Spm Mathematics 2006 K1

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SPM 2006 MATHEMATICS K1

nt is qur,stit)npoper cottsistsof. O rltu,stitnts. Aasri.,e| all quasti.on.s.Euch quesliort |-t;uctigy: L) ttttL((r o\' [t,ut. L.hotk,t ol ttrt5tr.q,7.5 A, B, C ond D. RDentlt question (lrno.r_r: one a ttsu.t,r'rtrtIt. progranmoble sciertti.fit:r.cLlt,ulatctr ! is aIlott,ecl. I

Round o1f50 941 correct to three sigrificant lrqLtres. .{ 509

B 5r0 c u0 940 D 50 900 rilah sei i al a h s e i girrls lur

T i m e : 1L h o u r s 1

r 1 0 0 1 "_ 1 0 1 ,= A 1001, B 1101, c 1000b, D 10100 I', I. Pelisf i.irr*rrrlirrpcrrrrgon li:I:lI r r n r i/ ' . s / ' l i s r p a r . ; r l l * l o g r r rSr Z r .l i _ r r straight line.

Erpre-<si351000 in stanclardrornr. .\ 11.51x 10tr B : 1 . 5 1x 1 0 ; C 3 . 5 1x 1 0 , r D 3 . 5 1x 1 0 .

Ii

11.0000025-1.3x10;A 1 . 2x t 0 ' t B 1 . 2x l 0 , C 2 . 3 7r t 0 , t D 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 ot. 2400cm and a length oi 3000 cm. 'fhe 1loor riill be covereclrvith tiles. llach tile is a square ol side 20 crn. Calculate the number of tilcs requirerJto cover thc floor fully. A f.il x 10r B 1 . 8x 1 0 . C 3.6x tol D 3.6 x 10" lngcn kep-:

.s.

oPQ .

What is thc value ofthe digit 2, rn birsclen. i n t l r c n u r n b e r1 2 0 8 , ? A10c200 850D250

Diagram

I

Filcl the yalueof r. A36 872 c 108 D 111 In Diagram 2. ellZ is a t&rrgent t0 tile circle centre O. at R. ptlS. OPQ rncl Ot ,t ar(' straight lines.

727

Lr I)ilgrarl 1 . t l r c s r l r r a 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 . tS' 7 ' I l ] . . r . : . : c l - i l i lr g ( ' l l l ( ' r l t .

Diagram 2 : : Ll the r':rlue o{ .r. \ r0 c50

a

r-

1;

D65

i!r'rrnl il sllo\\'s lilc :.1lc grirls.

Diagram tr.iangles rlral,n

urr

4

'Iht,

cc'ntrt ol' the cnlrrrgcrlcnt scal1' iirctol ltr(' Ct'ntre of Enlirrqemcnt

an(l ils

St'aleFactor l

A

tsa il Dt,'l tl

1 , ,D . ' , : , , ' , t-' . . \ i . r l t . r r r i r l p ' r r,,,r1- r r . j , , , . L . line QS7'.

II I

6 cnl

DiagXam B

I

i V h i c h o f t i r c t r i : r n g l e - r .A . B , C o r D . r: not :tn rnrage ol tr.ilrngle P u r t d e r a |,,tiltioD?

+a Diagl'am

I'29

5

'I'he

valuc ot cos r

I

ls

A ,i

c l1

u;

D

-+-+.r .

c

! 5

I n I ) i a g l r r m 6 . M p e i s r r r r g h t a ng l c d

it)

Trritlgle.

D

I

I

f*, r{)

Diagram

It is given that f/N = 1ll crn, Mp = 2q rrnd N is thc midpoint of lli\?. Find "r.r., the r:rlue of tal t,,.

A -rr., Lrah kulr 11'.

6

^o

12 r.3

C

_;) 12

D

13 12

\Vhiclr ol the ibllrrl ing reprcs(ints thc graph of .r' = cos -r for. 0 .,,. .. .r'

14 J)iagr.amT shou.sa ctrboiclrvith a horizontal basc ?'[.r!']V.

tE0,?

A

Diagram Z ..rtith PQ,

N r r r r l t l r " ; r n q l .b e l r r , . otnl r r , 1 , l . r nfee l l f and thc pliure S/?142. A IQI'R B lQTS c tQ\4;H D ..iQlIrS

ri ialah -

In Diagrarl8 t , P Q a n c lZ n a r i , r \ \ . ov r r r r L i i r

a llellgu!

poles on lr horizclntal pirrne. S i, (1 i)!tlt!

