SBP P1 2008 (2)

Embed Size (px)

Citation preview

• 8/6/2019 SBP P1 2008 (2)

1/24

SEKTOR SEKOLAH BERASRAMA PENUH

BAHAGIAN SEKOLAH

KEMENTERIAN PELAJARAN MALAYSIA

PEPERIKSAAN PERTENGAHAN TAHUN

TINGKATAN 5 2008

MATEMATIK

Kertas 1

Satu jam lima belas minit

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

1. Kertas soalan ini adalah dalam Bahasa Inggeris.2. Calon dikehendaki membaca maklumat di halaman 2.

Kertas soalan ini mengandungi 24 halaman bercetak.

1449/1

Matematik

Kertas 1

Mei 2008

14

1jam

• 8/6/2019 SBP P1 2008 (2)

2/24

1449/1

1449/1 2

INFORMATION FOR CANDIDATES

1. This question paper consists of 40 questions.2. Answerall 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 diagrams in the questions provided are not drawn to scale unless stated.7. A list of formulae is provided on page 3 to 4.8. You may use a non-programmable scientific calculator.

• 8/6/2019 SBP P1 2008 (2)

3/24

1449/1

1449/1 3

MATHEMATICAL FORMULAE

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

RELATIONS

1 a

m

v

a

n

= a

m+ n

2 amzan = a m n

3 (am )n = a mn

4 A-1

1

ac

bd

5 P(A ) =)(

)(

Sn

An

6 P(Ad ) = 1 P(A)

7 Distance = 2212

21 yyxx

8 Midpoint, (x, y ) =

2,

2

2121 yyxx

9 Average speed =

10 Mean =

11 Mean =

12 Pythagoras Theorem

c2

= a2

+ b2

13 m =12

12

xx

yy

14 m =

distance travelled

time taken

sum of data

number of data

sum of (class mark frequency)

sum of frequencies

y-intercept

x-intercept

• 8/6/2019 SBP P1 2008 (2)

4/24

1449/1

1449/1 4

SHAPES AND SPACE

1 Area of trapezium =2

1 sum of parallel sides height

2 Circumference of circle = Td= 2Tr

3 Area of circle = Tr2

4 Curved surface area of cylinder = 2Trh

5 Surface area of sphere = 4Tr2

6 Volume of right prism = cross sectional area length

7 Volume of cylinder = Tr2h

8 Volume of cone =31Tr

2h

9 Volume of sphere =3

4Tr

3

10 Volume of right pyramid =3

1 base area height

11 Sum of interior angles of a polygon = (n 2) 180

12Q

360

centreatsubtendedanglecircleofncecircumfere

lengtharc !

13Q360

centreatsubtendedangle

circleofarea

sectorofarea!

14 Scale factor , k=

A

A'

15 Area of image = k2

area of object

• 8/6/2019 SBP P1 2008 (2)

5/24

1449/1

1449/1 5

1

Round off 0.05078 correct to three significant figures.

A 0.05

B 0.0508

C 0.051

D 0.508

2

Express 410305.2 v as a single number.

A 0.0002305

B 0.002305

C 0.02305

D23050

3

61032.8 v + 5106.7 v

A510432.8

v

B610432.8

v

C51008.9 v

D 61008.9 v

4 !22

100110011

A 100112

B 10101 2

C 211010

D 11100 2

• 8/6/2019 SBP P1 2008 (2)

6/24

1449/1

1449/1 6

6

In Diagram 1, JKLMN is a regular pentagon. MNFandLEFare straight lines.

The value ofx +y =

A 57

B 42

C 36

D 21

5

2m4 8 = 10156 , find the value ofm.

A 0

B 1

C 2

D 3

K

L J

E

NFM

x

y

15

Diagram 1

• 8/6/2019 SBP P1 2008 (2)

7/24

1449/1

1449/1 7

7

Diagram 2 shows a regular pentagonPQRSTand an isosceles trianglePUM.

Calculate the value ofx +y

A 108

B 120

C 144

D 180

8

In Diagram 3,RSis a tangent to the circlePTSQ at SandPQR is a straight line.

The value of m is

A 54o

B 50o

C 46o

D 40o

TP

Q

R

S

U

M

xo

yo

Diagram 2

Diagram 3

y P

T

S

Q

50

86

m

• 8/6/2019 SBP P1 2008 (2)

8/24

1449/1

1449/1 8

9 Diagram 4 shows two pentagons,R and Son a Cartesian plane. Sis the image ofRunder a reflection in the linePQ.

Find the equation of the line PQ.

