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NAMA : ____________________  TINGKATAN : _____________ 

SMK JALAN TASEK 

PEPERIKSAAN PERTENGAHAN TAHUNTINGKATAN 4MATEMATIK 1449/2KERTAS 211 MEI 2015(7.45 – 10.15)

2 JAM 30 MINIT

 JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

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1. Kerta !a"a# $#$ %e#&a#'#&$ 'aa*a&$a# :  +a*a&$a# A 'a# +a*a&$a# +.

2. Ja,a semua sa!a" 'a"a% Ba#a$%a" A 'a#

%a#a-%a#a em&a' !a"a# 'ar$a'aBa#a$%a"B.

3. T"$ a,aa# a#'a a'a ra#&'$e'$aa#

'a"a% erta !a"a# $#$.

4. T#a# era %e#&$ra a#'a. I#$!"e*

%e%a#t a#'a #t %e#'aata#%ara*.

5. J$a a#'a *e#'a %e#ar a,aa#ata"a#

 a,aa# a#& te"a* '$at. Ke%'$a#t"$

U"'u( (e$u"aa" Peme)%(saBa#a$%

a"Sa!a"

Ma)(a#

Pe"u#

Ma)(a#D%&e)!

e#%

A

1 3

2 53 4

4 4

5 4

4

7 4

5

9 5

10 7

11

+12 12

13 12

14 12

15 12

 Jum!a# 100

KA*ALAN MUTU KERTAS SOALAN  IS6IAKANL68

N N 8A;ANIMAT SA

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  erta !a"a# $#$ %e#&a#'#&$ 23 *a"a%a#

er>eta .

Rumus Ma'ema'%(/Mathematical Formulae

Pe)(a%'a" /Relations

1 a

m

 ? a

n

 @ a

nm+

13. ( A) @ # ( A)  # (S)

2 a

m

  a

n

 @ a

nm−

3( )   mnnm aa   =

14. ( A’ ) @ 1 – ( A)

4 Jara /Distance  @ ( )   )(1212   y y x x   −+−

5 T$t$ Te#&a* / Midpoint  ( x,y ) @

   

     ++

2,

2

2121  y y x x

M$# @ *a$" ta%a* #$"a$ 'ata  +$"a#&a# 'ata

  Mea# @ % !B 'ata

  N%er !B 'ata

7 M$# @ *a$" ta%a* (#$"a$ t$t$ te#&a* e"a ? eeraa#  8a$" ta%a* eeraa#

Mea# @ % !B (>"a %ar ? BreCe#>)  % !B BreCe#>

. rata La @ ara a#& '$"a"$  Maa a#& '$a%$"

  ADera&e ee' @ '$ta#>e traDe""e'

  T$%e tae#

9 te!re% $t*a&!ra/t*a&!ra T*e!re% : >

2

 @ a

2

E

2

10 % @12

12

 x x

 y y

−−

11 % @ - $#taa#-  $#taa#-?

  % @ - -$#ter>et

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  ?-$#ter>et

12 AF @1

ad−bc (   d   −b−c a )

