Spm 2007 Mathematics P1

T im e :r lt

Paper 1

of 40 questions'Answer all questions.Each ''.', Instructio nszThis questionpaper cortsists questionchooseone on-cli'' o'f'"n'*u" A'.8' C an'd'D' For each by is four followed' -1g "ioi''"t ed' on-p, og,om mable scien'tific calutlator is allow 1 Round off30 106 correct to three significant figures. 30 106 betul kepada tiga angl<'a Biund.q,rl?an bererti. C 30 110 A 30 000 D 30 200 B 30 100 Express 1.205 X 10aas a single number' (Jngh,apkan1.205x 7Oasebagaisatu nombor tunggal. A 7205 B 12 050 c 1 205 000 D 12 050 000 0.0078-6x105= A 1.83 x 10-3 B 1.83 X 105 c 7.74 x ro3 D 7.74 X L0-5 110010,- 11101,=

A 1o1io1, B

11000r-

tii,,j 0ll

R

Diagram I Rajah I Find the value of r. Cari nilai x.

A65 870

c80 D9 0

In Diagram 2, PQRW is a rhombus i rrlt WVP ts a straight line' Dalam Rajah 2, PQRW ialah sebuah t-cn-""' dqn VWP ialah garis luru's' q

c

1oolo1'

D

101012

= 3420., find Given3x53+4x5'+5Y the value of Y. = Diberi 3 x 53 + 4 x 52 + 51' 3420-,,cari

nilai y. Ag 82D4

*n n

120",^

C3

In Diagram l, MNP]RS?[/ is a regular octagon and.TUWV is a straight line' Dcilim Rajah 1, MNP]RSTU ialah sebtt'q'h garis olrtagon iehata d.an' T\IVW ialah lurus.

Diagram 2 Rajah 2 Calculate the value of r + l' H i tungni l ai x+ )' .

A B

160 170

c $

220 230

Diagram 3 shows a circle, PFQ, centre O. EFG is a tangent to the circle at F. Raj ah 3 menunjukkqn sebuahbulatan, PFQ, berpusat O. EFG ialah tangen lzepada bul'qtan ittt diE

Semua sisiempat itu diputa:rkan' 90" pada pusctl O. Antara ya ng beril<,ut,yan'g manaltah putaran yang betul?

Clockwise Ihat arah jam Anticiockwise Lawan arah jam Anticlockwise Lqwan arah jam Anticlockwise Lawan arah jom

Diagram 3 Rajah 3

10 Diagram 5 shows two sqrrares,PQRS and

Find the value of r. Cari nilai x.

A32 848 /g

c61 D74

KLMN, drawn on square grids. Rajah. 5 menun,juhlzan dua segiempat samo, PORS dan KLMN, dilukis pada grid segiempatsQ,nra.

Diagram 4 shows four quadrilaterals, V7, X, Y and Z, drawn on square grids. Rajah 4 menuniuhkan empat sisiempat' W' X, Y dan. Z, dilulzis pada grid segiernpat san1.a.

\

s

L

t

a

M

w Diagram 5 Rajah 5

Diagram 4 Raiah 4 Ati the quadrilateralq.are rotated 90" about the centre O. : Which of the following is the correct rotation?

PQ,RS is the image of KLMN under an enlargement with centre O. Find the scale factor of the enlargement. PQRS ialah imej bagi KLMN di bawq'h swatu pembesaran pada Pusat O. Cari faktar skala pembesaran itu..

A+

{r2

B+

tr ) B

(f

ll

In Diagram 6, USn and VQ?S are straight lines. Dalam Rajah 6, USR d.an VQTS ialah garis Iurus. U

The value of cos 0 is Nilai bagi hos 0 ialah A, A' -;

4

c --3 o

B -+ o

D+o

L3 Which of the following graphs represents y=sinrfor0o
Diagram 6 Rajah 6 It is given that ?S = 29 cm, P@ = 13 cm, = @ft = 16 cm and .ir #. "' Find the value of tan yo. Diberi bahawa TS = 29 cm, PQ = 18 cm,

B

@ft = 16 cm d.an sin .ro - 9. 17' Cari nilai tan yo.

AL2 5 B5

12

c

*5 L2 t2 --:D

c

b

t2 In Diagram 7, O is the origin and JOI{is a straight line on a Cartesian plane. Dalam Rajah 7, O ialah asalan darv JOK ial.ah garis lurus pada suatu satah Cartesan,

D

Diagram 7 Rajah 7

t 4 Diagram 8 shows a pyramid with its

rectangle base @BS?. Rajah 8 menunjukkon sebuah piramid, dengan tapak segiempat tepat eRST.

16 Diagram 10 shows three points, p, e and R, on a horizontal plane. \ajah L0 menunjukkan tiga titik, p, e dan R, yang terletak pad,a suqtu sq,tah mengufuh.