A 1!x

B 1!y

C 2!x

D 0!y

y

-4

-3

-2

-1 0 1 2 3 4

4

3

2

1

-1

-2

-3

-4

x

R

Diagram 4

• 8/6/2019 SBP P1 2008 (2)

9/24

1449/1

1449/1 9

10 Diagram 5 shows an incomplete triangle KdLdMd , which is the image oftriangleKLMunder an enlargement.

Find the coordinates of point Ld.

A ( 3, -3 )

B ( 4, -2 )

C ( 2, -4 )

D ( 6, 2 )

Diagram 5

y

1 2 3 4 5 7

4

3

2

1

-1

-2

-3

-4

x

K

ML

M

d

Kd

• 8/6/2019 SBP P1 2008 (2)

10/24

1449/1

1449/1 10

11

In Diagram 6,PQSandRSTare straight lines. Given that tan x =2

1and

cos y =5

4 .

Find the length ofRQ.

A 12 cm

B 16 cm

C 20 cm

D 24 cm

Diagram 6

P

TR

Q

S

y

x

8 cm

• 8/6/2019 SBP P1 2008 (2)

11/24

1449/1

1449/1 11

13

Diagram 8 shows the graph ofy = cos x.

Find the value ofx.

A 60

B 120

C 300

D 330

12

In Diagram 7, PQRS is a rectangle, STR is a straight line and ST=3

1SR.

Find the value of tan PTR .

A 23

B 3

2

C 2

1

D3

2

1 1

y

x

1

1

1

1

Diagram 8

12 cm

Diagram 7

P Q

RS T

6 cm

1

y(x, 0.5)

-1

0

x

• 8/6/2019 SBP P1 2008 (2)

12/24

1449/1

1449/1 12

14

Diagram 9 shows a right pyramid with an isosceles triangle basePQR. Eia a midpoint

ofQR.

Calculate the angle between the lineESand the planePQR.

A '04133

B '02435

C '01438

D '02441

15

In Diagram 10,PTand QRSare two vertical poles on a horizontal plane.

Determine the angle of elevation ofQ fromP.

A QRP

B PRS

C PQR

D QPR

Diagram 9

Diagram 10

10cm

8cm

13 cm

S

R

Q

PyE

Q

P R

ST

• 8/6/2019 SBP P1 2008 (2)

13/24

1449/1

1449/1 13

16

!

3

12

4

2

A

1

3

B

1

4

C

1

4

D

2

4

17 In Diagram 11, JMNand JKL are tangents to the circle FKM.

Find the value ofx.

A 54

B 62

C 64

D 72

Diagram 11

L

MJ N

K F72

x

• 8/6/2019 SBP P1 2008 (2)

14/24

1449/1

1449/1 14

19

!2)3()3(2 yxyxx

A 22 963 yxyx

B 22 9122 yxyx

C 22 9123 yxyx

D 22 9123 yxyx

18

Diagram 12 shows the graph of y = 8 x3.

Find the value of k.

A -2

B -8

C 2

D 8

y

Diagram 12

x

y = 8 x3

y 0,k O

• 8/6/2019 SBP P1 2008 (2)

15/24

1449/1

1449/1 15

22 Given that nnn ! 8243 , find the value of n.A 3

B 4

C 5

D 6

20

Given that, 33

2!

t

express t in terms ofm.

A

3

)32( 2m

B2

3

32

m

C 9

922

m

D2

9

32

m

21

Express22

1

p

p

p

6

3 as a single fraction in its simplest form.

A2

2

6

33

p

pp

B 2

2

6

33

p

pp

C 2

2

6

31

p

pp

D

2

2

2

13

p

pp

• 8/6/2019 SBP P1 2008 (2)

16/24

1449/1

1449/1 16

23

3

214

a

acan be written as

A58

a

B18 a

C516 a

D a16

24

Simplify 983322 nmnm

A26 m

B26m

C28m

D148

m

25

The solution for 131219 e mm is

A2010 m

B 1410 e m

C 1410 e m

D 1210 e m

• 8/6/2019 SBP P1 2008 (2)

17/24

1449/1

1449/1 17

26

Diagram 13 is a pictograph showing the number of laptops sold on Monday and

Tuesday. The number of laptops sold on Wednesday is not shown.

