Spm Percubaan 2008 Sabah Mathematics Paper 1

NAMA KELAS NO K.P A. GILIRAN

SULIT 1449/1 MATHEMATICS

: _____________________ : _____________________ : _____________________ : _____________________

PAPER 1 AUGUST 2008 1 HOUR 15 MINUTES

JABATAN PELAJARAN NEGERI SABAH SIJIL PELAJARAN MALAYSIA TAHUN 2008

EXCEL 2 _______________________________________________________________________ _

MATHEMATICS (MATEMATIK) PAPER 1 (KERTAS1) ONE HOUR FIFTEEN MINUTES (SATU JAM LIMA BELAS MINIT) _______________________________________________________________________ _ JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

Calon dikehendaki membaca maklumat di halaman 2 _______________________________________________________________________ _ This question paper consists of 16 printed pages.

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(Kertas soalan ini terdiri daripada 16 halaman bercetak.)

INFORMATION FOR CANDIDATES 1.

This question paper consists of 40 questions.

2.

Answer all questions.

3.

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

4.

Blacken only one 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 3 to 4.

8.

A booklet of four-figure mathematical tables is provided.

9.

You may use a non-programmable scientific calculator.

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The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used. RELATIONS 1

a m ×a n =a m +n

2

a m ÷a n =a m −n

3

( a m ) n = a mn

4

A−1 =

5

P( A) =

6

P ( A' ) = 1 −P ( A)

d 1  ad − bc  − c

−b   a  

n( A) n( S )

7

Distance =

8

Midpoint,

9

Average speed =

10

Mean =

sum of data number of data

11

Mean =

sum of ( class mark × frequency) sum of frequencies

12

Pythagoras Theorem

( x1 −x 2 ) 2 +( y1 − y 2 ) 2

 x + x 2 y1 + y 2  ( x, y ) =  1 ,  2  2 

distance travelled time takenl

c 2 =a 2 +b 2

13

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m=

y 2 − y1 x 2 − x1

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m=−

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4

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y − int ercept x − int ercept

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SHAPES AND SPACE 1 × sum of parallel sides × height 2

1

Area of trapezium =

2

Circumference of circle = π d = 2πr

3

Area of circle

4

Curved surface area of cylinder

5

Surface area of sphere

= 4πr 2

6

Volume of right prism

= cross sectional area

7

Volume of cylinder

= πr 2 h

8

Volume of cone

=

1 2 πr h 3

9

Volume of sphere

=

4 3 πr 3

10

Volume of right pyramid

=

11

Sum of interior angles of a polygon =

12

arc length angle subtended at centre = circumference of circle 360 

13

area of sector angle subtended at centre = area of circle 360 

14

Scale factor,

15

Area of image =

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= πr 2

k=

= 2πrh

1 3

×

luas tapak

×

length

× tinggi

( n −2) ×180 

PA' PA

k2 ×

area of object

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6 Answer all question.

1

Round off 0.05098 correct to three significant figures. A B C D

0.051 0.0500 0.0509 0.0510

2 Express 52 700 in standard form. A B C D

5.27 × 102 5.27 × 104 5.27 × 10−2 5.27 × 10-4

3 0.0000398 − 2.9 × 10−6 = A B C D

1.08 × 10−5 1.08 × 10−6 3.69 × 10−5 3.69 × 10−6

4 A cuboid has a length of 1.4 × 10 2 cm, width of 0.8 × 103 cm and height of 500 mm. Calculate the volume, in cm 3 , of the cuboid. A 5.6 × 104 B 5.6 × 105 C 5.6 × 106 D 5.6 × 107 5 Express 2 × 5 2 − 3 as a number in base five A B C D

1 42 5 2035 342 5 4035

6 10001 2 ─ 110 2 = A B C D 1449/1

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7 In Diagram 1, PQRSTU is a regular hexagon. PUV and QPW are straight lines. Q

P

W 740 U

R

y0 x0

S

T

V

DIAGRAM 1 The value of x + y = A B C D

76 96 104 134

8 In Diagram 2, PQR is a tangent to the circle at point Q. Given that ∠ PQT = 56º. The length of the arc TQ is equal to the length of the arc SQ. P

T

x0

S

Q

R

DIAGRAM 2 Find the value of x . A B C D

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56º 68º 112º 124º

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8

In Diagram 3, which of the triangle, A, B, C or D is the image of P under a rotation of 90° clockwise about the centre (0,0)?

