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BAHAGIAN PENGURUSAN

SEKOLAH BERASRAMA PENUH / KLUSTER

KEMENTERIAN PELAJARAN MALAYSIA

PEPERIKSAAN AKHIR TAHUN SELARAS SBP 2008 1449/1TINGKATAN EMPAT

MATHEMATICS

Kertas 1

Oktober

1jam 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 belakang kertas soalan ini.

1449/1 2008 Hak Cipta Sektor SBP [Liha !"#"$ah

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Kertas soalan ini mengandungi 20 halaman bercetak.

MATHEMATI%AL &ORMULAE

The following formulae may be helpful in answering the questions. The symbols gien arethe ones !ommonly use".

RELATIONS

1 am x an# a m$ n

2 aman # a m % n

3 & am'n# a mn

4 (-1= b!a"1

a!

b"

5 istance = 2 22 1 2 1

! " ! ") ) y y +

# $id%oint& !)* y" =

++

2&

2

2121 yy))

' ()erage s%eed =

* $ean =

+ $ean =

1, thagoras /heorem

!2# a2$ b2

11 P & ( '="!

"!

Sn

(n

12 P & (' # + P&('

13 m=12

12

))

yy

14 m=


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2

sum o0 data

number o0 data

sum o0 !class mark 0reuenc"

sum o0 0reuencies

y-interce%t

)-interce%t

distance tra)elled

time taken

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SHAPES AN' SPA%E

1 (rea o0 tra%eium = 2

1

sum o0 %arallel sides height

2 Circum0erence o0 circle = "= 2r

3 (rea o0 circle = r2

4 Cur)ed sur0ace area o0 clinder = 2rh

5 ur0ace area o0 s%here = 4r2

# olume o0 right %rism = cross sectional area length

' olume o0 clinder = r2h

* olume o0 cone =3

1r2h

+ olume o0 s%here =3

4r3

1, olume o0 right %ramid = 3

1

base area height

11 um o0 interior angles o0 a %olgon = & n6 2" 1*,7

123#,

centreatsubtendedangle

circleo0ncecircum0ere

lengtharc=

133#,

centreatsubtendedangle

circleo0area

sectoro0area=

14 cale 0actor & k =P(

P(8

15 (rea o0 image = k 2 area o0 ob9ect


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1. :ound o00 3' 2*5 correct to three signi0icant 0igures.

( 3' ,,,

B 3' 2,,

C 3' 2+,

3' 3,,

2. ;x%ress 2

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#. = "3!"2!5 y)y)

( y) +2

B y) 112

C y) *

y) 3*

'. ( ) ( )= ))) 31432 2

( +** 2 ++ ))

B +*1# 2 + ))

C +*1# 2 ++ ))

+12* 2

+ ))

*. >ist all the subsets o0 setH= ?p* q@.

( ?p@* ?q@

B ?p@* ?q@& ? @

C ?p@* ?q@&?p&q@

?p@* ?q@& ?p&q@*? @

+. Ai)en the uni)ersal set& = T, & set,= ?a& b& c@ and set T = ?b& c& d& e& 0@&

0ind the )alue o0 n!".

( 2

B 4

C #

*

1,. iagram 1 is a enn diagram shoing the uni)ersal set& -= ?orm our students@&

set = ?tudents ho %la badminton@ and setH=?tudents ho %la tennis@.


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Ai)en n!-" = 5,& n!" = 23& n!H" = + and n ( ) #=H. & 0ind the number o0 students

ho do not %la the to games.

( 44

B 3,

C 24

1*

11. iagram 2 shos a straight lineP/on a Cartesian %lane.

/he distance o0 /is 2 units.

ind the gradient o0P/.

( 2

1

B4

3

C 1

2

12. In iagram 3&1,is a straight line on a Cartesian %lane.


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y

/

)

!*& #"P

#

H

I(A:($ 1

I(A:($ 2

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ind the gradient o01,.

( 2

B4

3

C43

2

13. ind the x-interce%t o0 the straight line )y 23 = 12.

( #

B#

1

C 4

4

1

14. iagram 4 shos the score obtained b a grou% o0 0i)e %u%ils in a ui here)is an

integer. /he mode score is #.

2 ) ) 4 +

/hen another three %u%ils ith scores o0 3& 3 and * 9oins the grou%.

ind the median score o0 the grou%.

( 3

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I(A:($ 5

/he total number o0 books sold in 0our months is 14,. /he ratio o0 books sold in

$arch to books sold in $a is 3 D 2. ind the number o0 books sold in $a.

( 14

B 1#

C 24

4,

1#. iagram # is a %ie chart hich shos the combined results o0 a time trial race taken

b to grou%s o0 %u%ils. /able 1 shos the results obtained b the to grou%s but it

is incom%lete.

Calculate the number o0 %u%ils in the Eello Arou%.

( 14,

B 14#

C 1#,

1+4

1' ( number is chosen at random 0rom setP= ?)D)is an integer & 2; 1

15#

Guali0

o not

uali0

I(A:($ #

Arou%Fumber o0 %u%ils

Guali0 o not uali0

Eello

Blue #, *,

/otal 13,

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(1,

1

B5

1

C1,3

5

2

1*. /able 2 shos the t%es o0 0ood bought b #, students at the canteen.