Diagram t0 Rajah 10

Diagram g Rajah 8 Vertex P is vertically above ?. Name the angle between the plane p?S and the plane PTQ. Puncak P berada tegak di atas T. Namakan sudut di antara satah pTS dengan satah PTQ. A LPQT C LSPQ B LPST D LSTQ

15 In Diagram g, PQ and fiS are two vertical

poles on a horizontal plane. The height of .RS is twice the height of pe. The angle of depression of P from vertex B is bB". Dalam Rajah 9, pQ d,on RS ialah d.ua batang tiang tegak yang terletah,pada satu perrnukaan mengufuk. Ttnggi RS ialah d.ua kali tinggi PQ. Sudut tund.uk p d,aripuncak R ialah 53",

It is given that Q lies due north of p and the bearing of .R from @ is 02b". Find the bearing of p from R. Diberi bahq,wa Q berada d,i utara p d,aru bearing R dari Q ialah 078". Cari bearing P dari R. A 0490 c 22go B 1010 D 28L" 77 In Diagram 11, N is the North pole, S is the South Pole and NOS is the axis of the earth. Dalam Rajah 11, IJ iq,lah Kutub Utara, S ialoh Kutub Selatan dan UOS iolah naksi bumi. N/U 250 250

ol

Diagram 9 Rajah 9 Calculate the height, in m, of RS. Hitung tinggi, dalam m, bagi RS. A 15.07 c 30.14 B 26.54 D 53.08

Diagram ll Rajah lt Find the position of point @. Cari kedudukan titik Q.

E) (52' ry_,15_'^

c

A (38"N. 15" E)

(52"!:11: iis" r, 1b"?) ") (52"\:95-1^E) D E) Gs" r, B iir (52" fJ,'65"T) iss" rr',6b" ?)

Equator 18 P and Q are two points on thelies and O is ttre centre of the earth' Q W 40" is 4"" *tt of P- The longitude of P a'rd LP)S= r25"' Find the longitud'e of Q' pada i ai" Q talih d'ua titik vang terletah' Khatulistiwa d'an O iatah pusat bumi' Q P ialah terletah ke timur P' Longitud bagi 40" B dan LPOQ= 125"' Cari longitud basi Q' C 140'E A bb"E 140" T bb" T 165" E gb'E D B t65" T gb" ?

of T and K. 1|f r Diberi f =*lryX,unghap

m dalam sebutan

T dan K.

p-

-

3X:

..

t

as

can be wntten

t'7

=L t ot"h ditulis sebogai 3Jco

t

A

' ;r-5

c

2 t r5

B

*r'

D

21xs

,l 7 J

I

24 SimPIifY (enl I'

x e-'f"'

Ringhasl<,an (esl-o;a

A e'f B e'f-"

A x< -

, expressm in terms 20 Given that T = +"1+ J V II

B m =BKT'

'I

23 -:-

x e-'f'. cef D ef-' 2x

ts

2x ialah PenYelesaianbagi 4x + 5 < 1 - ff

l t6

m =g KTz

D+

-5 2b The solution for 4x+ 5 < 1

19 \2x-Y)'-x(x-Y)= A 3x2_ 3xY+Y2 B 3x2-lxY+Y2 C af+xy-y2 D 3f-\xY-Y2

A

c+

A+ B+

c

T2

m--rK a

D * =#

B *..- t

7r Z

C ) c< - T

6-2

D ) c< - n

shows the 26 Diagram 12 is a bar chart which -August in of handphones' The sales ;i"t are not shown' Rajah 72 ialah carta Palang Yang jualan telefohbimbit' Jualan menunjuLtlzan pad,a 6ulan Ogos tidak' ditunjulehan' Numberof handPhones Bilangan telefonbim'bit

3

P+2 :--r^ r.as a single fraction -T 21 Express T in its simPlesbform' P-3 P+2 ' -" satu sebagai Unghapkan T T pecahan tunggal d'alarn bentuh termudah' -3-P-P2 ^ -3+P-P'

99.

AT

c--n -

- g- p- p2 B ---F-

D

".#-!

= 2x - 1, find the value Given that =-l of x+*-l = 2x - 7, cari nilai x. Diberi t;

0@ -

Mav Mei

June Jun

JulY Julai

August Ogos

Diagram 12 Raiah 12

Month Bulan

The sales in August is 4O% of the total sales during the four months, from May to August. How many handphones were sold in August? Jualan padabulan Ogosiqlah 40% d.aripada jumlah jualan seponjong empat bulan itu, dari bulan Mei hinggo bulan Ogos. Berapah,ah bilangan telefon bimbit 1,ang dijual pada bulon Ogos? A60 872 C L2O D 740 27 Diagram 13(i) is a bar chart showing the number of students from three schools.p. @ and -8, who participate in the ,,program Latihan Khidmat Negara". Diagram 13(ii) is a pie chart showing the number of these students, according to gender. Rajah 73(1) ialah carta palang yang menunjukkan bilangan mitrid dari tiga buq.h sekoloh E Q dan R, yang menyertai Program [,atihan Khidmat Negara. Rajah 13(ii) iqlah carta pai yang rnenunjukkan bilangan murid-murid ini, mengikut jantina.

