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SULIT 1449t1 MATHEMATICS KERTAS 1 I 1^ JAM 4 1449t1 MAJLIS PENGETUA SEKOLAH MALAYSIA (CAWANGAN PULAU PTNANG) MODUL LATIHAN BERFOKUS SPM 2013 MATHEMATICS KERTAS 1 lJAM 15 MINIT 1. 2. JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU Keftas soalan ini adalah dalam dwibahasa. Soalan dalam bahasa lnggeris mendahului soalan yang sepadan dalam bahasa Melayu. Calon dikehendaki membaca maklumat pada halaman belakang kertas soalan ini. www.myschoolchildren.com 3. Modul latihan berfokus ini mengandungi 31 halaman bercetak dan t halaman tidak bercetak [Lihat halaman sebelah more examination papers at : www.myschoolchildren.com

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Trial SPM 2013 / Kertas Percubaan SPM 2013 Penang

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Page 1: Trial spm penang_2013_maths_paper1_paper2_[q]

SULIT1449t1MATHEMATICSKERTAS 1

I1^ JAM4

1449t1

MAJLIS PENGETUA SEKOLAH MALAYSIA(CAWANGAN PULAU PTNANG)

MODUL LATIHAN BERFOKUS SPM 2013

MATHEMATICSKERTAS 1

lJAM 15 MINIT

1.

2.

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

Keftas soalan ini adalah dalam dwibahasa.

Soalan dalam bahasa lnggeris mendahului soalan yang sepadan dalambahasa Melayu.

Calon dikehendaki membaca maklumat pada halaman belakang kertassoalan ini.

www.myschoolchildren.com

3.

Modul latihan berfokus ini mengandungi 31 halaman bercetak dant halaman tidak bercetak

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M,4THEIVTAT ICAL FORMULAERUMUS MATEMATIK

The following formulae may be helpful in answering the questions. The symbolsgiven are the ones commonly used.

Rumus-runlus berikut boleh membanlu anda menjawab soalan. Simbol-simbol yangdiberi adalah yang biasa digunakan.

R.ELATIONSPERKAITAN

I a**an:a**n

2 a"' * a" : om+n

3 (o* )n - ot?,n

4 A-t--l-( d -b)r 1' -o4-6o[-, ,)

5 Distance I Jarakt-

- f,(rz - r)2 + (yz - y)2

6 Midpoint I Titik tengah

(x,y)-( *'**'.h+Yz\\_.,r, ( Z , Z )

7 Average speed - dist-ance travelledr - - -- time taken

10 Pythagoras' TheoremTeorem Pithagoras

,2 -12 +b2

lt P(A\-n(A)n(,s)

12 P(A'):1-P(A',)

13 *_lz-Ytx2-xr

t4 m--y-interT:.r.lx * mtercept

pinlasat?-* l'ln : -' .-:.

p intasan * x

8 Mean

Min -

Puratalaju -jarak yang dilaluimasa yang diambil

sum of data

number of data

hasil tambahnilai data

bilangandata

sum of (classmark x fiequency)sum of frequency

hasil tamfuh (nilaititik tengah data xkekerapan)

I Mean -

Min - hasil tambahkekerapan

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')J

SHAPES AI.JD SPACEBENTT]K DAN RUANG

I Area of trapezium: 1* ,r* of parallel sides x height,2

Luas trapeziuu, : :.x

ltasil tambah sisi selari x tinggi

2 Circumference of circle : nd : 2nrLilitan bulatan : nd : 2nj

3 Area of circle : nr2Luas bulatan : fi.i2

4 Curved surface area of cylinder : 2nrltLuas perruukaan ntelengkung silinder : Zn.jt

5 Surface area of sphere : 4 x 12

Luas permukaan sfera : 4n j2

6 Volume of right prism : cross sectional area x lengthIsi padu prisma tegak : luas keratan rentas x panjang

7 Volume of cylind er - xr2 hIsi padu silinder : lrj 2 t

8 Volume of cone : I nr'h3

IIsi padu silinder : ; nj't

J

g Volume of soher ": ! nr''3

Isi padu sf"ro - ! nr'J

I 0 Volume of right pyramid - 1 * base areax height3

Isi padu piramid tegok: I " fuas tapak x tinggi

1 1 Sum of interior angles of a polygon : (n -2) " 180'

Hasil tambah sudut pedalaman poligon: (n -2) " 180"

t449t1

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1., arc length _ angle subtended at centre

circurnference of circle 360"

panjanglengkok _ sudut pusat

lilitan bulatan 360o

I - area of sectoratIJ

angle subtended at centre

area of circle 360"

luas sehor _ sudut pusat

l"^ brt"t"r- 360"

14 Scale factor. k - PA'

'PA

Faktorskala. k-PA',PA

15 Area of image : P x area of object

Luas irnej : lP x luas objek

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t449 I t

Find the value of ( 6-0.418) x 0.005, and round off the answer correct to two

significant figures.

Cari nilai (6 - 0.418) x 0.005 , dan bundarkan jawapan itu behi kepada dua

angka bererti.

A 0.027

B 0.028

c 0.02

D 0.03

Express 0.000 021 9 in standard fonn.

Ungkapkaz 0.000 021 9 dalam bentuk piawai.

A 2.19 x 10-7

B 2.19 x 10-5

C 2.19 x 10s

D 2.19 x 106

In2012,the mean number of computers produced by factories P, Q and R was

20 000. Factory P produced 12 400 computers. Factory Q producod three tirnes

as many computers as factory R. Find the number of computers produced by

factory Q in20l2.

Pada tahun 2012, min bilangan komputer yang dikeluarkan oleh kilang P, Idan R ialah 20 000 buah. Kilang P mengeluarkan 12 400 buah komputer-

Kilang Q mengeluarkan tiga kali ganda bilangan komputer yang dikeluarkan

oleh kilang R. Cari bilangan komputer yang dikeluarkan oleh kilang Q pada

tahun 2012.