BENTUK DAN RUANG/SHAPES AND SPACE

1 La TraeH$% @ 1 ? *a$" ta%a* 'a $$ e"ar$ ? t$#&&$  2

Area !B traeH$% @ 1 ? % !B ara""e" $'e ? *e$&*t  2

2 L$"$ta# "ata# @

  jd    π  π     2=

  $r>%Bere#>e !B >$r>"e @  jd    π  π     2=

3 La "ata# @

2  jπ  

  Area !B >$r>"e @

2  jπ  

4. La er%aa# %e"e#&#& $"$#'er @  jt π  2

  rDe' rBa>e area !B >"$#'er @

  jt π  2

5. La er%aa# Bera @ 4

2  jπ  

  SrBa>e area !B *ere @ 4

2  jπ  

. I$ a' $"$#'er @t   j

2π  

  !"%e !B >"$#'er @t   j

2π  

7. I$ a' Bera @ 4 r  3

SrBa>e area !B *ere @ 4 r  3. I$ a' r$%a te&a @ "a erata# re#ta ? a#a#&

!"%e !B r$&*t r$% @ >r! e>t$!#a" area ? "e#&t*

9. I$ a' !# @ 1t   j

2π  

  3

  !"%e !B >!#e @ 1t   j

2

π  

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  3

10 I$ a' ra%$' te&a @ 1 ? "a taa ? t$#&&$  3

  !"%e !B r$&*t ra%$' @ 1 ? ae area ? *e$&*t  3

11 8a$" ta%a* 't e#'a"a%a# !"$&!# @ (# – 2) ? 10

0

 

S% !B $#ter$!r a#&"e !B a !"&!# @ (# – 2) ? 10

0

 12. a#a#& "e#&! @ 't at  L$"$ta# "ata# 30

ar> "e#&t* @ a#&"e te#'e' at >e#tre

  >$r>%Bere#>e !B >$r>"e 30

0

 

13 "a e>t!r @ 't at

  La "ata# 30

0

  area !B e>t!r @ a#&"e te#'e' at >e#tre

  Area !B >$r>"e 30

0

 

14 Bat!r a"a @ PA’   PA

  S>a"e Ba>t!r @ PA’   PA

15 "a $%e @ ? "a !e  Area !B $%a&e @ ? area !B !e>t

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+A8AGIAN A/S6TIN AO52 MAKA8/52 MAKSP

 Ja,a e%a !a"a# 'a"a% a*a&$a# $#$. Answer all questions in this section

1. Ga%araa* e## %e##a# '$ ra#& a,aa# %e##a# et P, setQ 'a# et

R 'e#&a# ea'aa# et e%eta ε= P∪Q∪ R .

The Venn diagram in the answer space shows set P ! and R suchthat the uni"ersal set

ε= P∪Q∪ R .

a'a raa* '$ ra#& a,aa# "!rea##n the diagram in the answer space shade

(a)  P∩ Q  

() (  P' ∩Q¿ᴜ   

 O3 %ara*/3 marksP

 Ja,aa#/ Answer  :

(a)

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()

 

2. e#&a# %e#&&#aa# &a%ar raa* e## e#ara$a# #r-#rer$t.

$sing Venn diagram list the elements o% the %ollowing&

  ξ

a)  A Q )  A Q ! R >)  A R ! Q ’ 

O5 %ara*/" marksP

 Ja,aa#/ Answer :

a)

)

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   A

  . .2.5

  . .1.9  .3 .4

 

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>)

3. Se"ea$a# era%aa# a'rat$ er$t.Sol"e the %ollowing 'uadratic e'uation&

7k(k – 2) @ k  E 4  3

O4 %ara*/# marksP Ja,aa#/ Answer  :

4. a# L$"a %e%aar M 150 #t (4 x  – 5) a* . $er$ a*a,a*ar&a et$a a* $t $a"a* M2 x  >ar$ $"a#&a# a#& '$e"$ !"e*a# L$"a.

Puan (ila paid an amount o% RM)*+ %or ,-. /*0 1oo2s& 3i"en thateach o% the 1oo2s costs RM4. 5nd the num1er o% 1oo2s 1ought16 Puan (ila&

O5 %ara*/" marksP

 Ja,aa#/ Answer  :

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5. 8$t#& #$"a$ x  'a# y  a#& %e%aa# era%aa# "$#ear ere#ta er$t :

Calculate the "alue o% . and 6 that satis%6 the %ollowingsimultaneous linear e'uations7

2 x  – y  @ 4 x  E 3 y  @ -5

O4 %ara*/# marksP Ja,aa#/ Answer  :

. Se%"a* 70 e$#& t$et !ra#& 'e,aa 'a# a#a-a#a '$a" '$ea*a#&&#& ,aa#&.

