5P|v|

, 1sa: r 4- J-: Daper I

Time:1 L1

hours

satu.Toir c:

r i l a h s e iia lah se igirrls lur

lngcn kep-:.s. oPQ .

|-t;uctigy: nt is qur,stit)n poper cottsists of. O rltu,stitnts. Aasri.,e| allL) ttttL((r o\' [t,ut. L.hotk,t ol ttrt5tr.q,7.5 A, B, C ond D. RDentlt question

! progranmoble sciertt i.f i t: r.cLlt,ulatctr is aIlott,ecl.

I Round o1f50 941 correct to three sigrif icantl rqL t res ..{ 509B 5r0c u0 940D 50 900

Erpre-<s i351 000 in stanclard rornr..\ 11.51 x 10trB : 1 . 5 1 x 1 0 ;C 3 . 5 1 x 1 0 , rD 3 . 5 1 x 1 0 .

1 1 . 0 0 0 0 0 2 5 - 1 . 3 x 1 0 ; -A 1 . 2 x t 0 ' tB 1 . 2 x l 0 ,C 2.37 r t0 , tD 2 . 3 7 \ t 0

. \ r c c t a n g u l a r . f l o o r h a s a r v i d t h o t .2400 cm and a length oi 3000 cm. 'fhe 1loorriil l be coverecl rvith tiles. llach tile is asquare ol side 20 crn.Calculate the number of tilcs requirerJ tocover thc floor fully.A f . i l x 10rB 1 . 8 x 1 0 .C 3 . 6 x t o lD 3.6 x 10"

What is thc value ofthe digit 2, rn birsc len.in t l rc nurnber 1208,?A 1 0 c 2 0 08 5 0 D 2 5 0

quasti.on.s. Euch quesl iort(lrno.r_r: one a ttsu.t,r' rtrt It.

r 1 0 0 1 " _ 1 0 1 , =A 1 0 0 1 ,B 1 1 0 1 ,c 1000b,D 10100

I ' , l i : I : l I I . P e l i s f i . i r r * r r r l i r r p c r r r r g o n

r r n r i / ' . s / ' l i s r p a r . ; r l l * l o g r r r r r . S Z l i _ r rstraight line.

I i

Diagram I

F i lc l the yalue of r .A 3 68 7 2c 1 0 8D 111

In Diagram 2. ellZ is acircle centre O. at R. ptlS.ar(' straight lines.

t&rrgent t0 ti leOPQ rncl Ot ,t

727

SPM 2006 MATHEMATICS K1

Lr I ) i lg ra r l 1 . t l r c s r l r ra r r , a ' l - l i _ l .i r t l i g c o 1 t h e s c l u r r r . t ' S 7 ' I l ] . . r . : . :c l - i l i l r g ( ' l l l ( ' r l t .

:\a

r -

Diagram 2

: Ll the r':rlue o{ .r.r01 ;

c50D65

i ! r ' rrnl i l sl lo\\ 's l i lc tr . iangles r lral,n urr: . 1 l c g r i r l s .

Diagram 4

'Iht, cc'ntrt ol ' the cnlrrrgcrlcnt an(l i ls

scal1' i irctol ltr( '

Ct'ntre ofE n l i r r q e m c n t S t ' a l e F a c t o r

l

A

tsa

i lD t , ' l

t l 1 , , D . ' , : , , ' , t ' - . . \ i . r l t . r r r i r l p ' r r , r , , 1 - r r . j , , , . L .

DiagXam B

iVh ich o f t i r c t r i : rng le - r . A . B ,r: not :tn rnrage ol tr. i lrngle P| , , t i l t i oD?

C o r D .ur tder a

line QS7'.

III

6 cnl

I+a

I'29

Diagl'am 5

' I 'he valuc ot cos

IA,i

u;

In I ) iag l r rm 6. Mpe is r rTrri t lgle.

r rgh t an g lcd

Diagram 6

It is given that f/N = 1ll crn, Mp = 2q "r.r.,rrnd N is thc midpoint of l l i \?. Find the

r : r lue o f ta l t , , .

A -rr . ,

^ 12o r .3

\Vhic l rgraph

o l the ib l l r r l ingof .r' = cos -r for. 0

A

c

14 J)iagr.am T shou.s a ctrboicl rvith a horizontalbasc ?'[.r!']V.

Diagram Z

N r r r r l t l r " ; r n q l . b e l r r , . o n t l r r , 1 , l . r n e f e l l fand thc pliure S/?14 2.A IQI'RB lQTSc tQ\4;HD ..iQlIrS

In Diagrar l t 8 , PQ ancl Zn ar i , r \ \ .o vr r r rL i i rpo les on l r ho r i zc l n ta l p i r r ne . S i , ( 1 i ) ! t l t ! ] t lZ/i such that PQ = S?.

r l s

c

D

l1!5

-+-+.r. i t )

I

f*,r { )

L r a h k u l r11'.