A 5.70 x 103

B 3.57 x 104

C 4.76 x 104

D 1.43 x 105

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0.0025 +7 xl0-3 :A 9.5 x 103

B 3.2 x 103

C 3.2 x 10-3

D 9.5 x l0-3

Given 2 x 53 + 4 x 52 + 5_t,:2430s, find the value of y.

Diberi 2 x 53 + 4 x 52 + 5y : 2430s, cari nilai y.

AOB1C3D6

110012 + 10112 :A 1001002

B 101 I l0z

C 101 I 112

D I 101002

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t449lt

In Diagram I , PQRST is a regular pentagon. STU is a straight line.

Dalam Ra.jah 1, PQRST ialah sebuah pentagon sekata. STU ialah garis lurus.

Diagram I

Rajah I

Find the value of x.

Cari nilai x.

A6Bt6c30D36

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In Diagr am:,, PQSis a tangent to the circle with centre o at point B'

Daram Rajah 2, pes iarah tangen kepada buratan berpusat o pada titik Q-

Find the value of x.

Cari nilai x.

A2l824c45D48

O

Dragram2Raiah 2

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IO 1449 I 1

In Diagratn 3, PQRS is a parallelogram and RSI is a straight line.

Dalam Raiah 3, PQRS ialah sebuah segi empat selari dan RST ialah garislurus.

Dragram 3

Rajah 3

Calculate the value of x + y.

Hitungnilaix+!.

A70880c t25

D 205

T I l0o

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ll 1149il

C

EIolotEl(t)lLIEl-clololol-clolaDl>lEI;l=t=IEIot9tLI(t)lLI

'tr1EIolololslolal>tEI

=l=l=tEIol9tLI(I)lLIEl-clololol-cl()lq)l>tel=l=l=t;(o(U

Eo.Eat(l)(DL

U;(Do-(UCL

o(l)(DL

l0 Diagram 4 shows two triangles, PQR and SQT, drawn on square grids.

Triangle PQR is the image of triangle SQT under an enlargement.

Raiah 4 menuniukkan dua segi tigct, PQR dan SQT, dilukis pacla gr"i4 segi

entpat sama. Segi tiga PQR ialah imej bagi segi tiga SQT di bau,ah syatu

perubesaran.

Dragram 4Rajah 4

The centre of the enlargenrcnt and its scale factor are

Pusat pembesaran dan./aktor skala bagi pembesaran itu ialah

Centre of EnlargementPusat Pembesoran

Scale FactorFaktor Skala

O1

3

a aJ

P I

3

P aJ

P

\\

\.s' \

\ \\ \

O T R

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t2 t449lt

1t ln Diagram 5, trapezium L

Dalam Raiah 5, trapeziuntputaran 90" ikut arah iam.

is the image of K under a clockwise rotation of 90".

L ialah intej bagi trapezium K di bawah suatu

t2

Diagram 5

Raiah 5

which of the points, A, B, C or D, is the centre of rotation?

Antara titik A,B, C danD,yang manakah pusat putaran itu?

Diagram 6 shows the graPh of Y: sin x.

Rajah 6 rnenunjukkan gra.f Y: sin x.

Diagram 6Rajah 6

The value of fr is

Nilai k ialah

900

1 80"

274"

3600

A

B

C

D

Y LA

ft 1-

It

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13 In DiagrantT,JKLMis a rectangle. KNLis a srraighr line a,d Kil :1or.Dalam Raiah 7,JKLM ialah

'ebtnh segi empat tepat. Klvl- ialah goris lurusdartKN-3 KL.

5

6 crn

Diagram 7Rajah 7

The value of tan ZMNK is

Nilai bagi tan /"Ml{K iuluh

_14

_T3

M

4

3

8

9

A

B

C

D

20 cm

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14

ij:ff[i;]r".:. a right-angred rriangurar prisnr with refia,gre peRsas rhe

Rajah B ruertunjukkan sebuahpeRs. .'-""'t'4't"L't" ovuuutt pr*ma segi figa tegak dengan tapak rutertgtlfirk

Diagram 8Rajah 8

Name the angre between the pran e eTUand the prane RsTu.Nqruakan sudut di antara satah eTtl dengart satah RsTu.A /8TSB zQUR

C ZRQU

D /PTQ

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t5 t44qt1

[5 In Diagram 9, JK is a vertical pole. KL is horizontal.

Dalarn Rajah 9, JK ialah sebatang tiang tegak. KL adalah mengufuk.

2Jm

Diagram 9Ra.iah 9

The height of the vertical p<lle

Tinggi tiang tegak iclult ?0 rn.

A 30"46',

B 36"32',

c 38"47'.

D 53"28'

is 20 m. The angle of elevation of -/ from L

Sudut dongakan J dari L ialah

/.s

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l6 1449n

r6 ln Diagram I 0, PQR and SZ are two vertical poles on a horizontal plane. Q ts a

point on PR such that QR: S7.

Dalam Rajah 10, POR dan ST ialah dua batang tiang tegak pada satah

mengduk. I adalah satu titik di atas PR dengan keadaan QR: SZ.

Diagram l0Rajah L0

The angle of depression of S from P is

Sudut tunduk S dari P ialah

A

B

C

D

tPSS

ZSPQ

ZQSR

/.SRT

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t1 t449ll

t7 Diagram l1 shows three points, P, Q and R on a horizontal plane. R lies due

north of Q.

Rajah ll menunjukkan tiga titik, P, I dan R yang terletak pada suatu satah

mengufuk. R berada ke utara Q.

Diagram 11

Rajah ll

Find the bearing of P from Q.

Cari bearing P dari Q.

A 040"

B 140"

c 145"

D 320"

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Itt 1449 n

t8 ln Diagram l2, Z ts a point on the eafih..fu is thc North

Pole and //OS is the axis of the eafih.

