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8/11/2019 Percubaan Matematik 2014 [Skema].doc
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KERTAS JAWAPANEXCEL II - 2011
MATEMATIK SPM KERTAS 2
Question Solution an Ma!" S#$e%e Marks
1
St!ai&$t otte linex '( #o!!e#tl) !a*n
Re&ion #o!!e#tl) s$ae+
Note ,1+ A##et soli line .'(/ a*a! K12+ A*a! P1 to s$ae !e&ion oune ) t*o #o!!e#t lines+
K1
P2 3
00
y = 8
y
x
y = x + 2
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2 p q' - o rp- 12q' or3p 12q'-12 o! e4ui5alent
Note ,Atte%t to e4uate t$e #oe66i#ient o6 one o6 t$e un"no*ns/ a*a! K1-7q' 13 or 7p ' 21 ore4ui5alent
OR
p ' 11 3 qorq -1 - p
1or e4ui5alent
Atte%t to %a"e one o6 t$e un"no*ns as t$e su8e#t/ a*a! K1-7q' 13 or 7p ' 21 ore4ui5alent
OR
=
11
11
3
939:1:919::
1
q
p
Note ,A*a! K1 i6
1+
qp '
;
inversematrix
11 or
=
11
1
31
q
p
2+
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3 2d2 =d 1> ' 0
:2d 9:d (9 ' 0 ore4ui5alent
d' or 1+?
d' (
Note ,1+ A##et *it$out @'0
2+ A##et t$!ee te!%s on t$e sa%e sie/ in an) o!e!
+
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5:a9
:9
6:a9
:9
Ienti6) BFC o! CFB
oBFC
BFC
7>+23
1
(tan
=
= or e4ui5alent
o! 23 37D
137
222
(0
=0
137
222
(0
=0
?0
13137
22
(0
=0 or 77
7
22
(0
3?
777
22
(0
3?1313
2
11313
7
22
(0
=0+
7?+2? or3
17?
Note,
1+ A##et 6o! K %a!"+2+ Co!!e#t ans*e! 6!o% in#o%lete *o!"in&/ a*a! KK2
P1
K1
N1
K1
K1
N1
KI
K1
N1
3
13 7 7
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>:a9
:9 :i9
:ii9
:2/S9/ :3/ S9/ :?/ S9/ :2/M9/:3/ M9/:?/M9F
:2/ S9/ :3/ S9F
(
2
1
:2/S9/ :2/ M9/ :3/ M9/ :?/S9/ :?/M9F
(
?
Note, A##et ans*e! *it$out *o!"in& 6o! K1N1
P1
K1
N1
K1
N1
=+ :a9
:9
p ' -k' 2:-(9 :9k' -21
P1
P1
K2
7 :a9
:9
:#9
All GG Se%ua
I6 3x' 1 / t$enx' 0 GGJi"a 3x' 1/ %a"a x' 0+
I6 x' 0/ t$en 3x
' 1 GGJi"a x' 0/ %a"a 3x' 1
/
Note , seen/ a*a! K1
P1
P1
P1
K2
5
5
7
8/11/2019 Percubaan Matematik 2014 [Skema].doc
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Note,
1+
2+
8/11/2019 Percubaan Matematik 2014 [Skema].doc
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8/11/2019 Percubaan Matematik 2014 [Skema].doc
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!a$ o! Question 12Graf untuk Soalan12
y= 4x- 10
y= 3x2+ x+4
x
y= -30
-2.7
-2.5
1.7 3.5
11 2 43
4
0
y
3
1
3
2
1
2
4
5
4
2
3
y= -2x-2
= -
x
8/11/2019 Percubaan Matematik 2014 [Skema].doc
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1:a9:i9 :>/39 P1
:ii9 :(/19Note,Point :3/19 %a!"e on ia&!a%/ a*a! P1+
P2
:9 :i9 Clo#"*ise !otation o6 =00 aout t$e #ent!e : 1/9 orPuta!an =00 a!a$ 8a% aa usat :1/9+
