set 12 skema k1 & k2.doc

8/10/2019 SET 12 SKEMA K1 & K2.doc

http://slidepdf.com/reader/full/set-12-skema-k1-k2doc 1/13

1449/1 & 2(PP)

Mathematics

Paper 1/2

SEKOLAH MENENGAH KEBANGSAAN BESE!

PEPE!KSAAN PE"ENGAHAN "AH#N 2$1%

"!NGKA"AN

MA"HEMA"!'S 1449/1/2

Paper 1 & 2

MAK!NG S'HEME

Mars %100)140

21( ×

+ Paper Paper

This Marking Scheme consist of 1% printed pages

8/10/2019 SET 12 SKEMA K1 & K2.doc


SULIT 44912(0TI 2)

MAK!NG S'HEME

S!T 12

"!NGKA"AN

MA"HEMA"!'S PAPE 1

1 " 11 # 21 # $1 %

2 " 12 # 22 & $2 &

$ # 1$ " 2$ % $$ "

4 % 14 & 24 & $4 #

' & 1' & 2' & $' %

# 1 % 2 & $ "

" 1 % 2 " $ #

* % 1* & 2* # $* %

9 # 19 # 29 # $9 #

10 % 20 " $0 " 40 %

MAK!NG S'HEME

144912 +TI 2 200 (,,) SULIT

2

8/10/2019 SET 12 SKEMA K1 & K2.doc


SULIT 44912(0TI 2)

SE" 12

"!NGKA"AN

MA"HEMA"!'S PAPE 2

Secti*+ A

-o. Marking Scheme Marks

1. (a)

(/)

-ote gie ,1

,1

,2

%

2 ∠ "#& or ∠ &#"

Tan ∠"#& $0

* or ∠"#& Tan 31 (

$0

*)

'.0° or '°.4

-ote #ccept '.1°

,1

52

-1

4

$.

26 2 7 '6 8 12 0

(26 8 $)(6 7 4) 0

6 2

$ 8 4

-ote #ccept :itho;t < 0 <

51

51

-1-1

4

144912 +TI 2 200 (,,) SULIT

$

=

>,

=

>,

=

>,

8/10/2019 SET 12 SKEMA K1 & K2.doc


SULIT 44912(0TI 2)

4. x 7 $ y 24 or 2 x 8 y 22 or x 117 $ y or y * 8 2 x or

any equivalent

x $' or 3 y=14 or any equivalent

x ' y −2

+=

−12

$1

y

x

*

11

(51)

y

x

)(1

1

−−

− 12

$1

*

11

(51)

6 ' (-1)

? @ 2 (-1)

' -ote #ns:er gie -1

2

÷−

51

51

-1 -1

4

'. $0 ×$

1 4 22

2 $ 2

× × × ÷

$

1 4 22 $0

2 $ 2

× − × × × ÷

or any equivalent

1

90

or 90.1 or'41

51

51

51

-1

4

144912 +TI 2 200 (,,) SULIT

4

8/10/2019 SET 12 SKEMA K1 & K2.doc


SULIT 44912(0TI 2)

(a) If (n 71) is an een integer then n is an odd integer

(/) ImpAication 1 Ifn

m

is a proper fraction then m and

n are integers :ith 0 B mB n

ImpAication 2 If m and n are integers :ith 0 B mB n

thenn

m

is a proper fraction.

(c) 4(n 2 ) 8 $

n 1 2 $ 4 C..

-ote

4(n 2 ) 8 $ gie 51

51

51

51

5151

(a)

*

20 19×

9'

14

(/)19

*

20

12× 7

19

12

20

*×

9'

4*

51

-1

52

-1

*.(a)

1*0 222 10.'

$0 × × × or

120 222

$0 × × ×1*0 22

2 10.'$0

× × × 7120 22

2 $0

× × × 7 7 7

*. or2

*$

or20

$

(/)21*0 22

10.'$0

× × or 2120 22

$0

× ×

21*0 22 10.'$0 × × − 2120 22

$0 × ×

121.92 or11

12112

or14$

12

51

51

-1

51

51

-1 ,

144912 +TI 2 200 (,,) SULIT

'

8/10/2019 SET 12 SKEMA K1 & K2.doc


SULIT 44912(0TI 2)

9 (a) 4

(/)0(

$012

−−

D $

(c) 1 4× 12 721 ( 12 7 ;) × * or any equivalent

; 20

,1

51

-1

52

-1 ,

10a) m#"

$

2−

0

'

y

x

−−

$

2− or 0

$

2− ( ') 7 c or c

1'

2

? $

2− 6 7

1'

2 or any equivalent

/)0 ( 4)

' $

− −−

or4 0

$ '

− −−

or 2

0

'

y

x

−−

2 or ( 4)

$

y

x

− −−

2 or 0 2(') 7 c or

D 4 2($) 7 c or ? 26 310

?3intercept 10− or ? −10

,1

51

-1

,1

51

-1

11.(a)

1(4$

1

×−×

−

−$1

(4

1

−

−$1

(4

or

−

−

2

1

1

1$

2

or any equivalent

(/)

41

$

y

x

=

10

12

y

x

=

1

−

−$1

(4

10

12

x @ 2

y $

-ote

−=

$

2

y

x gie -1

51

-1

,1

51

-1

-1

,

144912 +TI 2 200 (,,) SULIT

8/10/2019 SET 12 SKEMA K1 & K2.doc


SULIT 44912(0TI 2)

12 (a) (i) (2 2)

(ii) ($ 8 2)

(iii) ( 8 $)

(/) (i) (a) M- =otation 90 0 cAock:ise centre at ! E (3 2 1)

-ote

(1) =otation 90 0 cAock:ise or

(2) =otation centre at ! E (3 2 1) gie ,2

($) =otation onA? gie ,1

(/) N- !nAargement scaAe factor 2

&entre at ! E ( 3 2 1)

-ote

(1) #ccept M is enAargement - is =otation or

#ccept - is enAargement M is =otation as M-

-M for ,$.

