SET 12 SKEMA K1 & K2.doc
Transcript of SET 12 SKEMA K1 & K2.doc
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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
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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
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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
$
=
>,
=
>,
=
>,
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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
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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
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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
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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
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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= − +
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SULIT 44912(0TI 2)
144912 +TI 2 200 (,,) SULIT
9
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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
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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
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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
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