DIAGRAM 3 10

In Diagram 4, M is the image of N under a translation.

DIAGRAM 4 Which of the following represent the correct translation? A

 5     4 

B

 5     4

C

 5    4 

D

 5    4

11 In Diagram 5, QS = QR and PQR is a straight line. 1449/1

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S 8 cm P

Q

6 cm

R

DIAGRAM 5 The value of sin ∠ SQR is A

3 5

B

3 4

C

4 5

D

4 3

12 Diagram 6 shows the graph of y = cos x y 1

0o -1

x

S x DIAGRAM 6

The value of S is A 90o B 180o C 270o D 360o y 13

In Diagram 7, O is the origin of a Cartesan plane.

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r°

P(8, 15) x

O DIAGRAM 7

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10

The value of cos r ° is

14

A −

8 17

B −

15 17

C −

8 15

D −

17 15

Diagram 8 shows a pyramid with an equilateral triangle base, PQR. Point V is right on top of point R.

DIAGRAM 8 Name the angle between the two planes PQR and VPQ. A ∠VPR B ∠VRX C ∠VXR D ∠VQR

K

15 In Diagram 9, J and L are two points on a horizontal plane. LK is a vertical pole. 8m

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12 m DIAGRAM 9

L

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The angle of depression of point J from vertex K is A B C D

26° 24' 28° 46' 32° 24' 33° 41'

16 In Diagram 10, PQ and RS are two vertical poles on a horizontal plane. The angle of elevation of P from R is 35° . P

tm R Q

4m

15 m DIAGRAM 10

S

Calculate the value of t. A B C D

10.5 14.5 16.5 20.5

17 It is given that the bearing of point F from E is 028  . Find the bearing of E from F. A 028  B 062  C 152  D 208  18 P ( 64oN, 100o W ) and Q are two points on the earth’s surface such that P and Q is the diameter of the earth. The position of point Q is A (64o N, 80o E ) 1449/1

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B (64o N, 100o E ) C (64o S, 100o E ) D (64o S, 80o E ) 19

(2m – n)2 + 4mn = A B C D

20

21

2( h + 1) 4 − e − eh 2e in its simplest form.

Express

A

4 + eh 2eh

B

4 − eh 2eh

C

4 + eh 2eh 2

D

4 − eh 2eh 2

3 4 5 6

If 16 A B C D

23

as a single fraction

Given 2( 2 + 3m ) = 5 ( 2m – 4 ), then m = A B C D

22

4m2 + n2 4m2 – n2 4m2 – 8mn – n2 4m2 – 4mn + n2

−

3 2

n

1  =   , n is 4

1 3 5 7

m m − = 7 , express n in terms of m . 3 n 3m A n= m − 21 Given

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3m 21 − m 21 − m C n = 3m m − 21 D n= 3m B n=

24

List all the integers p that satisfy both the inequalities 4p + 3 ≤ 27 and A B C D

2 5

2p > 2. 3

4, 5 5, 6 4, 5, 6 5, 6, 7

Given that the mean of 2, 7, 8, 10 and x is 6, find the value of x. A B C D

3 5 6 9

Diagram 11 is a pictograph showing the number of computers sold in January and February. The number of computers sold in March are not shown. January February March represent 10 computers DIAGRAM 11 If the information above is represented by a pie chart, the angle for the sector of computers sold in February is 168° . The number of computers sold in March was A 20 B 30 C 40 D 50

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Table 1 shows the frequency and accumulated frequency for the length of leaves collected by Ahmad.