Monday

Tuesday

Wednesday

The sale on Tuesday was 20% of the total sale for the three days. The number oflaptops sold on Wednesday was

A 90

B 150

C 180

D 450

represents 30 laptops

Diagram 13

• 8/6/2019 SBP P1 2008 (2)

18/24

1449/1

1449/1 18

27

Diagram 14 is a bar chart which is incomplete, showing the number of fruit trees in anorchard.

The ratio of the number of Mango trees to the number of Durian trees is 5 : 3.

Find the total number of fruit trees in the orchard.

A 240

B 280

C 300

D 320

Type of tree

Diagram 11

20

40

60

80

100

Number of fruit trees

Dragon

fruit

Mango Durian

Diagram 14

0

• 8/6/2019 SBP P1 2008 (2)

19/24

1449/1

1449/1 19

29

Given \ = {a, b, c, d, e, i, o, u}, X= {a, i, u}, Y= {a, b, d} andZ= { b, c, d}.

Find ? AZYXn '

A 2

B 3

C 4

D 5

28 Diagram 15 shows a graph of a function .

The equation of the function is

A xy

5!

B5

xy !

Cx

y5

!

D5

xy !

y

O

5

1 5

1

x

Diagram 15

• 8/6/2019 SBP P1 2008 (2)

20/24

1449/1

1449/1 20

30

Diagram 16 is a Venn diagram with the universal set \ = X Y Z.

It is given that ][2 YXn

n ! . Find the value of k.

A 5

B9

C 10

D 12

31

Diagram 17 is a Venn diagram which shows the universal set \, setP, set Q and setR.

The shaded region in the Venn diagram represents the set

A QRP

B (P R )d Q

C (PdRd) Q

D (P R )d Q

Diagram 17

X Y

Z

62k

10

5

7 + k

7 6

Diagram 16

P Q

R

\

• 8/6/2019 SBP P1 2008 (2)

21/24

1449/1

1449/1 21

32

In Diagram 18 below, the gradient of the straight line3

4!TV .

Find the coordinates of point N.

A ( 4, 3 )

B ( 3, 4 )

C ( 3, 5 )

D ( 4, 5 )

33

Find they-intercept of the straight line 1056 ! yx

A 5

6

B3

5

C6

5

D 2

y

Diagram 18

V(3,0)

N

Tyy

O

• 8/6/2019 SBP P1 2008 (2)

22/24

1449/1

1449/1 22

34

Table 1 shows the distribution of teachers in three schoolsR, Sand T.

If a teacher is chosen at random from the three schools, what is the probability that a

male teacher from school Sis chosen?

A139

74

B139

44

C139

42

D139

20

35 A box contains a few good eggs and 15 rotten eggs. If an egg is chosen at random from

the box and the probability of getting a rotten egg is7

3, find the total number of eggs

in the box.

A 12

B 20

C 35

D 56

Table 1

• 8/6/2019 SBP P1 2008 (2)

23/24

1449/1

1449/1 23

36 Table 2 shows the relationship between three variables w, tand h.

w t h

2 2 4

4 m 9

Table 2

Given that w wh

t , calculate the value ofm.

A 3

B 6

C 12

D 18

37

Given that xy w and 32 ! zx . If 10!y when 4!z , calculate the value of z

when 8!y .

A 0.5

B 1.5

C 2.5

D 3.5

38

F varies directly as the square root of m and inversely as the square of n. Given that

5

4!F when 64!m and 5!n , express Fin terms ofm and n.

A22

3

n

mF !

B22

5

n

mF !

Cm

nF

3

2 2!

Dm

nF

4

3 2!

• 8/6/2019 SBP P1 2008 (2)

24/24

1449/1

1449/1 24

END OF QUESTION PAPER

39 Given that

x

4 5y =

11

2020, calculate the value ofx and ofy.

A x =5

1 , y = 5

B x =5

1, y = 5

C x = 5, y =5

1

D x = 5, y =5

1

40

M is a 22 v matrix where

1

0

2

32 M =

0

1

3

4

Find the matrix ofM.

A

2

1

7

2

B

2

1

7

2

C

2

1

7

2

D

2

1

7

2

S