(2) !nAargement scaAe factor 2 or

($) !nAargement centre at ! (3 2 1) gie ,2

(4) !nAargement onA? gie ,1

(ii) 14 × (2) 2

'

,1

,1

,2

,$

,$

51

-1 12

144912 +TI 2 200 (,,) SULIT

8/10/2019 SET 12 SKEMA K1 & K2.doc


SULIT 44912(0TI 2)

1$ (a) y 11 y 3 '

Note

(1) If not stated gie 5151 for the ta/Ae

E if points are correctA? marked on the graph

E the c;re passes e6actA? thro;gh the points.

(/) Graph :#6es are dra:n in the correct direction :ith ;niform

scaAe. in the range @$.' ≤ x ≤ $.' and −1' ≤ y ≤

1.

#AA points and 2 pointsF are correctA? marked

Smooth c;re and contin;o;sA? in range of @ $.' ≤ x ≤ $.' :ith no straight Aine part and passing

thro;gh aAA the correct 9 points.

Note

(i) E * points are correctA? pAotted 51

(ii) +ther scaAe ;sed min;s 1 mark from the 5-

marks o/tained.

(c) (i) '.4 ≤ ? ≤ '.'

(ii) $.$ ≤ x ≤ $. 4

(d) The eG;ation y ' x − '

Straight Aine y ' x − ' correctA? dra:n and meet the

c;re.

The aA;e of x $.2 ≤ x ≤ $.$

0. ≤ x ≤ 0.

Note(i) #AAo: - mark if x is sho:n on the graph.

(ii) The aA;e of x o/tained /? caAc;Aation gie -0

5151

51

52

-1

51

51

51

51

-1

-1

12

144912 +TI 2 200 (,,) SULIT

*

O.1 2 %1.2.%

x

4

y

2

1

%$

2$

1$

.

.1$

.4

.2$

.1

y ' x − '

$$ * y x x= − +

8/10/2019 SET 12 SKEMA K1 & K2.doc


SULIT 44912(0TI 2)

144912 +TI 2 200 (,,) SULIT

9

8/10/2019 SET 12 SKEMA K1 & K2.doc


SULIT 44912(0TI 2)

14 (a)

'ass !+ter0a Mip*i+t re3e+c5

I 65 - 69 2

II 70 - 74 2 $

III ' 3 9 '

IH *0 3 *4 *2 9H *' 3 *9 *

HI 90 3 94 92 $

HII 9' 3 99 9 1

&Aass interaA (II to HII) aAA correct Midpoint (I to HII) aAA correct

reG;enc? (I to HII) aAA correct

-ote ' or freG;enc? are correct gie ,1

(/)

$0

)19()$92()*()9*2()'()$2()2( ×+×+×+×+×+×+×

or$0

24''

*1.*$ or'

*1

or491

(c) Jistogram#6es are dra:n in the correct direction.

Uniform scaAe is ;sed and 63a6is is Aa/eAed /? midpoints.

#AA /ars are correctA? dra:n

&ompAete histogram

-ote ' or /ars are correctA? dra:n gie 51-0

(d) ModaA &Aass *0 8 *4

(e) Example

Man? :orkers at $1 3 $' ages or e: :orkers at '1 3 '' ages

or Top :orkers age is $$

or CCCCCCCCCC..

,1,1

,2

52

-1

51

52

-1

51

12

1'

144912 +TI 2 200 (,,) SULIT

10

reG;enc?

1

,

4

2

%

6

7

$

66 72 92 967662,6

9

1$

Mark

8/10/2019 SET 12 SKEMA K1 & K2.doc


8/10/2019 SET 12 SKEMA K1 & K2.doc


SULIT 44912(0TI 2)

1' (a) ,Aan

The shape Aooked correct :ith rectangAes >=UH and =STU.

#AA are in f;AA Aines.

>H HT UTK HU =S K >=

The meas;rements are ;p to ± 0.2 cm (one direction) . #ngAes are

190 ± at aAA corners of rectangAes.

51

51 %ept 51

-1 %ep

5151%

(/) (i)The !Aeation from

The shape Aooked correct :ith pentagon 5S=> rectangAe 5&%S

144912 +TI 2 200 (,,) SULIT

12

P

E

! "

#

$ % &

'

H U

>

T

= S

5

%=

>

&

S

J

8/10/2019 SET 12 SKEMA K1 & K2.doc


SULIT 44912(0TI 2)

and semi circAe S%J. #AA are in f;AA Aines.

> K 5K5& %S &% K=S semicircAe SJ%

The meas;rements are ;p to ± 0.2 cm (one direction). #ngAes are

190 ± at aAA corner of rectangAes.

51

51

%ep 51

-2%ep

5151 4

(/) (ii) The eAeation from N

The shape Aooked correct :ith rectangAe 5&%S 5!H> and &!OJ

-ote Ignore Aine %.

% − is connected /? dashed Aines.

>5 K 5! >H K JO &! K J% S% O

The meas;rements are ;p to ± 0.2 cm (one direction) and angAes

are

190 ± at aAA corners of rectangAe.

51

51

%ep 51

51 %ep 5151

-2%ep.515151

333

12

TJ! !-% + M#=5I-O S&J!M!

144912 +TI 2 200 (,,) SULIT

1$

S

5 &

J

%

>H

O

!

set 12 skema k1 & k2.doc

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