Dalarn Rajah 12, Z ialah titik di stas permukaan bumi..

ialah Kutub Selatan dan UOS ialah paksi bumi.

Greenwich MeridianMeridian Greenv,ich ,s

Dragram 12

Rajah 12

Find the location of potnt Z.

Cari kedudukan titik Z.

A (20'{ 50',8)

(20, u, 50o T)

B (2A" N,50o [4/)

(20" 11,50'B)

c (50' N,20 D(50" u,20' 7)

D (50' N,20o ,Ia

(50" u,20o B)

Pole, S is the South

U ialah Kutub [Jtaro, S

EquatorKhatulistiwa

N/U

50" \

ZtI

- - 'I- -

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l9 1419t1

zo Express 2+k-2h-l3k (th as a single fraction in its simplest form.

(Jngkapkan +! -?!| ,sebagai satu pecahan tunggal daiam bentttk3k (th u

termudah.

l9 (m - n)(m + n) -2n(,n -3n) _

A nf + 5n2 -2mnB m2 + 5n2 + 2rnn

C m2 - 7n2 - 2mn

D m2 + 7n2 - 2mn

4h+k6hk

4h-k6hk

4+3k-2hk6hk

2h-hk+k6hk

A

B

C

D

2t It is given that

Diberi bahawa

, express m in terms of p.

, ungkapkan m dalam sebutan p.

n1

m+lP -2 =

A

B

C

D

m-

m-

p+l

I

p-l1

p-2I

p-3

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20 t449lr

22 Given that -: * 4y - 2(l- y) , calgtrlate the value of 1'.3

Diberi bahav'a - I * 4y - 2(l - 1t) , hitttng nilai y-3

6A

1l

lll8

_ t8

11

1l

6

A2

23 I! - can be written as\lm-,l2/.n,.'' n

= boleh ditulis sebagai\lm'

A 1*'n-'2 <,

B u

m-'n'7

C l4m-s n-'

D l4m*s n2

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2t 144911

24 Sirnplify

Ringkaskan

J!:!'t'_-I

(h")'ko

A h-o k'B h-'k-'

c h-2 k2

D h2k2

25 Diagram 13 represents two simultaneous linear inequalities on a number line.

Rajah 13 mewakili duu ketak.sumaan linear pada garis nombor.

4-3-2*r01234Diagram 13

Rajah 13

rl

The inequahty which represents the common value of both the inequalities is

Ketalcsamaan yang mewakili nilai sepunya bagi kedua-dua ketalcsamaan ialah

A -3<x<1B -3<xS1C -3<x<1D -3<x<l

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22

List all the intcgcrs of /r which satisfy the inequality 5 - 2k < 7 .

Senaraikan semua integer k vang memua.skan ketalcsctmaan linear 5 - 2k

A -3,-2.-l ,...-2,-1,0,...-1,0n1,...0, I ,2,...

The pie chart in Diagram 14 shows hobbies of a group of teenagers.

Carta pai dalant Rajah 14 menunjukkan hobi sekumpulan remaja.

Diagram 14

Raiah 14

The number of teenagers whose hobby is reading is 800. The number ofteenagers whose hobby is swimming is the same as the number of teenagers

whose hobby is fishing. The number of teenagers whose hobby is drawing is

50% of the number of teenagers whose hobby is swimming.Calculate the number of teenagers whose hobby is drawing.

Bilangan remaja yang mempunyai hobi membaca ialah 800. Bilangan remaja

yang mempunyai hobi berenang adalah sama dengan bilangan remaja yang

mempunyai hobi memancing. Bilangan remoja yang mempunyai hobi melukis

ialah 50% daripada bilangan remaia yang mempun))ai hobi berenang.

Kira bilangan remaja yang mempunyai hobi melukis.

200

210

224

373

l449lt

26

<7 .

B

C

D

27

A

B

C

D

Fishing /Memancing

Drawing /Melukis

Reading /Membaca

Swimming /Berenang

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23 t449ll

2t| I)iagrarn l5 is a piclograph which shorvs the nunrbcr of houscs inl'arnan Pelangi. Thc nurnber of single storey serni-D houses is not slrown.

lla.jah 15 ialah piktogra/'yang menunjukkan bilangan rumah diTaman Pelangi. Bilungon rurnah kembar satu lingkat tidak diturtjukkan.

represents 5 houscs

mewakili 5 huuh nrmuh

Diagram l5Rujah l5

Tlrc ratio of single storey scmi-D houses to double storey terrace houses

is 4 : 3. Find the total number of houses in Taman Pelangi.

Ni.rbah rumah kembqr satu tingkat kepada rumah teres dua tingkat ialah4 : 3. Cari juntlah bilangan rumah di Taman Pelangi.

A

B

C

D

140

175

80

95

Double storey terraceTeres dua tingkat ooooo,a

oooooa

oao00

Single storey serni-DKembar satu tingkal

Double storey serni-I)Kembar dua tingkut

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24

29 Table I shows the weight, in kg, of a group of pupils in a certain school.

Jadual L menunjukkan berat. dalam kg, bagi sekumpulan murid disebuah sekolah tertentu.

Weight I Berat ( ke ) 30 -34 35 -39 40-44 45 49Frequency I Frekuensi 5 6 l0 4

Table IJadual I

Find the mean weight of the pupils.

Cari min berat murid-murid itu.

1449fi

A

B

C

D

36.9

39.6

369

396

30 Diagram 16 showsaVenndiagramwiththeuniversal set, { -- PwQw R.

Rajah 16 menunjukkan gambar rajah Venn dengan set semesta,

6=PwQuR.

Diagram 16

Rajah 16

Which of the regions A, 8,, C

Antara kawosan A, B, C dan

or D, represents the set P n Q' n R'?

D, yang manakah mewakili set P a Q' o R'?

