# SPM Sabah Trial Maths 09 P1 Q n A

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JABATAN PELAJARAN NEGERI SABAH

SIJIL PELAJARAN MALAYSIA 1449/1

EXCEL 2

MATHEMATICS

Paper 1

Sept 2009

1 Hour 15 Minutes One hour and fifteen minutes

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

1. This question paper consists of40 questions.

3. Answer each question by blackening the correct space on the answer sheet.

4. Blacken onlyone space for each question.

5. If you wish to change your answer, erase the blackened mark that you have done. Then

blacken the space for the new answer.

6. The diagram in the questions provided are not drawn to scale unless stated.

7. A list of formulae is provided on pages 2 to 4.

8. A booklet of four-figure mathematical tables is provided.

9. You may use a non-programmable scientific calculator.

This paper consists of 19 printed pages

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MATHEMATICAL FORMULAE

RUMUS MATEMATIK

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

Rumus-rumus berikut boloeh membantu anda menjawab soalan. Simbol-simbol yang diberi adalah

yang biasa digunaan.

1 nmnm aaa +=

2 nmnm aaa =

3mnnm aa =)(

4

=

ac

bd

11

5 Distance/ jarak

=2

21

2

21 )()( yyxx +

6 Midpoint/ Titik tengah

++=

2,

2),( 2121 yyxxyx

7

8 Mean =

dataofnumber

dataofsum

9 Mean =sfrequencieofsum

frequency)markclass(ofum s

10 Pythagoras Theorem /

Teorem Pithagoras222

bac +=

11

12 )(1)'( APAP =

1312

12

xx

yym

=

14erceptx

erceptym

int

int

=

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SHAPES AND SPACE

1 Area of trapezium = heights2

1 sidesparallelofum

Luas trapezium =

2 Circumference of circle = rd 2= Lilitan bulatan =d = 2j

3 Area of circle = 2r Luas bulatan =j2

4 Curved surface area of cylinder = rh2 Luas permukaan melengkung silinder = 2jt

5 Surface area of sphere = 24 r Luas permuaan sfera = 4j2

6 Volume of right prism = cross sectional area lengthIsipadu prisma tegak = luas keratan rentas panjang

7 Volume of cylinder = hr2 Isipadu silinder =j2t

8 Volume of cone = hr23

1

9 Volume of sphere = 33

4r

3

4r

10 Volume of right pyramid = 31 luas tapak tinggi

11 Sum of interior angles of a polygonHasil tambah sudut pedalaman poligon

=180)2( n

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12360

centreatsubtendedangle

circleofncecircumfere

lengtharc=

13360

centreatsubtendedangle

circleofarea

sectorofarea=

14 Scale factor,PA

PAk

'=

Faktor skala, k =

15 Area of image = 2k area of objectLuas imej = k

2luas objek

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1 Round off 80 715 correct to three significant figures.

Bundarkan 80 715 betul kepada tiga angka bererti.

A 80 700B 80 710

C 80 720

D 80 800

2 Express5

10564.6 as a single number.

Ungkapkan5

10564.6 sebagai satu nombor tunggal.

A 0.06564

B 0.006564

C 0.0006564D 0.00006564

3 510700013.0 +

A 3102

B 4102

C 8102

D 9102

4 A rectangular floor with a length of 36 m and a width of 28 m.

Find the number of square tiles of side 30 cm that are required to cover the whole floor.Lantai berbetuk segi empat tepat mempunyai panjang 36 m dan lebar 28 m.

Cari bilangan jubin segi empat sama dengan sisi 30 cm, yang diperlukan untuk menutupi

seluruh lantai itu.

A 41012.1

B 51012.1

C 41036.3

D 51036.3

5 The value of digit 2, in base ten, in the number 12578, is

Nilai digit 2 bagi 12578, dalam asas sepuluh ialahA 16

B 64

C 128

D 200

6 100112 11102 =

A 1012B 1112C 1002

D 10102

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7 In the diagram 1, PQRSTU is a regular hexagon TUV and RPV are straight lines. Find the value

ofx.

Dalam rajah 2, PQRSTU adalah sebuah heksagon, TUV dan RPV ialah garis lurus. Cari nilai x.

A 30

B 50

C 60

D 70

8 Diagram 2 shows a pentagon PQRST. Straight line PQ is parallel to straight line UTS

lurus UTS

Find the value ofx + y

Cari nilai bagi x + y

A 216o

B 222

o

C 250o

D 260o

P

QR

S

UT Vx Diagram 1

Rajah 1

SR

Q

P

U

x

yT

70

Diagram 2

Rajah 2

1000

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9 In diagram 3, QRT is a tangent to the circle with centre O, at R. PUS, OPQ and OUR are

straight lines.

Dalam Rajah 3, QRTialah tangent kepada bulatan berpusat O, padaR,PUS, OPQ dan OUR

ialah garis lurus.

Find the value ofx.

Cari nilai x.