I0 a student is chosen at random 0rom the grou%& the %robabilit o0 the student

buing 0ried noodles is1

4. Calculate the )alue o0 q.

( 11

B 13

C 15

2#

1+. ( container holds 2* red marbles and a number o0 blue marbles. ( marble is %icked

at random 0rom the container. /he %robabilit o0 %icking a red marble is *

'

.

Ho man blue marbles are there in the container

( 4

B *

C 21

24


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/%e o0 0ood Fumber o0 students

ried noodles m

Fasi lemak 24

Bread q

:oti canai 1,

+

/(B>; 2

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2,. ( student %uts 2, cards ith serial number 21 to 4, in a box. ( card is dran at

random. ind the %robabilit o0 draing a card ith a serial number hich is a

multi%le o0 5.

( 4

1

B5

1

C1,

1

2,

1

21. In iagram '&3is a tangent to the circle34Hat3.

ind the )alue o0).

( #4

B 5*

C 52

2#


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1,

I(A:($ '

4

#4J

)5

3

H

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22. In iagram *&671is a tangent to the circle centre & at7.64Pand,P7are

straight lines.

ind the )alue o0y.

( 2*

B 34

C 5#

#2

23. In iagram +&3H is a tangent to the circle centre & at .

ind the )alue o0 .

( ''

B 55

C 45

35


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11

3 H

P/

13J

#*J 5

1

,

2*J

y54

7

6

P

I(A:($ *

I(A:($ +

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24. In iagram 1,&P/9Sis a rectangle andP1=,9= 3 cm.

ind the )alue o0 tan .

(12

5

B12

5

C13

5

13

5

25. It is gi)en that sin)=25

24 and +,J x 1*,J.

ind cos).

(25

'

B25

'

C'

24

'

24

2#. iagram 11 shos the gra%h o0y = sin).


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12

P

S

$

, 9

/

13 cm

1

15 cm

I(A:($ 1,

y

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ind the )alue o0 m.

( 1+,J

B 21,J

C 24,J

3,,J

2' In iagram 12&P/and9Sare to )ertical %oles on a horiontal %lane.

Calculate the angle o0 de%ression o0 )ertex9 0rom )ertexP.

( 2# 34

B 41 5+

C 4* ,1

#3 2#


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13

1

1

!m& 5, "

I(A:($ 11

P

/

9

S

2, m

45 m

5, m

I(A:($ 12

)

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2* iagram 13 shos a steel 0rame76P1,%laced on a horiontal %lane.

67andP1, are )ertical hile61is horiontal.

/he angle o0 ele)ation o0 %oint10rom %oint7is #*.

Calculate the height& in m& o0P,.

( +

B 11

C 13

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ertex Sis )erticall abo)e

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I(A:($ 1'

Calculate the )alue o0pL q.

( 1'5

B 14,

C 135

1,,

33 iagram 1* shos 0i)e %entagons dran on suare grids.

I(A:($ 1*

Nhich o0 the %entagons (& B& C or & is an image o0 %entagon6under a rotation

34 iagram 1+ shos to uadrilaterals&7and1& dran on suare grids.


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1#

K

A

B

%

'

(

B M

L

71

;

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I(A:($ 1+

1is the image o07under an enlargement.

Nhich o0 the %oint& (& B& C& or & is the centre o0 the enlargement

35. Choose a suitable linear euation in one unknon 0or the 0olloing statement.

( 3!) L ' " = 34

B 3 L)L ' = 34

C 3 L ') = 34

3) L ' = 34

3#. Ai)en thatqr

rp

4+= & ex%ress qin terms o0pand r.

(2

4

1

= r

p

rq

B ( )

2

4

1

prrq =

C

= r

p

rq

2

1

( )prrq =2

1

3'.

2

2

5

32

1

25

5'

=


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1'

%

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('

1

B'

5

C '

35

3*. im%li03

*2

3

2 "!

n

nm .

( nm3

B 53nm

C nm 43

54

3

nm

3+ ol)e the ineualities * 6 3x x L 1# and 5 6 2x O x 6 1,.

(

B

C

4,. Ai)en that)is an integer& 0ind all the )alues o0)that satis0 both o0 the

ineualities2

4 ) 5 and )32 O 3 .

( 1&,&1

B 2&1&,&1


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1*

2

2

2

2

5

#

5

#

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C 1&,&1&2

2&1&,&1&2

EN' O& (UESTION PAPER

IN&ORMATION &OR %AN'I'ATES

1. /his uestion %a%er consists o0 4, uestions.

2. (nser a$$uestions.


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3. ;ach uestion is 0olloed b 0our alternati)e ansers& A) B) %or '. or each

uestion& choose *+"anser onl. Blacken our anser on the ob9ecti)e anser

sheet %ro)ided.

4. I0 ou ish to change our anser& erase the blackened mark that ou ha)e done./hen blacken the s%ace 0or the ne anser.

5. /he diagrams in the uestions %ro)ided are not dran to scale unless stated.

#. ( list o0 0ormulae is %ro)ided on %age 2 to 3.

'. Eou ma use a non-%rogrammable scienti0ic calculator.

1449/1 2008 Hak Cipta Sektor SBP [Liha !"#"$ah2,

sbp f4 final 2008

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