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25 1449/t

3t 'l'lrc Vcrln diagram in Diagram I7 shows the number of elements of setA,sct 1J and set C.

(iumbar raiah Venn dalant Rajah 17 menunjukkan bilangan unsur dalam set A,set B dan set C.

Diagram 17

Rajah 17

It is giventhatthe universal sct ( - A \-t B w C and n(B c\ C) - n(C') .

Find the value of x.

Diberibaltawasetsemesta € - Av BwC dan n(B ^rC):n(C').Cari nilai x.

A

B

C

D

6

r0

13

t9

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26

Whicir of thc follorving graphs represents 1: - -1 trYang manakah rJi antara graf berikut nrcv,okili )' -

t449ll

32

_!,x

A

ts

C

D

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Page 26: Trial spm penang_2013_maths_paper1_paper2_[q]

1-/-I

2

In Diagram 18, JKL is

Dalam Rajah 18, JKl,

2l

an ist'rsceles triangle.

iulalt ,segi ligo sama kaki.

1449fi

1,15

Ilrc srirdicnt ol'thc straight line 5r + hy -12 is - 1. Find the value of h.2

5Ke(crttnun garis lurus 5x + hy - 12 ialah -: Cori nilai h.

2

1

2

2

A

B

C

D

34

Diagram IBRajah 18

I:ind tlre x-intercept of the straight ltne JK.

('uri pintasan-x bagi garis lurus JK.

2

7

9

1t

A

B

(:

I)

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28 1419n

35 It is given that set R : t\21 <x < 40, x is an integer). A number is chosen at

random from the elernents of set R. Find the probability that the numberchosen is a multiple of 3.

Diberi bahawa set R - {21 Sx < 40 , x ialah integer}. Satu nombor dipilihsecara rawak daripada Ltnsur-unsur set R. Cari kebarangkalian bahawanombor yang dipilih itu ialah gandaan 3.

36 A box contains a number of red marbles and 6 blue marbles. A marble is chosen

at random from the box. The probability of choosing a red marb l" is 2-

.

5

How many red marbles are there in the box?

Sebuah kotakmengandungi beberapa biji gulimerah dan 6 biii guli biru. Sebiji

guli dipilih secara rawak dari kotak itu. Kebarangkalian mamilih sebiji guli

merah ialah | . A"ropakah biji guti merah yqng terdapat clalam kotak itu?)

A2B3C4D9

.|J

A10

7

20

)5

q

20

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29 l449lt

l7 lllrlc 2 shows some values of the variables m and ru such thatm varies inverselyrrs llrc scluarc root of z.

.ltrtlrrrtl 2 menunjukkan beberapa nilai bagi penfioleh ubah m dan n denganAcrrtluurt tn berubah secot"o songsang dengan punca kuasa dua n.

Table 2Jadual 2

f iirrd the relation betrveen m and n.

('ut'i hubungan antara m dan n.

A m *rTJi

t! m-20Ji10(' //r:-----:Jn

l) m: 20_..::J,

m n

l0 4

4 25

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30

Tablc 3 shows two sets of rralues of the variables 1', V and W.

Jadral 3 di bau,ah menunjukkan duu set nilai bagi pemboleh ubah Y, V dan W.

Table 3.Iadual 3

It is given that IZvaries directly as the square of V and inversely as W.

Calculate the value of m.

Diberi bahawa Y berubah secara langsung dengan kuasa dua V dan berubah

secara songsang dengan W. Hitung nilai m.

1449fi

38

5;J

4

9

10

9

6

25

A

B

C

D

Y V W

1J

5

aJ t2

m 5 18

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3r 1449fi

(t _2) ^(t 3) (t _8.3e ciu"" Ii -;

)-'[; ;]: [i -i,] n,d trre varuc or/'l

(t _2) ^(r 3) (t _s)niL,", i li ; )-

ri; ;,j

: l; - i). c,,ri ,,itai k

A-1

B3

C4

D8

41' t; ili -:):

A t: )B (: -:)( tl )D (;)

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END OF QUESTION PAPERKERTAS SOALAN TAMAT

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SULIT

144912MATEMATIKKERTAS 2

SEPTEMBER2 Yz J^LM

MAJLIS PENGETUA SEKOLAH MALAYSIA(CAWANGAN PULAU PINANG)

MODUL LATTHAN BERFOKUS SPM 2OI3

MATEMATIK

KERTAS 2

2 JAM 30 MINIT

JANGAN BUKA KERTAS SOALAN INISEHINGGA DIBERITAHU

1. Kertas soalan ini adalah dalam dwibahasa.

2. Soalan dalam bahasa Inggeris mendahuluisoalan yang sepadan dalam bahasa Melayu.

3. Calon dibenarkan menjawab keseluruhan atau

sebahagian soalan sama ada dalam bahasa

Inggeris atau bahasa MelaYu.

4. Caion dikehendaki membaca maklumat dihalaman belakang kertas soalan ini.

www. mvschoolchildren.com

Untuk Kegunaan Pemeriksa

Kod PenLeriksa :

Bahagian SoalanMarkahPenuh

MarkahDiperoleh

A

I J

2 3

3 4

4 4

5 4

6 5

7 5

8 5

9 6

t0 6

t1 7

B

t2 12

13 t2

t4 t2

15 l2l6 t2

Jumlah

Modul latihan berfokus ini mengandungi 31 halaman bercetak

SULIT

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SULTT2

MATHEMATICAL FORMULAERUMAS MATEMATIK

rr r(a) =_M

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[Lihat halaman sebblah

SULIT

The following formulae may be helpful in answering the questions. The symbols given are

the ones commonly used.

Rumus-rumus berikut boteh membantu anda menjawab soalan. Simbol-simbol yang diberiadalah yang biasa digunakan.