A 40

B 45

C 50

D 65

10 Diagram 4 shows point P on a cartesian plane

Which of the points labeled A, B, C and D is the image of point P under a 90 clockwise

Yang manakah antara tanda A, B, C dan Dadalah imej bagi titik P di bawah satu putaran 90

O

P

Q

R

T

S

x0

250

U

y

x0

-4

-2

-2

2

4

642

DCB

P

A

Diagram 3

Rajah 3

Diagram 4

Rajah 4

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11 Diagram 5 shows two squares, PQRS and KLMN draw on square girds.

sama.

PQRS is the image ofKLMN under an enlargement with centre O. Find the scale factor of the

enlargement.

PQRS ialah imej bagiKLMNdibawah suatu pembesaran pada pusatO. Cari faktor skala

pembesaran itu.

A

3

1

B

2

1

C 2

D 3

P

K

QL

M

N

R

S O

Diagram 5

Rajah 5

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12 In the Diagram 6, S is the midpoint of straight line QST.

Dalam Rajah 6, S ialah titik tengah bagi garis lurus QST.

What is the value of cosx0?

Apakah nilai kosx0?

A

3

4

B

5

4

C

4

3

D

5

3

13 Diagram 7 shows the graph ofy = sin x0

Rajah 7 menunjukkan graf y = sin x0

The value ofp is

Nilai p ialah

A 900

B 1800

C 2700

D 3600

Q

S

T

6 cm

R

5 cm

x0

p

00

-1

1

y

x

Diagram 6

Rajah 6

Diagram 7

Rajah 7

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14 It is given that cos = - 0.7721 and .360180 00 Find the value of .

Diberi bahawa kos = - 0.7721 dan .360180 00 Cari nilai .A 140

032

B 219027

C 230033

D 309027

15 Diagram 8 shows two vertical poles, PS and QR, on a horizontal plane. The angle of

depression of vertex Q from vertex P is 420. Calculate the angle of elevation of vertex Q

from S.

Rajah 8 menunjukkan dua batang tiang tegak, PS dan QR,yang terletak pada permukaan

mengufuk. Sudut tunduk puncak Q dari puncak P ialah 420. Hitungkan sudut dongakan

puncak Q dari S.

A 320

B 420

C 580

D 680

16 Diagram 9 shows a cuboid with a horizontal base PQRS . Name the angle between the plane

RQVW and the plane QUR.

Rajah 9 menunjukkan sebuah kuboid dengan tapak mengufuk PQRS . Namakan sudut diantara

satah RQVW dan satah QUR.

A VQR

B VUQ

C VRU

D VQU

P

Q

S R

25 m

10 m

Diagram 8

Rajah 8

Diagram 9

Rajah 9

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17

In diagram 10 , NOS is the axis of the earth. PQ is the diameter of the earth.

Dalam rajah 10 , NOS ialah paksi bumi. PQ ialah diameter bumi.

The position of Q is

Kedudukan Q ialah

A ( 40oS, 100

oE )

B ( 50oS, 100

oE )

C ( 40oS, 80

oE )

D ( 50oS, 80

oE )

18 Diagram 11 shows the position of point E and F.

Rajah menunjukkan kedudukan titik E dan F.

Find the bearing of F from E

Cari bearing F dari E

A 070o

B 110o

C 2500

D 2900

19 = )1(25 xx

A 233 xx

B 23 x

C 24 x

D 27 x

North

North

70o

E

F

Diagram 11

Rajah 11

N

S

O

P( 40oN, 80

oW)

Q Diagram 10

Rajah 10

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20=

x

x

x 6

121

A

x

x

6

27

B

x

x

6

25

C

x

x

3

5

D

x

x

3

7

21Express

m

p

m

p

1

3as a single fraction in its simplest form.

Ungkapkan

m

p

m

p

1

3

sebagai satu pecahan tunggal dalam bentuk termudah.

A23

3

m

pmpm

B23

3

m

pmpm +

C

m

p

3

34

D

m

p

3

32

22Given that 52

3

1=+m find the value ofm.

Diberi 523

1=+m cari nilai m.

A 1

B 6

C 9

D 13

2353

7x

can be written as

53

7

xboleh ditulis sebagai

A 5

3

7 x

B 5

3

7x

C 521

x

D 521x

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24

Simplify

3

2

3

1

2

14

78

3

2

3

1

2

14

78

A 34 72

B 26 72

C 512 72

D 116 72

25 List all the integers x which satisfy both the inequalities

Senaraikan semua integerx yang memuaskan kedua-dua ketaksamaan

xx

13

and xx >+ )4(2

1

xx

13

dan xx >+ )4(2

1

A -1, 0, 1, 2, 3

B 0, 1, 2, 3

C -1, 0, 1

D 0, 1

26

Given that the mode of the gifts is flowers, find the maxsimum value ofx.

Diberi mod hadiah ialah bunga, cari nilai maksimum bagi x.

