Trial spm kedah_2013_maths_paper2_[a]
-
Upload
karthik-karunanithy -
Category
Education
-
view
135 -
download
4
description
Transcript of Trial spm kedah_2013_maths_paper2_[a]
SULIT 1449/2(PP)
[Lihat halaman sebelah 1449/2(PP) SULIT
PROGRAM PENINGKATAN PRESTASI AKADEMIK SPM 2013
ANJURAN
MAJLIS PENGETUA SEKOLAH MALAYSIA (KEDAH)
MODUL A
MATEMATIK KERTAS 2
PERATURAN PEMARKAHAN
UNTUK KEGUNAAN PEMERIKSA SAHAJA
Peraturan pemarkahan ini mengandungi 14 halaman bercetak
SULIT 1449/2(PP)
1449/2(PP) SULIT
2
Section A [ 52 marks]
Question Solution and Mark Scheme Marks
1
2
40-2
-4
-6 -4
-2
6
4
2 x
y
y = - x - 1
y = 2x + 2
Straight dotted line x = 1 correctly drawn. K1 Region correctly shaded P2 3 Note: 1 Accept solid line x = 1 for K1 2 Award P1 to shaded region bounded by two correct lines,
including part of R. (Check one vertex from any two correct lines
2(a) ∠MFH P1
3 (b)
137tan =∠MFH or equivalent
K1
28.3° or 28° 18′ N1
SULIT 1449/2(PP)
[Lihat halaman sebelah 1449/2(PP) SULIT
3 Question Solution and Mark Scheme Marks
3
049 2 =−x
( )( ) 02323 =+− xx or equivalent
32
=x or 0.67
32
−=x or –0.67
Note : 1. Accept without ‘= 0’
2. Accept two terms on the same side, in any order.
3. ( )( )0 67 0 67x x− ⋅ + ⋅ with 0 67, 0 67x x= ⋅ = − ⋅
award Kk2
K1
K1
N1
N1
4
4 14 3 2x y+ = − or 7 21 77x y+ = or equivalent K1 Note :
Attempt to equate one of the coefficients the unknowns, award K1 OR
( )
31 2 1 711 211 33 7 3
y xxx y or y or x or y− − − −−
= − = = =
or equivalent (K1)
Note :
Attempt to make one of the unknowns as the subject award K1.
3913 13 782
x or y− = = or equivalent K1
OR
3 113123 1(1) (3)(7) 7 1
2
xy
− = − − −
(K2)
Note : Attempt to write without equation, award (K1)
1x = − N1 4y = N1 4
Note :
14
xy
− =
as final answer, award N1
SULIT 1449/2(PP)
1449/2(PP) SULIT
4
Question Solution and Mark Scheme Marks 5(a) 20
214
214
722
21
×××× K1
4
1540 N1
(b) 202
142
14722
21
×××× + ( )1 20 10 14 67902
AB× + × × = K1
25 N1
Note : 1. Accept π for K mark. 2. Correct answer from incomplete working, award Kk2.
6 (a) benar / true P1
5
(b) Jika n adalah nombor negatif maka 0n < . If n is a negative number then 0n < . benar / true
P1
(c) Set R ialah subset bagi set K Set R is subset of set K
P1
(d) Bilangan subset bagi suatu set yang mempunyai 7 unsur ialah 72
The number of subsets in a set with n elements is 72 .
K1
72 128= N1
7 (a) 5x = − P1
5
(b) 45SR PQM M= = P1
( )
*44 55
c= − + or ( )
*4 45 5
yx
−=
− − K1
8
54
+= xy N1
y-intercept = 8 N1 8 (a) 12 P1 1
(b) 12 010 0
or equivalent−−
K1
6 1 25
or ⋅ N1 2
Note: Accept answer without working for K1N1
(c) ( )1 1(18 28) 12 (( 28)(12 20) 4682 2
t+ + − + = or
equivalent method K2 Note:
1 1(18 28)(12) (( 28)(12 20)2 2
or t+ − +
equivalent, award K1 40 N1 3 6
SULIT 1449/2(PP)
[Lihat halaman sebelah 1449/2(PP) SULIT
5 Question Solution and Mark Scheme Marks
9(a)
(b)
147222
360120
××× or 77222
360180
×××
14 + 14 + 14 + 147222
360120
××× + 77222
360180
×××
3280 or
3193 or 93.33
214722
360120
×× or 27722
360180
××
214
722
360120
×× − 27722
360180
××
3
385 or 31128 or 128.33
Note :
