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Transcript of Mid Year 2015
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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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. .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 *+& $sing the %re'uenc6 pol6gonin ,c0 5nd the num1er o% students who passed the test&
O1 %ara*/' mark P
Ja,aa#/ Answer :
(a)
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Mara*/Mark T$t$ Te#&a*/Midpoint Keeraa#/7requency
10 - 19
()
(>)
(') ea'a erta &raB a#& '$e'$aa#. Re%er to graph paper pro"ided .
(e)
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SALAN TAMAT
6N = U6STIN
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SALAN TAMAT6N = U6STIN