Flowers

Bunga

Toys

Mainan

Books

Buku

Pens

Pen

Frequency

Kekerapan18 10 5 x

A 16

B 17

C 18D 19

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27 Diagram 12 is a pictograph which shows the number of fruit trees in an orchard.

Rajah 12 ialah piktograf yang menunjukkan bilangan pokok buah-buahan dalam sebuah dusun.

Durian

Durian

RambutanRambutan

Mangosteen

Manggis

Represent 25 tress

Mewakili 25 pokok

The ratio of rambutan trees to mangosteen trees is 3:2. Find the number of durian trees and

maggosteen tress altogether.

Nisbah bilangan pokok rambutan kepada pokok manggis ialah 3:2. Carikan jumlah pokok durian

dan pokok manggis.

A 225

B 275

C 300

D 400

28 Which graph reperesents

Graf manakah yang mewakili

A B

C D

0 x

y

0 x

y

0 x

y

0 x

y

Diagram 12

Rajah 12

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29 Diagram 13 is a Venn diagram which shows the element of set X, Y, Z.

Rajah 13 ialah gambar rajah Venn yang menunjukkan unsur-unsur bagi set X, set Y dan set Z.

If the universal set ,ZYX = then set Y is

Jika set semesta ,ZYX = maka set Y ialah

A {a,b,e}

B {a,b,c,f}

C {a,b,e,f}D {a,b,e,c}

30 List all the subsets of Set X = { m, n }

A {m},{n}

B {m},{n},{ }

C {m},{n}, { m, n }

D {m},{n}, { m, n }, { }

31 Diagram 14 is a Venn diagram shows the elements of set R, S and T.

Rajah 14 ialah gambar rajah Venn menunjukkan unsur-unsur bagi Set R , S dan T.

It is given that the universal set T).Sn()Sn(and == TSR Find the value ofx.

Diberi set semesta T).Sn()Sn(dan == TSR . Cari nilai x.

A 5

B 6

C 10

D 11

5

98

3 1

x - 3

x - 4R

S

T

YX

Z. a

. b

. c

. d

. e . fDiagram 13

Rajah 13

Diagram 14

Rajah 14

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32 In Diagram 15, PQ is a straight line.

Dalam Rajah 15, PQ ialah garis lurus.

What is the gradient of PQ?

Apakah kecerunan PQ?

A -2

B

2

1

C

2

1

D 2

33 State they-intercept of the straight line 3x = 4y 24.

Carikan pintasan-y bagi garis lurus 3x =4 y - 24A -8

B -6

C 6

D 8

4x

y

0

8

P

Q

Diagram 15

Rajah 15

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34 Diagram 16 shows 20 identical rectangular cards, red, blue and green.

Rajah 16 menunjukkan 20 keping kad yang serupa berwarna merah, biru dan hijau.

Diagram 16 /Rajah 16

A card is chosen at random, State the probability that the card chosen is blue or green.

Sekeping kad dipilih secara rawak. Nyataan kebarangkalian bahawa kad yang dipilih itu

berwarna biru atau hijau.

A

B

C

D

35 Table 2 shows the distribution of boys and girls in class 4 Arif and 4 Bijak.

Jadual menenujukkan taburan pelajar lelaki dan pelajar perempuan dalam kelas 4 Arif

dan 4 Bijak.

4 Arif 4 Bijak

Boy 12 20

Girl 22 k

The probability that a girl is chosen from the 2 classes of students is . Find the value ofk.

Kebarangkalian seorang pelajar perempuan dipilih daripada kedua-dua kelas ialah .Cari

nilai k

A 10

B 16

C 18

D 24

Green Red Blue Green Red

Green

Blue Green

RedGreen Green Red

Red Green Red

Green

Blue

Red

RedGreen

Table 2

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36 Table 3 shows two sets of values of variables X and Y.

Y 1

X 2 p

It is given that Y varies inversely as X. Find the value ofp.

Diberi bahawa Y berubah secara songsang dengan X. Cari nilai p

A 4

B 6

C 8

D 9

37 Given that P varies directly as the square of t , and that P = 24 when t= 4. Express P in

terms oftDiberi P brubah secara langsung dengan kuasa dua t , dan P=24 apabila t = 4. Cari

hubungan antara P dan t.

A

B

C

D

38Given that and and whenp = 4 and q = 3. Calculate the value ofT

whenp = 1 and q =

A 18

B 24

C 36

D 72

Table 3

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39

A

B

C

D

40 Given that P = and Q = , then PQ is

Diberi P = dan Q= , maka PQ ialah

A

B

C

D

END OF QUESTION PAPER

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JAWAPAN KERTAS 1

Matematik EXCEL 2 SPM 2009

1. A 21. C

2. D 22. C

3. B 23. A

4. A 24. C

5. C 25. A

6. A 26. B

7. A 27. B

8. D 28. A

9. A 29. A

10. D 30. D

11. D 31. C

12. B 32. A

13. D 33. C

14. B 34. B

15. C 35. C

16. D 36. B

17. A 37. C

18. B 38. D19. D 39. C

20. A 40. D