7F den.

Z/i such that PQ = S?.

131

]tl

B

l)iagranr 8 C flr, ,rngl" rleprF--ion ,'l'/' flrrtr 7'is

.\ _rPs

c _r'r.s

B

I)

RPT

QTS

I r r f ) i r g l a n r 9 . . / A i . r r r . r ' t i c r lflrrg 1,o1". A-l is horizontal. .I

f,

i-<

;15 n1

f)iagrarn .tub I'lrrr. ,ll llusat b,-l

,titud ll0 -'

\;ro

North

I

T l r e angle of eler':rtion o1 -,/ {ronr L is ,12' Tirc h e r g l r t .i n r r r .t . , lt l r , l l a g 1 , , , 1i.-. A 23.12 Cl ;l1.r-r 1 B 2Ci.0l D:lE.8i

18 In l)iag'am 10. N is the North l)ole. S is tl.re South Pole iind O is thc centre ofthe calth. R is tlrc tcntrc oi tht'circlc ol latitudc ll0 \. N

Points M and ,\' lie on a ]rorizontal pllnt'. The beLrring of M fionr N is 0tj0 . W h i c h o l t h e f o l l o * ' i n g d i a g r a m s shorvs the positions of .Ll ar.rdN?

{' N o tt l r

Diagram 'fhe 'i

20"Tr I . 1 OT

A B

133

10

position ol point P is (l ,.i; >. lil E ( 1 5 - S . 2 0E r r 1 5 S . 1 . 1 0I i ) I) , 1:):.. 11r E

r)unjukka,-. rlam bula.:telur" var a .\pril tid:s.

19 3tr r(1 rl = A 2-t: 1 B 2.r: r

Dl n'ltn + 3nI 1n

.lr) Sin\)lify lilnr + nn t r

All

0

B'!l

ll

f)iagrarn 11 is a pictogral)h jnL)\r.r..: ,:. trtttrrlret,rf r'69- -nlri ,rt .1.,r,J.,,. .. . F p l ' r ' r r l r r . T l r l r r r r r r r [ r , , or 'l , 1 l , ; - , . 1 , r NIalch ar.rd April ar.e not shos'n.

C D

,2n Given th:rt q7i

l't bruarv

1lt

N{arch

4rt

April

= ////t + ll.

3

.lanujrrJ.

express

/lt rn ternls ol t. A Ititnr ent I n

m=

,r, =

urrlda-.:l I.lll

ll

8-3rr

D

" 3n8

m=

. , i ' . (. ii r \ n n l l r r i

A B

ti

z;

lh _

jl 7' . r'2 l; lo

Z3

c -n

replcsents 200 eggs Diagram

5n 3n8 5n. 83n

II

A total o1 5000 eggs were sold in those four morrths. The nurnber of cggs sold in Nlarch was three tincs thc number of eggs sold in April. The numbcr cif eggs sold il N'larch rvas A 1500 c 2250 B 2000 D 3000

IL -

B i l r in : . , : \ l r i c i ai . - -

!

000000 000000000

l r ' , r h o n / , ,- _

" 6 17 4

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

J,

. l : i S i m'o l i f v I ] 1 - " i l . A B C D ll

\ 2tt.7l 2\72 2t, x7. 216x7l

14t I

Thc mode for the data i-qB and the meciiarr rs 4. Trvo netv picces of data. 4 and i rier.c put into the sct. ClalcLrlatethe nrean fbr those eight piece-r oi data. A ,1.00 c .1.25 B 4.13 D 4.50

List all the inteElers r rvhich satisfv both thc rncqualities l. r . . ' , n , 1 '2 , . r r 4 r .r.. l. .1 A -1.0, 1,2,3

B 0, 1,2,3 c 1.0,1 D 0, 1 li

\Mriclr of the follo',ring glayrh. represenrs 2lt? J' = 10 A'

T.rblc 1 shows the distribution of tl.rescores o l a g r o u p o f y , u p i l si r r ; r q u i z .

Table I The median scoreof tht: clistribution is C2 1.5 D 2.5

Ai B

135

,/1..