RELATIONSPERKAITAN

10 Pythagoras TheoremTeorem Pithagorasc2=a2+b2

1 afr xo" = 11mtn

2 a* n an -- gil-n

3 (a*)n = dmn

, (s)\.) /-l

t I a, ul4 A'='((t -blad-Dc\-c a) LZ p(A,) :1-f(ri

5 Distance I Jarak ^ v, - lt= 13 m=ffi

pintasan - x

distance travelled7 Average spe,ed = i

time te*.en

Purata taiu= iqral Y:rEfitrlYlmasa yong diambil

I Mean = -sIllirf data

number of data

hasil tambah nilai dataMin=

bilangan data

g Mean :

t ,. hasil tambah(nilai titik rengan *etos x X,f"'pan)Min=

. 144912 @ 2013 Hak Cipta JPN Pulau Pinang

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SULIT 144912

SHAPES AND SPACEBENTUK DAN RAANG

I

ILuas trapezium : Z * hasil tambqh dua sisi selari x tinggi

2 Circumference of circle = xd = 2nrLilitan bulatan : nd : Znj

3 Area of circle = rc P' Luas bulqtan : fijz

4 Curved surface area of cylinder = ZnrhLuas permukaan melengkung silinder = 2ttit

5 Surfacc arca of sphere - 4 n P{.uas permukaan- sfera :- 4njz

6 Volume of right prism : cross sectional area x lengthIsipadu prisma tegak = luas keratan rentas x paniang

7 Volume of cylinder - n Phtsipadu silinder = njzt

8 Volurne of corre - | **,-1

Isipudukon = inizt

g Volume of sphero - t nr'Isipadusfera: :r*i3

Ifsipctdu piramicl tegak = 7 x luas tapak x tinggi

t I Surn of interior angles of a polygonHasil tambah suclut peclalcttnan poligon

= (n-Z)* l8O'

l44gl2 O 2013 Hak Cipta JPN Pulau Pinang tl-ihat halaman sebelah

SULIT

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SULIT 1449t2

12.

ln

I J area of circle

arc lenglh angle subtended at centreangle subtended at centreded

circumference of circle 3600

panjan_g l3ngfu!( sudut pusat

lilitan bulatan 360o

area of sector - angle subtended at centre

3600

luas seHor sudut pusat

luas bulatan 3600

L4 Scale factor, k = #

Faktorskala,k=#

15 Area of imag e = P x area of objectLuasimej=Pxluasobiek

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5

SULIT

1 On thc graph in the answer space, shade the region which satisfy the three inequalites

2y *x )B,x <7andy 1x.

Padq graf di ruang jawapon,lorekkan rantau yang memuaskan ketiga-tiga ketaksamaan

2y *x >B,x <7dany 1x.

1449t2

[3 marks ]

13 ruarkah)

[Lihat halaman sebelah

SULIT

Alal

I

I

7 x -'7

6 \

\ 2y+x -8

5

0 1eI I 7 , 0

144912 O 2013 Hak Cipta JPN Pulau Pinang

ITor

Exeun iner's(Jse

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6

SULIT

2 Solve the following quadratic equation using factorization method.Sel es a i kan pers amaan kuadra t ik b erikut menggunakan kaedah pentfaktoran.

AnswerlJawapan

1449t2

ForExaminer's

(Jse

[ 4 rnarks]

[4 ruarkah]Answer/Jawapan

3 Calculate the value of x and ofy that satisfy the following sirnultanc()us linear equation:

Hitungkan nilai x dan nilai y yang memuaskan persamaan linacrr scrt:nltrk berikut:

x *3y - 9

1-ix-Y: -5

[4 rnarks ]

1"4 murkahl

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SULIT

4 Diagram 4 shows a cuboid ABCDEFGH u,ith a horizontal square base EFGH.

Rajah 4 menunjukkan sebualt kuboid dengan tapak segi empat set?to EFGH cLi atassotah mengufuk.

Diagram 4

Rajah 4

/ is tlre midpointof AD. BC: 14 cmandCG:5 cm.

I udulah titiktengah AD. BC: 14 cm dan CG:5 cm.

a) Name the angle between the plane HIG and the plane CDHG.Namakan sudut di ontara satah HIG dengan satah CDHG.

b) Calculate the angle between the plane HIG and the plane CDHG.I"litung sudut di antara satalt HIG dengan satah CDHG.

, [3 marksl' [3 markahl

Answer I .lawapan :

(o)

1449t2

(b)

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SULIT144912 O 2013 Hak Cipta JPN Pulau Pinang

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Use

8SULIT

5 (a) State whether the following compound statement is true or false.

144912

Nyatakan somo ada pernyataan majmuk berikut benar alau palsu.

0 x 12: 0 and 12":0

0x12:0danl\i:0

(b) Complete the following statement with the quantifier "all" or "some"so that it will become a true statement.Lengkapkan pernyataan berikut dengan pengkuontiti "semua" otuu"sebilangan" supaya menjodi suatu pernyataan benar

(i) : ,;:i:;,';ff"Y;;"fr:":';;i";';;,:X;:i)ll]r'ffo,

(c) Write down Premise I to complete the fotlowing argument:Tuliskan Premis I untuk melengkapkan hujah berikut:

Premise 2: n is not an even number.Premis 2: n bukan nombor genop.Conclusion: ( -3)' is not a positive number.Kesimpulan: (-3)' bukan nombor positif.

