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8/10/2019 MM2 Jawapan Pecutan Akhir Set1-2-3-4
1/14
MODUL PECUTAN AKHIR SPM
MATHEMATICS 2
AnswersSET 1
Section A
1.
2. 3,2
1== qp
* matrices method can be used
3. 1,5
2== xx
4.(a) Non-statement
(b) Implication 1: I ,SetBSetA then e!er"
element o # is also the
element o $.
Implication 2 : I e!er" element is also the
element o $ then
SetBSetA
(c) xxn
+ is not a %uadratic e&pression.5. (a) 5'm
(b) 24 ms
(c) 124 ms
. (a) m4 , n 2 , k -2
(b) 1',11 == yx
.(a) $oth letters
( ){ ( )
( )}VRUR
QUQTQVPUPTP
,),,(
(),,(),,(),,(,,,,
+( $oth letters) 2,
-
(b) number and letter
( ){ ( )
( ) 2,(),1,(),-,(),,(,2,),1,(
,5(),,5(),-,(),,(,2,,1,
RRQQQQ
UTPPPP
+(number and letter) 2,
15
Section B
12. (a)
x -2 -1 ' 1 2 3 4 5
y 11 1 -5 - -5 1 11 25
(b) refer to graph
(c) (i)y 5.5
(ii)x -'., 2.5
(d)y 4x-
x '.45, 3.55
13. (a)
ass (/0) re%uenc" idpoint
1-3 2 2
4- 5-
1'-12 11
13-15 5 14
1-1 4 1
1-21 2 2'
22-24 1 23
1
4
"
4o
" 4
2" &
&
1 2
+ (+,1) (+,2) (+,) (+,) (+,) (+,) (+,
5 (5,1) (5,2) (5,) (5,) (5,) (5,) (5,
(,1) (,2) (,) (,) (,) (,) (,
6 (6,1) (6,2) (6,) (6,) (6,) (6,) (6,
8/10/2019 MM2 Jawapan Pecutan Akhir Set1-2-3-4
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MODUL PECUTAN AKHIR SPM
MATHEMATICS 2
(b) ean 3(
3-'
= 1'.3 /0
(c) refer to graph
(d) The modal class is 1!1"
14. (a)
(b)
(c)
2
cm
3 cm
3 cm
cm
3 cm
3 cm2 cm
1 cm
2 cm
cm
3 cm
1 cm
2 cm
3 cm
2 cm
8/10/2019 MM2 Jawapan Pecutan Akhir Set1-2-3-4
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MODUL PECUTAN AKHIR SPM
MATHEMATICS 2
SET 2
Section A
1.
2.2
1,
2
1== yx
* matrices method can be used
3. 3,3
1== pp
4. (a) (i) #ll
(ii) 7ome
(b) I 2x8 thenx8 4
(c) 5y
5. (a) 1- ms
(b) 2(.1 ms
(c) t1
. (a)
52
42
2
1
(b) 3,5 == yx
.
3 4 N
# (#,) (#,3) (#,) (#,4) (#,N)
+ (+,) (+,3) (+,) (+,4) (+,)
5 (5,) (5,3) (5,) (5,4) (5,N)
n(7) 15
(a) ( ){ (),,(),,(),,(),,(,, P$PTP#A$ATA
+($oth letters) 5
2
(b)
( ){ ,5(),,5(),4,(),3,(),4,(,3, $TPPAA
+(number and letter) 15
*
Section B
12. (a) m 4 , n -5
(b) refer to graph
(c) (i)y -2.2
(ii)x -'.4, 2.4
(d) y -& -3
x -1.4, 4.4
13. (a)
9lass Inter!al
7elan0 ;elas
4'
8/10/2019 MM2 Jawapan Pecutan Akhir Set1-2-3-4
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MODUL PECUTAN AKHIR SPM
MATHEMATICS 2
14.
SET 3
1.
2. p , q -5* matrices method can be used
3. m2
1, m -2
4. (a) 1'1'' = and is a actor o
(b) Implication 1 : Ix> 8 12 thenx8 5
Implication 2 : Ix8 5
(c) +remise 1: #ll positi!e number are 0reaterthan ?ero.
5. (a) seconds
(b) -4.5 2ms
(c) 5 1ms
. (a) a 3 , %3
1
(b)x 3,y 4
.
@ A B 6
- (,@) (,A) (,B) (,6)
@ (@,) - (@,A) (@,B) (@,6)
A (A,) (A,@) - (A,B) (A,6)
B (B,) (B,@) (B,A) - (B,6)
6 (6,) (6,@) (6,A) (6,B) -
n(7) 2'
(a) $oth consonant
{ (),,(),,(),,(),,(),,( RT&R&TTRT&
+(both consonant) 1'
3
(b) and 6 { }),(),,( TRRT
+(CD and C6D) 1'
1
Section B
12.
(a)& -3 -2.5 -1.5 -1 ' 1 2 2.5 3
" -2 . 14.1 14 1' 13.1 22
4
"
'
" & > 3
&
&
8/10/2019 MM2 Jawapan Pecutan Akhir Set1-2-3-4
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MODUL PECUTAN AKHIR SPM
MATHEMATICS 2
(b) refer to graph
(c) (i) " .5
(ii) & 2.5
(d) " 2& > 5
& -2.2, '.5, 2.2
13. (a)ime
spent
(hrs)
pper
boundar"re%uenc"
9umulati!e
re%uenc"
2'-2 2.5 ' '
3'-3 3.5 2 2
4'-4 4.5 5
5'-5 5.5 15
'- .5 1' 25
'- .5 34'- .5 5 3
'- .5 1 4'
(b) ' =
(c) refer to graph
(d) (i) 4.5 hours
(ii) here are 3' students Eho surin0 the
internet or 4.5 hours or less in a month.