. . r t i t h P Q ,

_ ; )1 2131 2

reprcs( in ts thc.,,. .r ' .. tE0,?

D

C

D

r i ia lah -a l le l lgu!

7 F d e n .

I

1 3 1

7 ' i s

flrrg 1,o1".

Nor th

B

l)iagranr 8

f l r , , r n g l " r l e p r F - - i o n , ' l ' / ' f l r r t r

.\ _rPs c _r'r.sB RPT I) QTS

I r r f ) i r g l a n r 9 . . / A i . r r r . r ' t i c r lA-l is horizontal.

.I

C

f,

i - < ;15 n1

23.122Ci .0 l

. t u b I ' l r r r ., l l l lusat b,- l, t i tud l l0 - '

\ ; ro { '

20"T rI .1O T

Cl ;l1.r-r 1D : l E . 8 i

TlreTircAB

f)iagrarn I

angle of eler':rt ion o1 -,/ {ronr L is ,12'

h e r g l r t . i n r r r . t . , l t l r , l l a g 1 , , , 1 . . i -18 In l)iag'am 10. N is the North l)ole. S is t l.re

South Pole i ind O is thc centre ofthe calth.R is t l r c tcn t rc o i th t ' c i rc lc o l la t i tudc l l0 \ .

N

Diagram 10

'fhe position ol point P isA ( 1 5 - S . 2 0 E r ( l , . i ; > . l i l EB r15 S. 1 .10 I i ) I ) , 1 : ) : . . 11r E

Points M and ,\ ' l ie on a ]rorizontalThe beLrring of M fionr N is 0tj0 .Which o l the fo l lo* ' ing d iagramsthe positions of .Ll ar.rd N?

Not t l r

pllnt ' .

shorvs

'i

133

r)unjukka,-.r lam bu la . : -

telur" var a.\pri l t id:s.

0

I t i t n r e n t I n

u r r l d a - . : lI . l l l I L -

B i l r i n : . , :\ l r i c i a i . - -

1 9 3 t r r ( 1 r l =A 2-t: 1B 2.r: r

. lr) Sin\)l i fy l i lnr + nn t r

A l l

B ' ! l

l l Given th:rt q7i3

/ l t r n t e rn l s o l t .

A m = l l8 - 3 r r

,r, = "3 n 8

A iB 1 . 5

8 3 n

ti. , i ' . . i ( i r \nn l l r r i ; lh _ Z3 l r ' , rhon / , , -_

zl 7

A j ' . c "r'2 6B l ; n 17

lo - 4

J,. l : i S imol i fv I ]1-" i l .'

\ 14t I

A 2 t t . 7 lB 2 \ 7 2C 2 t , x 7 .D 2 1 6 x 7 l

l l List all the inteElers r rvhich satisfv boththc rncqua l i t ies

l . r . . ' ,n ,1 l . , . r r 4 r . r . ..1 '2

A - 1 . 0 , 1 , 2 , 3B 0 , 1 , 2 ,3c 1 .0 , 1D 0, 1

l i T.rblc 1 shows the distribution of t l.re scoreso l a g r o u p o f y , u p i l s i r r ; r q u i z .

Table I

The median score of tht: clistribution is

f ) i ag ra rn 11 i s a p i c tog ra l ) h j nL ) \ r . r . . : , : .

t r t t t r r l r e t , r f r ' 6 9 - - n l r i , r t . 1 . , r , J . , , . . . .

F p l ' r ' r r l r r . T l r l r r r r r r r [ r , , r ' o l , 1 l , ; - , . 1 , rNIalch ar.rd Apri l ar.e not shos'n.

. l anu j r r J . 000000l ' t bruarv 000000000N{arch

April

! replcsents 200 eggs

Diagram I I

A total o1 5000 eggs were sold in those fourmorrths. The nurnber of cggs sold in Nlarchwas three tincs thc number of eggs soldin Apr i l . The numbcr c i f eggs so ld i lN'larch rvasA 1500 c 2250B 2000 D 3000

Diaglan 12 shows a sct ot six pieces ofdata rvhere r rcpresents an integcr.

Thc mode for the data i-q B and the meciiarrr s 4 .Trvo netv picces of data. 4 and i rier.cpu t in to the sc t .ClalcLrlate the nrean fbr those eight piece-roi data.A ,1.00 c .1.25B 4 . 1 3 D 4 . 5 0

\Mriclr of the follo',r ing glayrh. represenrsJ' = 10 2lt?A '

CD

Dl

n ' l t n + 3n I1n

1lt4rt

, 2 n= ////t + l l . express

D m =

5n3 n 8

5n.

C 2D 2.5

135

,/1..