1. Accept π for K mark. 2. Correct answer from incomplete working, award Kk2.
K1
K1
N1
K1
K1
N1
6
10 (a)
{(P, M), (P, 4), (P, 5), (P, N), (Q, M), (Q, 4), (Q, 5), (Q, N), (3, M), (3, 4), (3, 5), (3, N), (R, M), (R, 4), (R, 5), (R, N)} Note :
1. Accept 8 correct listing from not more than 16 outcomes for P1
P2
(b)(i) {(3, 4), (3, 5)}
K1
162 or
81
N1
(ii) {(P, 4), (P, 5), (Q, 4), (Q, 5), (3, M), (3, N), (R, 4), (R, 5)}
168 or
21
K1
N1
NOTE : 1. Accept other method for K mark.
2. Accept answer without working from correct listing, correct tree diagram or correct grid for K1N1.
SULIT 1449/2(PP)
1449/2(PP) SULIT
6
Question Solution and Mark Scheme Marks 11 (a)
( ) ( )1 216 33 1 2 6
− − −× − − ×
1 215 156 1
15 5
−
P2 2
(b) 3 2 96 1 7
xy
= − −
P1
1 2 916 3 7(3)( 1) (2)(6
xor
y− −
= − −− −
* 9
7x Inversey matrix
= −
K1
13
x = − N1
y = 5 N1 4 6 Note:
1. 13
5
xy
− =
as final answer, award N1
2. Do not accept any solution solved no using matrix method.
3. Do not accept * 3 26 1
inversematrix
= −
or * 1 00 1
inversematrix
=
12 (a) x = -4, y = 3
x = -1.5, y = 8 K1 K1
12
(b) Graph Axes drawn in correct direction, uniform scales in -6<x< -0.75 and 0 < y < 16.
P1
All 6 points and *2 points correctly plotted or curve passes through these points -6 < x < -0.75 and 0 < y < 16.
K2
A smooth and continuous curve without any straight line and passes through all 9 correct points using the given scale for -6 < x < -0.75 and 0 < y < 16.
N1
Note : 1. 6 or 7 points correctly plotted, award K1.
2. Ignore curve out of range.
SULIT 1449/2(PP)
[Lihat halaman sebelah 1449/2(PP) SULIT
7
.
.
. .
. . . . .
0 -6 -5 -4 -3 -2 -1
2
0
4
6
8
10
12
14
16
Graf untuk Soalan12 Graph for Question 12
SULIT 1449/2(PP)
1449/2(PP) SULIT
8
(c) (i) 4.6 < y < 5.0 P1
(ii) -1.0 < x < = - 0.8 P1
(d) y = 2x + 12 or garis lurus y = 2x + 12 dilukis
K1 K1
-4.8 < x < -4.65 , -1.35 < x < -1.20 N1N1
13(a)(i) (2 , 6) P2
12
Note: (4, 5) or (4, 5) marked , award P1
(ii) (7, 8) P2
Note: (9 , 7) or (9 , 7) marked, award P1
(b)(i)(a) W: Rotation, 90° clockwise at (10 , 10)
P3
Note :
1. P2 : Rotation 90° clockwise or Rotation, at (10 , 10) / Putaran 90°
ikut arah jam atau Putaran pada (10,10)
2. P1: Rotation// Putaran
(b) V: Enlargement at centre (13 , 10), with scale factor 31 P3
Note:
P2: Enlargement at centre (13 , 10), or Enlargement with scale factor
31 // Pembesaran pada (13 , 10) atau pembesaran dengan faktor
skala 31
P1: Enlargement// Pembesaran
(ii) 21 1803
= ×
K1
20
N1
SULIT 1449/2(PP)
[Lihat halaman sebelah 1449/2(PP) SULIT
9Question Solution and Mark Scheme Marks
14(a)(i)
Marks : (II to VII)
Mid point : (II to VII)
Frequency : (I to VII)
Note : Allow two mistake in frequency for P1.