(d) It is given that the gradient of a straight line can be defined by

m: -Jr - intercept

. Make one conclusion by deduction on the value ofx - intercept

m glen that y- intercept : 5 and x- intercept: -: .,2Diberi bahawa kecerunan suatu garis lurus ditakriftan sebagai

m - - pintasan - y

. Buat satu kesimpulan secora dedulcsi tentang nilaipintasan - x

m jika diberi pintasan- y: 5 dan pintason -x: i[5 marks]

AnswerlJawapon: 15 markahf(a)

(b)

(c) Premise I I Premis I:

(d)

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9

STJ LIT(r In Diagraln 6, thc straight line AB is parallel to ttre straight linc C.D. Point O is thc

origin. Given that the equatiou of the straight hne CDis J,- -f t-+2

Dalam Rajah 6, garis lurtts AB odtrlalt .selari dengan garis lttnt,s CD. Titik O ialolt

asalon. Diberi persamaan garis lurtrs CD iatah l, - + x - 4 .-2

[)iagrarn 6

lluiult 6

t449t2

I;ind('ut"i

(a)

(b)

(c)

tlre equation of tlrc straight line AB .

persamaan bagi guri.r lttrus AB.

valuc oIt.nilai k.

value of p.nilai p.

[5 marksJ

15 markahl

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SULIT

c (2,-3)

144912 O 2013 Hqk Cipta JPN Pulau Pinang

ForEraminer's

Usc

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ForExaminer's

Use

l0SULIT

AnswerlJawapon:

r449t2

[Lihat halaman sebelah

SULIT :

(a)

(b)

(c)

144912 O 2013 Hak Cipta JPN Pulau Pinang

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11

STJI,IT

1 Diagrarn 7 shows a composite solid, formed by a combination of a cylinder and twoidentical cones. Given the diameter of the cone is 7 cm and its height is 9 crn. Thevolume of the composite solid is 1078 .*t.Raiah 7 menunjukkan gabungan pepe.lal yang terbentuk daripada cantuntan satusilinder dan dua kon yang sama. Diberi diameter kon ialah 7 cm dan tingginyq 9 cm.Isipadu gabungan pepejal ialah I078.rrr'.

Using , calculate the height, in cm, of the cylinder.

Menggunakan hitung tinS;gi, dalam cm, bagi silinder itu.

t449 t2

22

7

22

7

Diagram 7

Rajah 7

[4 marks]

[4 markah]

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SULIT

AnswerlJawapan:

144912 O 2013 Hak Cipta JPN Pulau Pinang

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t2$ULIT l44gt2

' -3 rz) (l -z\g (a) It is givcn that +l : -' ll, the inverse matrix of I | . pina rhe value ofe 3(-8 7 )- - [a 4) -"'p and of m.

(t -2\Diberi bahawa +(-: "-'\,otot, matriks songsutlg basi | ' - l. Cari nilai p3[-s 7) o-----.-.[8 4)dan nilai m.

(b) Write the following simultaneous linear equations as a matrix cquations.Tulis persamaan linear serentak berikut dalam bentuk persamoan mcttriks.

7 x-2Y:58x - 3Y:10

Hence, by using matrix method, calculate the value ol'x and of -y.Seterusnya, dengan menggunakan kaedah matriks, hitung nilai x dannilai y.

[6 marks]

16 markah)

[Lihat halaman sebelah

AnswerlJowapon:

(a)

(b)

SULIT ;

144912 O 2013 Hak Cipto JPN Pulau Pinang

F'or

[:xaminer's{Jse

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t3ST]LIT

() In Diagram9, OQS is a quadrant of a circle with centre O. OPT is another quadrant alsowith centre O. OUR is a straight line.Dalam Rajah 9, OQS ialah sukuan bulatan berpusat O. OPT ialah satu lagi sukuanbulatan jugo berpusqt O" OUR ialah garis lurus.

Diagram 9Rajah 9

1449t2

[3marksl13 ntarkaltl

[3 marl<s.]

13 mar"kahl

[Lihat halaman sebelah

SU LTT

OT : TS : J cm and /- QOR : (r0"

))Usins lr - ::. calculatee7

OT : TS : 7 cm dan /- 7OR: 60o))LLGunatr- _,hitungl

(a) the perimeter, in cm, of the wholc diagram,perimeter, dalam cm, seluruh ra.jcth itu,

(b) the areain cm2, of the shaded region.luas dalam " ' , kawasan yqng herlorek.

l449lz @ 2013 Hak Cipta JPN Pulau Pinang

IiorExaminer'',s

[-J,se

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ForExaminer's

[Jse

t4SULIT

Answer I Jawapan:

(a)

144912 O 2013 Hak Cipta JPN Pulau Pinang

(b)

144912

::

[Lihat halaman sebelah a

SULIT ]

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l5SULIT

l0 Diagram l0 shows two spinning discs. Disc K is divided into four equal sectors anddisc L is divided into three equal sectors. The pointers at the centr. of tlr. discs arespun simultaneously so that they will stop at random at one of the sectors.

Rajah l0 menunjukkan dua buah cakera berputar. Cakera K dibohagikan kepadaempat sektor yang sama besar dan cakera L dibahagikan kepada tiga sektor yang san?ctbesar. Petunjuk -petunjuk pada pusat cakera itu diputorkon serentak sehingga merekaakan berhenti secara serentak pada mono-mena satu sektor. www.myschoolchildren.com

t 449 t2

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SULIT

Disc KCakera K

Disc LCakera L

Diagram l0Rajah 10

(a) List the sample space.Senaraikan ruang sampel

(b) List all the possible outcomes and find the probability thatSenaraikan semuo kesudahan peristiwa yang mungkin dan cari kebarangkalianbagi

(i) both pointers stop at a number,kedua-kedua petunjuk berhenti pada nombor,

(ii) one pointer stops at a number and one pointer stops at a letter.satu petuniuk berhenti pada nombor dan satu petunjuk berhenti pada huruf.

[6 marks]

f6 markahl

1449/2 O 2013 Hak Cipta JPN Pulau Pinang

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(Jse

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ForExaminer's

U.se

l6SUI-[T

AnswerlJa\uapan .

(a)

(ii)

1449t2

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l7STJ I,I T

I I Diagram l l shows the speed-tirne graphI 8 seconds .