TABLE 1 Find the value of x. A 29 B 31 C 40 D 50 28

Diagram 12 shows the graph of the function y = −xn + b. y

x

`

2

DIAGRAM 12 The value of b is A B C D 29

2 4 6 8

It is given that the universal set, ξ = {x : 19 ≤ x ≤ 31, x is an integer} and set R = {x : x is a number such that the sum of its two digits is a prime number} . Find set R' . A {19, 23, 29, 31} B {21, 23, 25, 27, 29} C {20, 21, 23, 25, 29, 30} D {19, 22, 24, 26, 27, 28, 31}

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15 Given that ξ = {9 ≤ x ≤ 18, x is an integer}, E = {x : x > 14} and F = {x : x is a multiple of 3}, find n( E ∩ F ).

30

A B C D 31

2 4 6 8

The Venn diagram in Diagram 13 shows the set U, set V and set W. Given that ξ = U ∪V ∪W . V U •4

•2

•5

W

•1

•9 •6

•7 •3

DIAGRAM 13 List all the elements of the set U∩W∪V' A B C D

{ 2, 4, 9 } { 2, 3, 4, 7 } { 1, 5, 6, 9 } { 1, 2, 3, 4, 5, 6, 7 }

32

Determine the x-intercept for the straight line 5y – 3x = 9 A -5 B -3 C 3 D 5

33

Diagram 14 shows the straight line UV in a Cartesian plane y

V

x

O U

DIAGRAM 14 The gradient of the straight line UV is A 3 B 4 C 7 D 9 1449/1

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Given that the probability of choosing a man at random from a group of tourists is

4 11

.

If there are 28 women in the group, find the total number of tourists in the group. A B C D 35

36

37

16 44 56 64

A bus had 28 passengers which 8 are men. At a bus stop, 5 men boarded and 3 women alighted from the bus. If a passenger is then chosen at random from the bus, find the probability that the passenger is a man. A

3 26

B

23 26

C

13 30

D

17 30

 1 3  7 − 1  =   , find matrix M Given that M +   − 6 5   2 − 3  − 6 4  A   − 8 8  8 2  B  − 4 1  − 8 − 2  C   4 −1  6 − 4  D  8 − 8 0 k   = (12 0) , find the value Given that ( 2 − 4 )  h 3 of h and k. A B C D

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h=3 , k= 6 h = 6, k = 3 h = -3, k = 6 h = -6 , k = 3

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T varies directly as the square root of p and inversely as the square of g. This joint variation can be written as A T ∝ pg B T∝ C T∝

p

2 g p g p

D T∝ 2 g 39

It is given that y varies directly as the square root of x and y = 6 when x = 16. Calculate the value of x when y = 9. A B C D

40

25 36 64 81

Table 2 shows the variables, h, m and p, which satisfy the relationship h ∝ 4 64 2

h

m p

m . p

6 144 y

TABLE 2 Find the value of y. A 2 B 6 C 8 D 12

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END OF QUESTION PAPER JAWAPAN KERTAS 1 EXCEL 2 SPM 2008

1. D 2. B 3. C 4. C 5. A 6. B 7. A 8. B 9. C 10. B 11. C 12. D 13. A 14. C 15. D 16. B 17. D 18. D 19. A 20. A

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21. D 22. B 23. A 24. C 25. A 26. B 27. C 28. D 29. D 30. A 31. A 32. B 33. A 34. B 35. C 36. D 37. C 38. D 39. B 40. A

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CO-ORDINATOR Judy Lian Yee Ling SEKTOR PENGURUSAN AKADEMIK

LIST OF PANEL MEMBERS 1.

Wong Teck Sing

SMK Likas, Kota Kinabalu.

2.

Mercy Mathew

SM Stella Maris, Kota Kinabalu.

3.

Aau Fui Lin

SMK Elopura, Sandakan

4.

Dodibitius Bangin

SMK Tamparuli, Tamparuli

5.

Frederick Leyong Soh Andu

SM Shan Tao, Kota Kinabalu.

6.

Judy Fung Siew Jin

SMK ST. Michael, Penampang.

7.

Lim Kien Kwok

SM Tinggi K.K, Kota Kinabalu.

. .

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