,;.1

l-t nta Ll

r r l ipero i t :' 100 orar . :. i r l l g i t lnb. . l

, . l rahag i : . :

Bilangan:)enonton

Diagram l3

' l 'hc rcgion t1) ; 'legiolA 1 ' . , Q 'B P ' r Q '

Q) i s eqr r i va l ( 'n t to th { '

C P . rD I

0Q

t 2

i l1 ' l ' r l l le

2 sl ious clt i t l r ol t tr t i t t t ' t l frott l a sulr 'cr

of 100 lclevision vicu'r ' rs. Diagrant 14 is a

\ icnn <l i lgtanr that 1'( ' l )resetl ts part of t i l t '

i n { i r l r n r t i on i n T r rb l e 2 .

PropJrammesrrYatched

-t{'-}..

t^-l \ ( , \ \ : 55

- l ) o l r s 61I

No ts r i nc l Spo l t s o t r l r 12

\ . r r - : r r r , l E | l l . r ' l j l i r ' t l ) . l l l , ' r r l \ ;

5 5

6 1

t g menon l

r lnenonl tr

, 1 . 1 ) d ,2. Koordtr.l i l l 1

1 )l - . '

\eu's anrl Etrtcttrt irtttrurt orrlt I 5 ]

N"ru",r,rt, ' I % IS 1 , , . r L + r l l 2 9

Tablc 2

f , n t ( , r ' l . u D l l l f r r r

I t i s g i v c r t l r r t t h e u n i v c ' r s a l s e t .

i = { r : l9 , . . r ' l l 1 . r i s a l r i r t tegcr ' l a r t r l

set R = l.r : r is a ntLntbcr slrch that the

sum o{ i t s tuo d ig i ts i s l t t r cver t r lu l lberJ .

! ' i 1d -se t R.A l2o. 22. 2. r . 26. 2s lB l 2 l . 2 3 . 2 r ' . 2 1 . 2 9 1c {19. 21. 23. 25. '2 i . '291

D 1 2 t . 2 3 . 2 5 . 2 i . 2 9 . i J ( J i

Diagram 13 is a \irrrn rliagranl shorvttrgthe univclsal sct -i. set P ald set Q.

Diagram 1,1

Find thc nutnbel ol viervers rvlto \! i i t(h. l

: l ' , ) r ' 1 - " r t l e \ v . : r l l r l j r l : , , , n l ' r t r i r r ' l l ' .p rog faDrn les .4 2 6B 3 9

c .17D 51

' l l re coorc l j tu t tes o t po in t P l r r t ' 1 . 1 . , r : :

t h e , g l a d i c r t t o i t h t ' s t r a l g h t l i r r r ' 1 ' ] Q : - - .' l hc coor r l iua tcs o f po in l Q c r rLL l r i i "

A , ; 1 . 3 r C r j l . 1

13 . : r . 9 , D r . .

1 3 7

rl langsungS apabila

) i .

l i 3 in D iagranr 15 , !? ' i s 11 s t ra igh t l inc w i th

graclient ].

Diagram 15

I,'ind thc r intercept of thc straigl.rt l inc El'.

a1L 2

B J .1

I t i s g iven tha t se t G is 11 , 2 . j l ,9 , 15 . 1 ,1 , 15) .,A nuntbel is chosen irt randourelr:rnents of sct Ci.

TLrtrlr:3 shorvs t\\ 'o setsand l *'hich satisfi r .,

I t i s g iven thn t & ,thc cube o f Tr i tnd t .C la lcu la tc thc va iuc

' l

A ' lE

B32

va l i cs t l i l ec t l1 r ' , i t i t= 8 r v h e n 2 = - 1 .

0 l p when l { , = 2 ;

C 6

D 2 4

:3 apab i l r ,

L

, s c t b a s

lr=

C 3

D 1 2

It is given

.t = 36.Calcu latt:A 2B9

tha t .v - ,1 .

t l rc va lue o l . r 'cD

an t i 1 ' = t 11 ' 11s1

rvhen r = 4.l 84u

of values o1 p. 17p q .

Tablc 3

( la lcu la l ,c the value of r r .A 0 . 2 C 2 . . 1B 1 . 2 D ; . 1

Find the probabil itv that thr: numbel chosenis a primc n unr bcr..

A j - - c 6

1 1 1 1

ts+ D 7l t I i

A box conta ins 4 re t l marb les . 2 I 'h i ternarbles and lr number o{ blue nrarorcs.A rnarble is cliusrn at rand(rn from the box.1'he probabil ity of choosing Lr rvhite ntalble. 1t "

8 'Find the probabil it,vmarble.

A 11

B 3o

5. 6. 7 . E.

from thc

3e 15! 7

A

B

c

, \ , r ' )- l + 3 l -1 ' \ 2

I 1 1 l1 5 t 3 r

1 3 4 j1 6 4 l

8 1 l1 5 1 3

7 ; ]1 0 0 '

lli 3

of choos ing a b lueDl

4 0 I f ( 3

A I

B 2

2 r l + 2 1 - 1 7 1 .then 7r

C 12

D 7

C ,!8:JI

D

1 3 9