P1
P1
P2
4
(b)(i) 40 – 49
P1
4
(ii)
( ) ( ) ( ) ( ) ( ) ( ) ( )* * * * * * *
* * * * * * *
2 24.5 5 34.5 8 44.4 6 54.5 4 64.5 3 74.5 2 84.52 5 8 6 4 3 2
× + × + × + × + × + × + ×
+ + + + + +
or 30
1555
Note: 1. Allow *midpoint for K1
6
311 or 6551 or 51.83
Note: Correct answer from incomplete working, award Kk2
K2
N1
(c) Axes drawn in correct direction and uniform scale for 5.845.24 ≤≤ x and 0 ≤ y ≤ 8. *7 points correctly plotted Note : *5 or *6 points correctly plotted or bar passes through using at least 6 correct mid-point, award K1. Correct bar passes all 7 correct points for using given scales 5.845.24 ≤≤ x
P1
K2
N1
4
Marks Markah
Mid-point Titik tengah
Frequency Kekerapan
20 – 29 24.5 2 I
30 – 39 34.5 5 II
40 – 49 44.5 8 III
50 – 59 54.5 6 IV
60 – 69 64.5 4 V
70 – 79 74.5 3 VI
80 – 89 84.5 2 VII
SULIT 1449/2(PP)
1449/2(PP) SULIT
10
Graf untuk Soalan14 Graph for Question 14
8 7 6 5 4 3 2 1 0
24.5 34.5 44.5 54.5 64.5 74.5 84.5 Mark
frequency
SULIT 1449/2(PP)
[Lihat halaman sebelah 1449/2(PP) SULIT
11
Question Solution and Mark Scheme Marks
15
Note : (1) Accept drawing only (not sketch). (2) Accept diagrams with wrong labels and ignore wrong labels. (3) Accept correct rotation of diagrams. (4) Lateral inversions are not accepted. (5) If more than 3 diagrams are drawn, award mark to the correct ones only. (6) For extra lines (dotted or solid) except construction lines, no mark is awarded. (7) If other scales are used with accuracy of ± 0.2 cm one way, deduct 1 mark from the N mark obtained, for each part attempted. (8) Accept small gaps extensions at the corners. For each part attempted :
(i) If ≤ 0 4⋅ cm, deduct 1 mark from the N mark obtained.
(ii) If > 0 4⋅ cm, no N mark is awarded. (9) If the construction lines cannot be differentiated from the actual lines:
(i) Dotted line : If outside the diagram, award the N mark.
If inside the diagram, award N0. (ii) Solid line : If outside the diagram, award N0.
If inside the diagram, no mark is awarded.
(10) For double lines or non-collinear or bold lines, deduct 1 mark from the N mark obtained, for each part attempted.
SULIT 1449/2(PP)
1449/2(PP) SULIT
12
Question Solution and Mark Scheme Marks
15(a)
P
J K
L
MN
3.5 cm
3.5 cm
7 cm
8 cm
Correct shape with rectangles JKMN , JKLP and PLMN All solid lines.
K1
3
JK > KM > KL=LM
K1 dep K1
Measurement correct to ± 0 2⋅ cm (one way) and all angles
at vertices of rectangles = 90° ± 1°
N1 dep K1K1
15(b)(i)
J
P L
K
FR
S
QE4 cm
3 cm
3 cm
2 cm
2 cm
8 cm
Correct shape with rectangle PLKJ, SQ perpendicular to EQ All solid lines
K1
4
PL > LF > EQ > LK = KF > RF = QR = QS
K1 dep K1
Measurement correct to ± 0 2⋅ cm (one way) and all angles at the
vertices of rectangles = 90° ± 1°
N2 dep
K1K1
SULIT 1449/2(PP)
[Lihat halaman sebelah 1449/2(PP) SULIT
13 Question Solution and Mark Scheme Marks
15(b)(ii)
S
G
V
M
L
K
F
1 cm
2 cm
7 cm
5
Correct shape All solid lines Note : Ignore *SV
K1
5
12
S and V joined with dashed line to form rectangles SVFG
K1 dep K1
FG > LM > MG K1 dep K1K1
Measurement correct to ± 0 2⋅ cm (one way) and all angles at the vertices of rectangles = 90° ± 1°
N2 dep K1K1K1
16(a)
105 o E ∕∕ 105 o T) Note :
105 o or θo E ∕∕ θo T, award P1
P2
12
(b)(i) 390060
35 o N // U
K1
N1N1
(ii) 60 cos35 4669oθ × × = 20
K2
N1 (c) ( )
60030cos6010575 ××+
15.59
K2K1
N1 Note :
* cos 45 + * (75 105 )+ , award K1
SULIT 1449/2(PP)
1449/2(PP) SULIT
14