14.(a)
cm
2cm 2cm 3 cm
(b)
cm
5cm
cm
2cm4cm
3 cm
(c)
1cm
2cm
2 cm
2cm
cm
SET 4
1. (a)
(b)
5
6
+
6
+
8/10/2019 MM2 Jawapan Pecutan Akhir Set1-2-3-4
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MODUL PECUTAN AKHIR SPM
MATHEMATICS 2
2. m 3, m1
4
3. p 3, q -2
4. a) i) alse
ii) true
b) k > 1is not an odd inte0er
c) 4n = 3, n 2, 3,4F
5. (a) 25 minutes
(b)5
2
(c) 5
.Sample B1 B2 B3 G1 G2
B1 - (B1,B2) (B1,B3) (B1,G1) (B1,G2)
B2 (B2,B1) - (B2,B3) (B2,G1) (B2,G2)
B3 (B3,B1) (B3,B2) - (B3,G1) (B3,G2)
G1 (G1,B1) (G1,B2) (G1,B3) - (G1,G2)
G2 (G2,B1) (G2,B2) (G2,B3) (G2,G1) -
a) ($1,$2), ($1,$3), ($2,$1), ($2,$3),
($3,$1), ($3,$2)
3
1'=
b) ($1,G1), ($1,G2), ($2,G1), ($2,G2), (G1,$1), (G1,$2),(G1,$3), (G1,G2), (G2,$1), (G2,$2), (G2,$3), ($3,G1), ($3,G2),
(G2,G1)
1'=
. (a)
3k =
(b)
2
11
1
11
p
q
=
=
Section B
12 (a) " 1.5, y 3.5
(b) refer to graph
(c) (i) 1.2 HyH 1.'
(ii) '.5 x '.
(d) 1. x 1. 1. x 1.
13.Class
IntervalMipoint !re"#enc$
I "1 ! "( 23 4
II ") ! * 2
III 31 - 35 33 12
I 3 - 4' 3
41 - 45 43 4
I 4 - 5' 4 3
II 51 - 55 53 2
(b) 35.25
+c, Refer to graph
(d) The modal class is *1 ! *( age
14.(a)
(b)(i)
8/10/2019 MM2 Jawapan Pecutan Akhir Set1-2-3-4
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MODUL PECUTAN AKHIR SPM
MATHEMATICS 2
(iii)
Grap% &or '#estion 12 ( Set 1
1 2 3 4 *1*2
*
*1+
1
1+
2+
2
3+
$
+
$ = 22* 4 *
-
*+-./ 2-0+-4
3-/2
'#estion 13 ( Set 1
2
1
2
3
4
/
.
0
1+
. 11 14 1
Mass )
!re"#enc$
2+ 2
8/10/2019 MM2 Jawapan Pecutan Akhir Set1-2-3-4
8/14
MODUL PECUTAN AKHIR SPM
MATHEMATICS 2
Grap% &or '#estion 12
1 2 3 4 *2 /
$
*1+
*/
*12
*2
*4
+
2
4
*.
$ =
$ = 3 5 2 * 2
*+-4
*1-3
2-4
$ = 2
*2-2
*1
4-3
8/10/2019 MM2 Jawapan Pecutan Akhir Set1-2-3-4
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MODUL PECUTAN AKHIR SPM
MATHEMATICS 2
'#estion 13 ( Set 2
3
1
2
3
4
/
.
0
1+
. 13 1. 23 2.
Ae
!re"#enc$
8/10/2019 MM2 Jawapan Pecutan Akhir Set1-2-3-4
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MODUL PECUTAN AKHIR SPM
MATHEMATICS 2
1'
Grap% &or '#estion 12
y
1
2'
25
15
3'
5
1'
'1 5J2 2 3 4J3
5
1'
y - 15
y - 2x> 5
0-
'.2.2
2.5
8/10/2019 MM2 Jawapan Pecutan Akhir Set1-2-3-4
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MODUL PECUTAN AKHIR SPM
MATHEMATICS 2
11
'#estion 13 ( Set 3
1+
1
2+
2
3+
20- 30- 40- 0- /0- 0-
3
4+
C#m#lative &re"#enc$
Time %o#rs)
T%ir "#artile
4-
.0- 00-
8/10/2019 MM2 Jawapan Pecutan Akhir Set1-2-3-4
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MODUL PECUTAN AKHIR SPM
MATHEMATICS 2
12
" &
"
y
4
+
/
.
1+
*/
*4
2
*.
*2
*1+
*1 2 31*2*3 4*4
"
'#estion 12 ( Set 4
+-/.1-.*1-3
*1-1
8/10/2019 MM2 Jawapan Pecutan Akhir Set1-2-3-4
13/14
MODUL PECUTAN AKHIR SPM
MATHEMATICS 2
13
8/10/2019 MM2 Jawapan Pecutan Akhir Set1-2-3-4
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MODUL PECUTAN AKHIR SPM
MATHEMATICS 2
14
1
3
2
12
11
1'
5
4 6
6
6
6
6
6
6
'#estion 13 ( Set 4
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