Rajah I I meruujtrkkan gruf'laju-n'tasasaat'

Speed (*, ')Lqju (*t ')

for the ffrovement of a particle for a period of

bagi pergerakan sattt zarah dalam tempoh l8

Time (s)Masa (s)

1449 t2

16 marksl

16 markah)

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SULIT

Diagram l1Rajah ll

(a) State the uniform speed, in rns ' , of the pafticle.

Nyatakan laju seroganl, dalarn *r-' , zarah itu.

(b) Calculate the distance, in m, travelled by the particle with unifonn speed.

Kira jarak, dalam m, yang rJilalui oleh zarah itu dengan laju seragonl .

(c) Given that the average speed in the first 15 seconds is 14 ms -' , find the

value of v.

Diberi bahawa purata laju dalam 15 saat yang pertama'ialah 14 ms -r,

tentukan nilai v.

144912 O 2013 Hak Cipta JPN Pulau Pinang

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ForExaminer's

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I8SULIT

Answer I Jawapan;

(a)

t44912

[Lihat halaman sebelah

SULIT

(b)

(c)

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SULITt9

Section BBahagian B

148 marksl

f48 markah)

Answer any four questions from this section.Jawab nlana-mana empat soalan daripada bahagian ini.

12 (a) Complete Table 12 in thc answer space for the equation !: -x3 +2x+8 bywriting down the values o{'.y when x : -Z and x - 3. [2 marks]Lengkapkan Jadual 12 di ruang jawapan bagi persamaan y:-x3 +2x+8dengan menulis nilai y apabila x - -2 dan x * 3. [2 markah)

(b) For this part of the qucstion, use the graph paper provided on page 21. You mayuse a flexible curve rulc.By using a scale of 2 crn to I unit on the x-axis and 2 cm to l0 units on they -axis, draw the graph <>f y: _x' +2x+8 for -4 < x < 4 and

[4 marks]-48<y<64.

Untuk ceraian soalan ini, gunakan kertos graf yang disediakan padahalaman 21. Anda boleh menggunakan pemboris flelrsibel.Dengan menggunakan skctla 2 cm kepada I unit pada paksi-x dan 2 cm kepadal0unit padapaksi-y, lttkiskan graf l:*x3 +2x+8 bagi -4< x34dan -48 < y < 64. t4 markah)

(c) From the graph in 12(b), IindDari graf 12(b), cari

(i) the value of y when x : 1.5,nilaiyapabilax:L.5,

(ii) the value x when ! : 20.nilaixapabilo!:20.

[ 2 marks ]12 markah)

(d) Draw a suitable straight line on the graph in 12(b) to find the values ofx whichsatisfytheequationx 3 :8x_ 4. Statethevalues of x for *4<x<4.

[ 4 marks]Lukiskan satu garis lurus yang sesuai pada graf anda untuk mencari semua nilaix yang memuaskan persamaqn x' _ 8x - 4 bagi -4 < x < 4

Nyatakan nilai-nilai x itu. | 4 markah )

1449t2

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ForExaminer's

Use

20SULIT

(a)

Answer/awapan :

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SULIT

Table l2

Jadual 12

(a) Reftr graph on page 21.Rujuk graf di halaman 21.

(c ) (i) y: . .........

x -4 -J -2 -t 0 I 2 3 3.5 4

v 64 29 7 8 9 4 -27 .9 -48

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22

13 (u) Transformation R is a reflection in the straight line y : 5.( z\

Transformation T is a translation I /-

I .

[- 3,]

State the coordinates of the image of point (1, 3) under the followingtransformations:PenjelmaanR ialah satu pantulan pada garis lurus y : 5.

( z\PenjelmaanT ialah satu translasi I - l.

[- 3/

Nyatakan koordinat imej bagi titik (1,3) di bawah penjelmaan berikut:(i) r(ii) rR

SULIT

AnswerlJawapan:(a) (i)

(ii)

1449/2

[3 marks]

[3 ntarkah)

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23

SULIT

l3 (b) Diagram 13 shows threc quadrilaterals, ABCN, KLMN and PQRS, drawn on aCartesian plane.Rajah 13 menunjukkan tigu sisi emltat, ABCN, KLMN dan PQRS, dilukis padasatah Cartesan.

I)iagram 13

llujah 13

KLMN is the image of PQlfS undcr transformation E and ABCN is the image ofKLMN under transformation F.

Describe, in full, the transfbrrnation:zuMN ialah imej bagi POlf.T ili hetwah penjelmoanV dan ABCN ialah imei bagiKLMN di bawah penjelmaun li .

Huraikan s elengkapkan, peni e I maa n :(a) E,(b) F.it-is given that quadrilateral ABCN represents a region of area 56 c*'.Calculate the area, in cm', of quadrilateral KLMN.Diberi bahowa sisi empat ARAN mewakili rantau dengan luas 56 c*'.Hitungkan luas, dalam

"*2, boggi slsi empat KLMN.

[9 marks]

[9 markah)

AnswerlJowapan:(b) (i) (a)

144912

(i)

(ii)

(b)

(iD

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ForExaminer's

(Jse

SULIT

14 Table 14.1

Jadual 14.ldari laut.

24

144912

shows the frequency distribution of the lengths of 84 fish caught fi orn the sea.

menunjtrkkan taburon kekerapcrn bagi panjang 84 ekor ikan.t'ctng tlitcrngkap

Length (cm)Panjang km)

FrequencyKekerapan

1l 15 5

16-20 8

2t -25 l426-30 243l - 3s 2l36-40 9

4t -45 3

Table I4.lJadual 14.l

(a) Calculate the estimated mean of the length ol the fish.Hitung min anggaran bagi panjang ikan.

[3 marks]

13 markahl

(b) Based on table 14.1, complete Table 14.2 tn the answer space by writing down thevalues of the upper boundary and the cunrulative frequency. [3 marks]Berdasarkan jadual 14.1, lengkapkan.ltulrtul 14.2 di ruang jawapan denganmenulis sempadan atas dan kekerap(In lorrggokan 13 markahf

(c) For this part of the question, use the graph paper provided on page 26. You may use

flexible curve rule.Untuk ceraian soalan ini, gunakan kerttt.s graf yang disediakan di halaman 26.Anda boleh menggunakan pembaris ./l ali.r i bcl.