Set$a e$#& t$et !ra#& 'e,aa 'a# a#a-a#a er*ar&a M5 'a#M3 %a$#&-%a$#&  'a# %"a* t$a# $a"a* M290. ar$ $"a#&a# ee$#& t$et !ra#&'e,aa 'a# $"a#&a#

e$#& t$et a#a-a#a a#& '$a".

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U

S

 T

1 >%

10 >%

>%

12 >%

4 >%

9

  A total o% 8+ adult and children tic2ets were sold in a cinema&Each adult and children tic2et

cost RM9 and RM* respecti"el6 and the total collection wasRM4:+& Find the num1er o%   adult tic2ets and the num1er o% children tic2ets sold&

O4 %ara*/# marks

P

 Ja,aa#/ Answer  : 

7.

aa* 7 %e##a# >a#t%a# ea* eea" a#& ter'$r$ 'ar$a'aea* !$' 'a# ea* $"$#'er.Diagram 8 shows a com1ined solid consisting o% a cu1oid and ac6linder &

aa* 7 / Dia$ram %

e#&a# %e#&&#aa#7

22=π  

  *$t#& $$a' 'a"a% >% 3  a&$&a#&a# eea" $t.

;6 using7

22=π  

+  calculate the "olume in cm 9  o% thecom1ined solid &

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[ 4 markah/4 marks]

 Ja,aa#/answer  :

. L$%a $$ !"a 'e#&a# ear$ 1 >% '$$%a# '$ 'a"a% ea* t!#& a#&ere#t $"$#'er  erear$ 3 >% eert$ '$t#a# 'a"a% aa* . a$r '$ta#& e 'a"a%t!#& teret #t

%e%e#*$ e%a ra#& !!#& '$ a#tara !"a 'a# t!#&.

  Fi"e 1alls with radius ) cm is 2ept in a c6lindrical 1in with radius9 cm as shown in Diagram

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O5 %ara*/5 marksP

 Ja,aa#/Answer  :

9. a) Le#&aa# er#ataa#-er#ataa# er$t %e#&&#aa#e#&a#t$t$ Ve%aW

ata Ve$"a#&a#W aa er#ataa#-er#ataa# teret a'a"a*e#ar.

  Complete the %ollowing statements using the 'uanti5ersallB or someB so that

the statements are true&

($) _____________________e&$t$&a %e%#a$ t$&a $$. _____________________ triangles ha"e three sides.

($$) _____________________ e#ta&!# a'a"a* e#ta&!# eata. _____________________ pentagons are regular pentagons.

) Nataa# a%a a'a er#ataa# er$t a'a"a* e#ar ata a"state whether the %ollowing compound statement is true or

%alse&

5   ³  @ 125 'a# - X -7

5   ³  @ 125 a#' - X -7

>) T"$ ,ua $%"$a$ er'aara# er#ataa# er$t :

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rite down two implications 1ased on the %ollowingcompound statement 7

 x @ -4 $a 'a# *a#a $a x  @-4 . ? /- i% and onl6 i% . ? /-

O5 %ara*/" marks

P Ja,aa#/A#,er:

(a)($)YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY.....

  ($$)YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY..

()

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY..

(>) I%"$a$ 1/I%"$>at$!# 1 :

 YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

  I%"$a$ 2/I%"$>at$!# 2

 YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

 YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

10. a"a% raa* 10 A! 'a# D $a"a* &ar$ "r a#& e"ar$ '$ A#tara ata%a "a$#.

n the diagram )+ A; and CD are straight lines which are parallelto one another&

   y 

 

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  !(2) 

  x 

  A

(-1) D(-2-)

aa* 10/dia$ram '(

ar$/Find 

a) e>er#a# &ar$ A+the gradient o% the line A;

) era%aa# &ar$

the e'uation o% the line CD

>) $#taa#-? &ar$ the ./intercept o% the line CD

O7 %ara*/% marksP

 Ja,aa#/ Answer :