P
Note,1+ P2 , Rotation =00 anti#lo#"*ise orRotation at #ent!e :1/9 or
Puta!an =00 la*an a!a$ 8a%orPuta!an aa usat :1/9
2+ P1 , Rotation orPuta!an+
:ii9 Enla!&e%ent at #ent!e o! :0/29 *it$ s#ale 6a#to! 2 or
Pe%esa!an aa usat atau :0/ 29 an 6a"to! s"ala2+
Note,1+ P2 , Enla!&e%ent #ent!e :0/29 orEnla!&e%ent s#ale 6a#to! 2 or
Pe%esa!an usat :0/29 orPe%esa!an 6a"to! s"ala2+
2+ P1 , Enla!&e%ent orPe%esa!an
P (
:#9 a!ea o6EHJ' :2 92X a!ea o6ABC
= 3 X =0
A!ea o6EHJ ' (0 unit 2
A!ea o6 t$e s$ae !e&ion' (0 - =0
' 270 unit 2
K2
N1
12
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13:a9
Class inte!5alSelan kelas
Mioint!itik tena"
!e4uen#)#ekerapan
0 = 3+? 30 3=
33+? 2?0 ?= ?3+? >(0 (= (3+? 1070 7= 73+? 11>0 >= >3+? 3=0 == =3+? 2
Class inte!5al , all t$e ans*e!s a!e #o!!e#t P1
!e4uen#) , all t$e ans*e!s a!e #o!!e#t P1!e4uen#) , all t$e ans*e!s a!e #o!!e#t P1
:9 ?+=32?+>33?+7311?+(310?+?3>?+332?+3 ++++++
(?+? or (?2
K2
N1
:#9
Note,1+ Allo* t*o %ista"es 6o! K1+
i+e+ %i oint *!on&l) #oie o! *!on& %ultili#ation2+ In#o%lete *o!"in& 6ollo*e ) #o!!e#t ans*e!/ a*a! KK2
i+e+2(20
' (?+?
A.es !a*n in #o!!e#t i!e#tion *it$ uni6o!% s#ales 6o!23+? . 103+? an 0 ) 11
;7 oints #o!!e#tl) lotte usin& t$e #o!!e#t %ioints+
:23+?/09 an :103+?/09 lotteS%oot$ an #ontinuous st!ai&$t line asses t$!ou&$ all #o!!e#t oints usin&t$e &i5en s#ales
P1
K2
K1
N1
?
:9 ( P1 1
12
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Graph !r "#$s%&!' 14
1
24(5
3
4
5
8
)
10
11
34(5 44(5 54(5 74(5 84(564(5 )4(5 104(5
2
7
6
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1?:a9
Co!!e#t s$ae *it$ !e#tan&leABC$% an se%i #i!#le A
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1?:9 :i9
Co!!e#t s$ae *it$ t!aeBiu%JCSHan!e#tan&le#$CJ an'%$(All soli lines+
%' CS=SH=(# $%&$#J
Measu!e%ents #o!!e#t to 2+0 #% :one *a)9 anS'(%$C ///// an = 1=0#
K1
K1e K1
N2 eK1K1 3
1?:9 :ii9
LM
3 #%
J2 #%
3 #%
#% 3 #%
K
D S
H
P +? #% C
#%
E
1 #%
#%
7 #%$A
(
H
#
)
G
8/11/2019 Percubaan Matematik 2014 [Skema].doc
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Co!!e#t s$ae *it$ !e#tan&le)GH( an GA$H*All soli lines+
Note, I&no!eE#
Ean# 8oine *it$ as$e line to 6o!% !e#tan&le GE#H
A$AG G) E
Measu!e%ents #o!!e#t to 2+0 #% :one *a)9 an all an&les at5e!ti#es o6 !e#tan&les = 1=0
K1
K1e K1
K1
N2 eK1K1
?12
1( :a9 : )(0 / E1?0 9 GG : +(0 / !1?0 9
Note , 1?0 o! E o! !/ a*a! P1
P1P2
:92:=0 (09 (0
(00 n+%+
K1
N1 2
:#9
(0#os(09200: +
Note, + 9200: o! usin& (0#os / a*a! K1
1?00 n+%+
K2
N1
:i9
:ii9
(00 7 o! 3200
(0(0
7(00
S10
K2
K1
N1
12