PQRS represents a region ol area,15.6 cm,in cm', of the region represented by the shaded region.

-{ltstoer.

' b ) ( i ) ( a )

, calculate thU ir re it.

[7 uior-lrsI

quadrilaterals,

1 1 5

(b. )

( i i )

, ) fang n1ua H The data in Diagram 8 shows the marks for an English Langrrage monthly tcst for 42 pupil.

l t l

25

33

25

2032383 53417

,1036233 128:14

3 72812263 l

3 1 2 647 21-it1 3929 3835 1:)48 11

3038392:l22lr4

Diagram 8

et Llsing data in Diagram 8 and a class interval ofb marks, conplete Table 2 in the ansrverl mar t a

rn anda be:I1 ntorka,

le ngk a pk

' t t n 1 1 8 .2 cm kepai t u .

spacc.

-{l sruer:

a l

14 tnorhsl

Table 2

bt Based on your tablc in (a),(i) state the modal class,

(i i l calculate the mean mark Ibr the Engtish Language monthly test and give your ans\\ (.:correct to dccin.ral places. 11 nort:,

.\nsuter:

b ) ( i )( i i )

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 trl jcr.,axis, draw a histogram for the data.

Midpoint

i4 morkc '.

1 1 7

(iraph for Question

r i !k segler-

! 'ratan Ier-:

. \ | s r? r . '

- ttefir graph on pago 119.

, D iagranr g r i r shows a so l id l igh ttable. Thc surface 1'IFGHJ is thers an inclint_'cl plant'and r.cctanglccclgt:s.

prism l ' i t lr recl. irrrgular birscunil irnl cross,-section ot t l lrLHCIl ts a horizontal plane.

PI,'IN on il horiz(rr::,.-prism. Rcctangle AJHI_.lE antI CF- are vertt(rt.r I,HGM t

Diagram 9(i)

,g yang s€

l3 m.ari.:

- vs=3

I)rrru full -scalc.1i om X.

1 / t s ruc f .

thc e lcva t ion o f the so l id on a lelt ic[] plane palrl lcl to _EF as vicrved

l i l r i ra i l i s l

Rajah 9 ' : :A so l id . ig t r t pr isnr wi th r rn i {b.nr cross-scct ior r Lr ! ,11. { is rcr rovcc l l i . 'nr the. , ,1 , , iI)iagranr 9rir. Th. rcmaining soiid is as sho*.n i. Ditrgram g(iil. Rccl.anglo \,.(/li ihorizontrrl planc. a.ll 'and,Yitr'ar.e r.ertical cdges. l. 'S = jl crl ancl ,>-C - 2 t,nr

12I

'+ tnerkcclengan f

i mqrl:c

kaan bu

Diagrarn 9(ii)

Draw full scale,(i) the plan of the rernaining solid.

(ii) the elevation of the remaining solid on a vertical plane parallel toliom Y.

,lirsa.'er'.

b ) ( i ) . ( i i )

14 narhslP1,l as vicu'ed

15 tnrtrhs)

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

Point Latitude Longitude

J

K

L

M

20" LJ

20" u30"s

25" T25" T

.v"Br"B

P is a point on the surfirce of theState the position of P.

Table 3

earth such that JP is the diameter of thc t,arth.l2 nr crl i.r I

r23

: t l ui t u d

i

r r l r l sepu I :

nilu

sepu r-nl Qrl? a:

ingltan ni:i l ntorl :c

(b) Calculate(i) the value ofr, if thc distance from J to K measured along the nleridian is 1200 n:..::rc----

miles,(ii) the value ofy, if the distance from J due west to -L mcasured along the common paralie-

of latitude is 3 270 nautical miles. Ii nrcrl:,

(c) An aeroplanc took off from J ar.rd flcw due rvest to 1- along the common parallel of latirudeand then due south lo M.II the average speed for the whole flight is 600 knots, caiculatc thc timc taken for the rvholeflight. 13 rnarAsl

Ansuer:

: 6 ( a )

( b ) ( i )

( i i )

( c )

125