(a)

()

(>)

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11. a"a% aa* 10 )PQ 'a# )RS*  $a"a* et!r a&$ 'a "ata# a#&er"a$#a# teta$ %e%#a$ at a#& a%a ).

n diagram )+ #P! and #RST are sectors o% two diGerent circleswhich ha"e the same centre #

  aa* 11/Dia$ram ''

  $er$ @ 0Z T @ 45Z 'a# T @ 90Z. e#&a#

%e#&&#aa#7

22=π  

8$t#&a#

a) er$%eter 'a"a% >% e"r* raa* $t.) "a 'a"a% >%2 a,aa# a#& er"!re

  3i"en P#! ? + R#T ? -* and P#T ? :+&$sing7

22=π  

 calculate

a0 perimeter in cm o% the whole diagram+ area in cmI o% the shaded region-

O %ara*/. marksP

 Ja,aa#/ Answer  :

(a)

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()

+A8AGIAN +/S/*0)1 !O4 MAKA8/#& MAR2SP

 Ja,a e%a !a"a# 'ar$a'a a*a&$a# $#$. Answer all 'uestions %rom this section.

12. (a) aa* 12 %e##a# 'a t$t$ M 'a# 1 a'a at ata* artea#.  Diagram )4 shows two points M and N on a Cartesian plane.

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    aa* 12/Dia$ram '

  e#e"%aa# T  $a"a* at tra#"a$ (   3−1)

  e#e"%aa# R $a"a* at tara# 90 "a,a# ara* a% a'a at (02)

  Trans%ormation T is a translation (   3−1)

  Trans%ormation R is an anticloc2swise rotation o% :+J a1out thecentre ,+40&

($) Nataa# !!r'$#at $%e a&$ t$t$ M '$ a,a* e#e"%aa# R.State the coordinate o% the image o% point M undertrans%ormation R.

($$) Nataa# !!r'$#at $%e a&$ t$t$ 1 '$ a,a* e#e"%aa# T .State the coordinate o% the image o% point N undertrans%ormation T .

O2 %ara*/ marksP

  () aa* 12() %e##a# t$&a a* e&$ t$&a 4 2  'a# 5 a#&'$"$ a'a ata* >artea#.

2  $a"a* $%e a&$ 4 '$ a,a* at tara# 90.  Diagram )4,10 shows three triangles K L and ( which aredrawn on a Cartesian Plane&

L is the image o% K under a rotation o% :+J&

aa* 12()/Dia$ram '6+

($) Nataa#State(a) Ara* tara# $t

The direction o% the rotation

() !!r'$#at a&$ at tara# $t

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the coordinates o% the centre o% the rotation

($$) 5 $a"a* $%e a&$ 4 '$ a,a* e#e"%aa# * . 8ra$a#e"e#&a#a e#e"%aa# * .( is the image o% K under trans%ormation T& Descri1e in %ull trans%ormation T 

. O4 %ara*/# marksP

  (>) a'a raa* 12(>) a'a ra#& a,aa# %e##a# $$ e%at/’7’8’9’  $a"a* $%e a&$ $$

e%at 6=G8 '$ a,a* at e%eara#.  n the diagram )4,c0 in the answer space 1elow shows'uadrilateral EF3H is the

image o% 'uadrilateral EF3H under an enlargement .

($) a'a raa* 12(>) '$ ra#& a,aa# ta#'aa# T ea&a$ ate%eara#.

#n the diagram )4,c0 in the answer space mar2 T as thecentre o% enlargement&

($$) Nataa# Bat!r a"a a&$ e%eara# $t.State the scale %actor o% the enlargement .

($$$) La $$ e%at /789 $a"a* 7>%. 8$t#& "a 'a"a% >% $$e%at /’7’8’9’ .The area o% 'uadrilateral EF3H is 8 cmI& Calculate thearea in cmI o% 'uadrilateral EF3H.