,;.1 Diagram l3 'l'hc

rcgion t1) ;' Q ) i s e q r r i v a l ( ' n t t o t h { ' legiol C P .r 0 A 1'.,Q' DI B P'r Q' Q

l-t nta Ll

r rliperoit: ' 1 0 0o r a r . :

il1

.irll gitlnb..l

,.lrahagi:.:

'l'rllle

2 slious cltitlr olttrtittt'tl frottl a sulr'cr of 100 lclevision vicu'r'rs. Diagrant 14 is a \icnn
-t{'-}..

PropJrammes rrYatched

Bilangan :)enonton

t^l\ (,\\ :

55 61

- l)olrs

t2

Nots

55 61 I rincl Spolts otrlr

' r r l \I E | l l . r ' l j l i r ' t l )l .l l ,orrlt \ . r r - : r anrl r r , l Etrtcttrtirtttrurt \eu's

N"ru",r,rt,'

I

12 ;5

]

%

I

29

S1,,.rL+rll

Tablc 2

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

tg menonl r lnenonl tr

, 1. 1) d, 2. Koordtr. lil l1

It is givcr tlrrt the univc'rsal set. ' l l 1 . r i s a l r i r t t e g c r ' la r t r l i = {r : l9 ,.. r set R = l.r : r is a ntLntbcr slrch that the sum o{ its tuo digits is lttr cvert rlullberJ. ! ' i 1 d - s e tR .

A B c D

Diagram

1,1

Find thc nutnbel ol viervers rvlto \!iit(h. l tle\v. :rllrljrl:,, , nl' rtrirr'll'. :l',)r'1"r progfaDrnles.

l 2 o . 2 2 . 2 . r .2 6 . 2 s l l 2 l . 2 3 .2 r ' . 2 1 . 2 9 1 '2i. '291 { 1 9 .2 1 . 2 3 . 2 5 . 1 2 t .2 3 . 2 5 . 2 i . 2 9 . i J ( J i

426 B39

c .17 D 51

'llre

c o o r c l j t u t t e so t p o i n t P l r r t ' 1 . 1 . , r : : t h e , g l a d i c r t to i t h t ' s t r a l g h t l i r r r '1 ' ] Q: - - . 'lhc c o o r r l i u a t c so f p o i n l Q c r r L L l ri "i C rjl. 1 A ,;1.3r

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

1)

13 .:r.9,

l-.'

137

D

r. .

rl langsung S apabila

li3 in Diagranr 15, !?'is graclient

1 1s t r a i g h t l i n c w i t h

I t i s g i v e n t h n t & , v a l i c s t l i l e c t l 1 r ' ,i t i t t h c c u b e o f T r i t n d t . = 8 r v h e n2 = - 1 . C l a l c u l a t ct h c v a i u c 0 l p w h e n l { , = 2 ;

].

'l

)i.

A'l

B3

C6

E

D24

2

It is given t h a t . v - , 1 . a n t i 1 ' =

:3 apabilr,

t

11'11s1

.t = 36. Calcu latt: t l r c v a l u e o l . r ' rvhen r = 4. A2 c l8

L

B9 , sct bas

D 4u

TLrtrlr:3 shorvs t\\'o sets of values o1p. 17 and l *'hich satisfi r ., p q .

Diagram 15 I,'indthc r interceptof thc straigl.rtlinc El'.

a1

L2

BJ

.1

C3 D12

I t i s g i v e n t h a t s e t G i s 1 1 ,2 . j l , 5 . 6 . 7 . E . 9 , 1 5 . 1 , 1 ,1 5 ) . ,A nuntbel is chosen irt randour from thc elr:rnents of sct Ci. Find the probabilitv that thr: numbel chosen is a primc n unr bcr..

lr=

A

j-11

ts+

lt

c

B3

1

3e 1 5 !7

D I7i

o

C

D

( l a l c u l a l , ct h e v a l u e o f r r . A 0.2 C 2..1 B 1.2 D ;.1

6 11

A box contains 4 retl marbles. 2 I'hite rnarbles and lr number o{ blue nrarorcs. A rnarble is cliusrn at rand(rn from the box. 1'he probability of choosing Lrrvhite ntalble .1 t" 8' Find the probabilit,v o f c h o o s i n g a b l u e marble. A1

Tablc 3

,!

139

r')

l + 3 \l 2 1'

A

I1 15

1l t3r

B

13 16

4 j 4l

c

8 15

1l 13

Dl

7;] 10

0'

40 If (3

8 :J I

,-\ ,

lli 3

2 r l + 21 - 1 7 1then . 7r

AI

C1

B2

D7

2