MM2 Jawapan Pecutan Akhir Set1-2-3-4

8/10/2019 MM2 Jawapan Pecutan Akhir Set1-2-3-4

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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,


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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


3/14


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'


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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

&

&


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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

+


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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)


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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


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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


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MATHEMATICS 2

'#estion 13 ( Set 2

3

1

2

3

4

/

.

0

1+

. 13 1. 23 2.

Ae

!re"#enc$


10/14


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


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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-


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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


13/14


MATHEMATICS 2

13


14/14


MATHEMATICS 2

14

1

3

2

12

11

1'

5

4 6

6

6

6

6

6

6

'#estion 13 ( Set 4

MM2 Jawapan Pecutan Akhir Set1-2-3-4

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