O %ara*/. marksP

 Ja,aa#/ Answer  :

(a)($) _____________________________________________________________________________ 

  ($$) _____________________________________________________________________________ 

()($) (a) ________________________________________________________________________ 

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  ()($) () ________________________________________________________________________ 

  ($$) ____________________________________________________________________________ 

  ____________________________________________________________________________ 

(>)($)

 aa* 12(>)/Dia$ram '6c

  ($$) _____________________________________________________________________________ 

  ($$$)

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13. (a) a'a raa* 13(a) a'a ra#& a,aa# '$ a,a* %e##a# t$t$* (-13) 'a# &ar$ "r  x  @ 1 '$"$ a'a at ata* >artea#.  n the diagram )9,a0 in the answer space 1elow the point T,/)90 and the straight line

 . ? ) on a Cartesian plane.

($) Ta#'aa# !!r'$#at $%e a&$ t$t$ *  '$ a,a* a#t"a# a'a x  @ 1 a'a ata* artea# $t.Mar2 the coordinate o% the image o% point T underreection . ? ) on the Cartesian plane.

($$) L$ $%e a&$ M '$ a,a* a#t"a# a'a x  @ 1 a'a ata*artea# $t.Draw the image o% M under reection o% .?) on theCartesian plane.

($$$) Nataa# !!r'$#at $%e a&$ t$t$ 1 '$ a,a* a#t"a# a$- x .State the coordinate o% the image o% point N underreection in the ./a.is.

O4 %ara*/# marksP

 Ja,aa#/ Answer  :

($)($$)

  aa* 13(a)/Dia$ram '36a

($$$) _____________________________________________________________________________ 

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  () aa* 13() %e##a# 'a a* e&$ t$&a 'a# a#& '$"$

a'a ata* >artea#. $a"a* $%e a&$ '$ a,a* e#e"%aa# . 8ra$a#e"e#&a#a e#e"%aa# .

  Diagram )9,10 shows two triangle P and ! drawn on aCartesian plane& ! is the  image o% P under trans%ormation & Descri1e in %ulltrans%ormation &

 aa* 13()/Dia$ram '36+

O2 %ara*/ marksP

  (>)

  aa* aa* 13(>)/$a&ra% 13(>)

a"a% raa* 13(>) a#& '$er$ PQ*  $a"a* $%e a&$ SQR '$a,a* at e%eara# terte#t. >ar$n the diagram in )9,c0 P!T is the image o% S!R under a certain enlargement& Find 

($) =a>t!r a"aThe scale %actor 

($$) at e%eara#

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The centre o% enlargement 

($$$) La S $a "a T $a"a* 54 >%.The area o% S!R i% the area o% P!T is *- cmI&

O %ara*/ %arP

 Ja,aa#/A#,er :

13() ____________________________________________________________________________ 

  ____________________________________________________________________________ 

13(>)($)

  ($$)

  ($$$)

14. aa* '$ a,a* %e##a# $"a#&a# a#& '$a>a !"e* e%"a#24 !ra#& %r$'  a'a ta*# 2014.  The diagram 1elow shows the num1er o% 1oo2s read 16 a group

o% 4- students in the  Oear 4+)-&

31 43 49 24 2 223 30 32 39 43 2223 3 31 30 41 3745 33 2 27 3 33

 aa* 14/Dia$ram '#

(a) +er'aara# 'ata 'a"a% raa* 14 'a# 'e#&a# %e#&&#aa# a$H e"a 5

"e#&aa# a'a" 14 a'a ra#& a,aa#.;ased on the data in diagram )- and 16 using a class inter"al o%

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* complete ta1le )- in the answer space.O4 %ara*/# marks:

() +er'aara# Ja'a" 14 '$ (a) *$t#&a# %$# a#&&ara# a&$ $"a#&a#

a#& '$a>a !"e* e!ra#& %r$'.;ased on Ta1le )- in ,a0 calculate the estimated mean %or thenum1er o% 1oo2s read 16 a students.