Byusing a scale of 2 cmto 5 cm on thc horizontal axis and} cm to l0 fish on the

[4 rnarks]vertical axis, draw an ogive for the dala.Dengan menggunakon skala 2 cm kepuclu 5 cm pada paksi ruengufuk dan 2 cm

kepada l0 ekor ikan kepada paki n'ten(:un(:ung, lukis satu ogf bagi data tersebut.

t 4 markah)

(d) Those fish with a length of greater than 24 cm are exported. Using the ogive in14 (c), find the number of fish which will be exported [2 marks]Ikan ))ong berukuran melebihi 24 cm dieksport. Menggunakan ogf di l4(c), caribilangan ikan yang akan dieksport 12 markoh)

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St ]l,ll'Answcr /Jawapan:

(a)

(c) Refer graph on page 26Rujuk graf di halaman 26

(b)

25

I-able 14.2

.ladual 14.2

r449t2

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Upper boundarySempadan atas

Cumulative frequencyKekerapan Longpokan

10.5 0

15.5

45.5 84

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27

l5 You urc not allorved to use graph paper to answer this questiou.Attdu tidak dibenarkan menggunokun kertqs gra/'untuk menjavt'ob soulun ini.

(a) Diagrarn 15.1 shows a righl prism with rectangular base ABCD on a hori zontalplane. The surface AEHII-D is tlrc unifbnn cross-section. The reclangle IJKL is aninclined plane. The rectanglc Ef'-Gt"l is a horizontal plane. The edges AE , BF, CK,DL, GJ and HI are vertical cdges. Given EH: FG:2 cn. www.myschoolchildren,com

Raiah 15.l menunjukkutt ytri,srrtu tagak dengan dengan tapak segiempat tepatABCD terletak di atas :;uluh murgtfirk. Permukaan AEHILD ialah keratan rentasseragam prisma itu. Scgi urtltul Ittt'GH adalah satah menguJirk. Tepi AE, BF, CK,DL, GJ dan HI adalah si.si tt,gul;. Diberi EH : FG : 2 cm.

2cm K

3cm

Diagram 15. 1

Rajah 15.l

Draw to full scale, the elevation of the solid on a vertical plane parallel to AD as

viewed from X. [3 marks]Lukis dengan skala penuh, dongakan pepejal itu pada satah mencancang yangselari dengan AD sebagaimana yang dilihat dariX. t3 markah)

s U LI't' 1449t2

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H Il{ \ \

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28SULTT

Answer / Jawapan :

(a)

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SULIT

(b)

Diagram 15.2Rajah 15.2

Draw to full scale,

Lukis dengan skala penuh,

(i) the plan of the combined solid,

yte lan gabungan pepejal it,.

(ii) the elevation of the combined solid on aviewed from Y,

[4 marlcs]

14 markahl

vertical plane parallel to DM as

[5 marks]

1449/2

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29

A solid right prism is joined to the solid in Diagram 15.1. The combined solid isshou'n in Diagram 15.2. Triangle CMN is the unifonn cross section of the prismand NMRQ is an inclined plane. The base ABSRMCD is a horizontal plane andNK:2 cm.

Sabuah pepejal prisma dicantumkan kepada pepejal dalam Rajah 15.1.

Guhungan pepejal adalah seperti dalam Rajah 15.2. SegitigacMlv adalah keratan rentas seragam kepada prisma itu danNMRO adalah satah condonE;. T'apctk ABSRMCD adalah satah mengq/uk danNK :2 cm.

dongakan gabungan pepejal itu pada satah mencancang yong selari denganDM seperti dilihat dari Y . 15 markahl

I.l

,IIIII

-- q I\ L-,r

-k,-\ \ \

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{Jse

30SULIT

Answer I Jawapan :

(b)(i)

(ii)

1449t2

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3lSULIT

I6 V((r5"N. 40"W) and R are two points on the surface of the earth such that VR is thediantctr:r' o1- il parallel of latitude.V(r5 tl' 4O tl) clan R ialah riua titik padct permukaan bunti dengan keadsan YR iatahdi ttrrrcIt, t' lru,gi selarian latitud.

Diagrarn l6lRajah 16

[6 marks]

f6 markohl

diukur sepanjang permukaan bumi

[2 marks]

12 markah)

1449t2

[2 marks]

12 markahl

[2marks]12 markah)

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(a)

(b)

ljirxl tlrrr location of R.('(rrt lt',ltulukan R.

( ir vq:rr that VZ is a diameter of thc carth. State the locat ion of Z.l)ilu,r i \//. ialah diameter bumi. Nvotakan kedudukan Z.

(iil thc longitude of E.hurpiitud E.

(c ) Att rcntplane departed from V and flew due east along the common parallel ofIttttlurfu rvith an average speed ot'375 knots. The aeroplane took 2.5 hours tonn'rlr al point E. Calculate

lir:l,trrtlr Atrytal terbang berlepas dari Y dan terbang arah ke timur di sepanjangsrlttrttttt lulitud sepunyo dengan purata laju sebanyak 375 knot. Kapal terbang itunt,,tt;;(unhil 2.5 jam untuk tiba di titikE. Hitung

(i) tlrr: clistance, in nautical mile, from V to E,ytu'ult, dalam batu nautika, dariY keE,

(d ) ('ttle ulatc the shortest distance, in nautical mile; measured along the surface of thecaltll t}onr E to the North Pole.l{ituttg jtu'uk terpendek, dalam batu nautika,tltu'i l;. kr Kutub Utara.

N/U

S/.S

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Answer I Jawapan :

(a)

(b)

(c ) (i)

(d)

(ii)

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