Boys Lelaki

Girls Perempuan

Diagram l3(ii) Rajoh L}(ii) Calculate the value of r. Hitung nilai x. t A T2O c 200' B 150 D 2IO 28 Mlhich of the following graphs represents y=-i+5? Antarq yang berikut, yang manakcr.h mewakiligrdfy=-x2+5? A

B Number of students Bilangan murid

t20 (

///

n

100

C

80

'//l

60

772

40 20

D

a

R

ffiflGlrls ffi ru Prrr,,,p,ro, W

Boys toioni

P

Diagram 13(i) Rajah 13(i\

School Sekolah

w

List all the subsets of set X = {m, n}. Senaraikan senl .ua subset bagi set y = {m, n}. A {m} , {n} B {n},{n\.{} C {m} , {n} , {m, n} D {m\,{n},{m,n},{}

30 Diagram 14 is a Venn diagram showing the

universal set, ( = {Form Five students}, set | = {Students who play badminton} and set 14 = {Students who play tennis}. Rajah 14 ialah gannbar raiah Venn yang menunjukkan setsen1.este,, f = {Murid-murid Tingkatan Lima), setL= {Murid-muridyang bermain badmintonj dan set 14 = {Murid" murid yang bermain tenis\.

SB Determine the y.intercept of the straiglrt line4r+2y+5=0. Tentukan pintdsan-y bagi garis lurus 4x+2Y+5=0. 5 5 A 4 2 5 5 D B 4 2

l4 A box contains 5 red marbles and 21 gleem rnarbles. Lim puts another 4 red marblcm and 1 green marble inside the box. A marbb is chosen at random from the box. What is the probability that a red marhle is chosen? Sebuahkotak mengand.ungi5 biii euli mer& d,an2I biji euli hij au. Lim mernasukkan 14fr 4 biji Suli rnerah dan I biii euli hiiau k dalam kotak itu. Sebiji guli dipilih sec(ma rawak daripada kotah itu. Apakah kebaranghalian sebiji gu.li merffi akan dipilih?' a5c5 31

3 1 Given the universal set, t = P U Q, set P = {0, 1, 2} and set Q - {2, 3, 4, 5}, find the value of z(€). Diberi set senlesta, t = P U Q, set P = {0, L, 2\ dan set Q = {2, 3, 4, 5\, cari nilai bagi n(l). C 5 A7 D4 86

3 2 The gradient of the straight line 3l + 2y = 5is Kecerunart bagi garis lurus 3x + 2y = 5 icilah

B-2

C D

D*

Bt

Given n(€) = 60, n(L) = 25, n(M = 12 and n(L n M) = 8, find the'number of students who do not play the two games. Diberi n(t) = 60, n(L) = 25, n(M = L2 dan n(L n Xl) = 8, cari bilangan murid yang tidah berrnain d.uapermainan itu. c3 1 A15 D 52 B23

A- 3

26

q

Diagram 14 Raiah !4

3 2 2 3

35 In a training session,Ann has many triah to score a goal. The probability that Ann scores a goal in a trial it

. # In 60 trials chosen randomly, how ma4p times does Ann fail to score a goal? Dalam satu sesi latihan, Ann mernbu&, beberapa percubaan meniaringkan gol* Kebarangkalian Ann meniaringkan gN 9 nlan

Dalam^. 6O- percubaan yang dipilih , seccna rawah, berapa kq.lihah Ann gogod rnenjaringkan gol? A11C33 827D49

36 Table 1 shows some vhlues of the variablem r and y. Jadual l, menunjukkan beberapanilai bqd pembolehubahx dan y. JC

2

n

J

4

32

Table 1 Jad.ual I

It is given that y varies directly as the cube of r. Calculate the value of n. Diberi bahawa y berubah secaro langsung dengan huasa tiga x. Hitung nilai n.

c1 6 D30

A4 B8

g7 P varies inversely as the square root of M. Given thht the constant is ki find the relation between P and M. P beiubah secara songsang dengan punca h,uasa duq. M. Diberi k ialah pemalar, cari hubungan ontqra P dan M. A

P=h,Mz

z=8. Hitung niloi z apabilat = *o d.anY = 6.

c32 D72

A2 B r.8

= " (_i;)H) A [3)

B g)

c ffi ?on) DH_?)

40 Find the value of m in the following matrix equation: Cari nilai m dalam persafiraan matriks berikut:

B p= 4 M2

C P = kM

( z - g \_ z/o -\ a

b

D P = * ,.

\+

twJ

38 The relation between the variables r, y and.zisrol.

Diberi baho.wa r = +4 ' apabila ! = 2 don

z

It is given that r =

f

when ! = 2 and

z-= 8. Calculate the value of z when a = fr and y=6. Hubungan antara Pernbolehubah' pembolehubahx, y d'an z talah x'

I'

1 .A 83

7l

1 \= ( ?

ml - \ -2 C 4 D6

-?\ rl

SPM 2OO7EXAMINATION Paper 1 1B 28 6C 7A 11 D 12 B 16 C L7 C 2t B 22 D 26 C 27 C 31B 32 C 36A 37 B

3C 8B 13C 188 23 A 28 B 338 38B

PAPER

4D 9C 14 D 19A 24 C 29 D 34 B 39A

5B 10D 15D 20 A 25 B 30C 35C 40 B