O3 %ara*/3 marksP

(>) U#t >era$a# !a"a# $#$ &#aa# erta &raB.e#&a# %e#&&#aa# a"a 2 >% ea'a 5 a* a'a a$%e#&B 'a# 2 >% ea'a e!ra#& %r$' a'a a$ %e#>a#>a#& "$at *$t!&ra% a&$ 'ata teret.

For this part o% the 'uestion use graph paper&

;6 using a scale o% 4 cm to * 1oo2s on the horiontal a.is and 4cm to ) student on the "ertical a.is draw a histogram %or thedata&

O4 %ara*/# marksP

(') +er'aara# *$t!&ra% a#& '$"$ '$ (>) #ataa# $"a#&a# %r$' a#&%e%a>a ra#& 'ar$a'a 3 a* .;ased on the histogram drawn in ,c0 state the num1er o%students who read less than 9 1oo2s.

O1 %ara*/' mark P

 Ja,aa#/ Answer  :

(a)

Se"a#& e"a/classinter;al

Keeraa#/7requency   T$t$ Te#&a*/midpoint 

22 – 2 527 – 31

()

(>) ea'a erta &raB a#& '$e'$aa#.  Re%er to graph paper pro"ided 

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(') 

15. ata 'a"a% aa* 15 %e##a# %ara* a#& '$er!"e* e%"a# 30!ra#& %r$' 'a"a%

at $a# Mate%at$.  The data in Diagram )* shows the mar2s o1tained 16 a group o%9+ students in a  Mathematics test&

11 22 4 44 45 4929 44 35 29 45 3239 40 25 34 59 29

32 0 3 3250 5 29 53 59 55

aa* 15/Dia$ram '"

(a) +er'aara# 'ata '$ ata "e#&aa# a'a" 15 '$ ra#& a,aa#.;ased on the data complete Ta1le )* in the answer space&

O3 %ara*/3 marksP

() Nataa# e"a %!'a".State the modal class.

O1 %ara*/' mark P

(>) +er'aara# Ja'a" 15 '$ (a) *$t#& %$# a#&&ara# %ara* a&$ e!ra#&%r$'.;ased on the Ta1le )* in ,a0 calculate estimated mean mar2 o% astudent .

O3 %ara*/3 marksP

(') e#&a# %e#&&#aa# a"a 2>% ea'a 10 %ara* a'a a$%e#&B 'a# 2>% ea'a 1 !ra#& %r$' a'a a$ %e#>a#>a#& "$at !"$&!# eeraa# a&$ 'ata teret.;6 using the scale o% 4 cm to )+ mar2s on the horiontal a.is and 

4 cm to ) student on the "ertical a.is draw a %re'uenc6 pol6gon%or the data.O4 %ara*/4 marksP

(e) Mara* "" $a# $t $a"a* 50. Me#&&#aa# !"$&!# eeraa# '$ (>)#ataa# $"a#&a# %r$' a#& "" 'a"a% $a# $t.The passing mar2 %or the test is *+& $sing the %re'uenc6 pol6gonin ,c0 5nd the num1er o% students who passed the test&

O1 %ara*/' mark P

 Ja,aa#/ Answer  :

(a)

1449/2 SULIT

8/17/2019 Mid Year 2015

24/26

24

Mara*/Mark   T$t$ Te#&a*/Midpoint  Keeraa#/7requency 

10 - 19

()

(>)

(') ea'a erta &raB a#& '$e'$aa#.  Re%er to graph paper pro"ided .

(e)

1449/2 SULIT

8/17/2019 Mid Year 2015

25/26

25

SALAN TAMAT

6N = U6STIN

 

1449/2 SULIT

8/17/2019 Mid Year 2015

26/26

2

SALAN TAMAT6N = U6STIN