TRIAL ADDMATE SPM 2011 Sarawak Zon a Paper 2 Answer
Transcript of TRIAL ADDMATE SPM 2011 Sarawak Zon a Paper 2 Answer
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Matematik
TambahanKertas 22 jam
Sept 2011
SEKOLAH-SEKOLAH MENENGAH ZON A KUCHING
PEPERIKSAAN PERCUBAANSIJIL PELAJARAN MALAYSIA 2011
MATEMATIK TAMBAHAN
Kertas 2
Dua jam tiga puluh minit
JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU
Skema Pemarkahan ini mengandungi 13 halaman bercetak
MARKING SCHEME
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ADDITIONAL MATHEMATICS MARKING SCHEME
TRIAL SPM exam Zon A Kuching 2011 PAPER 2
QUESTION
NO.SOLUTION MARKS
1
( )
( )( )
2
2 1
(2 1) 2 1 3
2 1 2 0
x y
y y y
y y
= +
+ + =
+ =
1, 2
2
@
2, 3
y y
x x
= =
= =
5
2
(a)
(b)
(c)
2 2 2
2 2
2
( ) 3[ 2( 2) ( 2) ( 2) ] 7
5or 3[( 2) 4] 7 or 3[( 2) ]
3
3( 2) 5
f x x x
x x
x
= + + +
+
=
(2, 5)min
Shape
(2, 5) and (0, 7)
(1, 22) and (4, 7)
2
1
3
Solve the quadratic
equation by using the
factorization @ quadratic
formula @ completing the
square must be shown
Eliminate orx y
Note :
OW 1 if the working of solving
quadratic equation is not shown.
5
6
P1
K1
K1
N1
N1
K1
N1
N1
N1
N1
N1
Ox
(2, 5)
(1, 22)
(4, 7)7
y
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QUESTION
NO.SOLUTION MARKS
3
(a)
(b)
(c)
T10 = 100 + 9(4) or 64
Area = 512
2
100 + (n 1)(4) = 4 or100
4@ 100 + (n 1)(4) > 0
n = 25
2
[ ]8640
2(100) ( 1)( 4) or 10802 8
nn+ =
(n 36)(n 15) = 0
n = 15
3
4(a)
(b)xy
5
4=
Number of solutions = 3
4
3
Shape of sine curve
Modulus
Amplitude or period
Translation
P1
P1
P1
P1
y
x0
-1
1
3
1 2siny x=
2
2
2
3
xy5
4=
K1
N1
K1
7N1
K1
N1
K1
K1
N1
7
P1Sketch straight
line correctly
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QUESTION
NO.SOLUTION MARKS
5
(a) 43 2 48 4 53 8 58 11 63 9 68 4 73 2 2325fx = + + + + + + =
2325
40x =
58.125=
3
(b)
Q3 = 60.5 +3
(40) 2554
9
= 63.28
OR1
1(40) 6
450.5 58
53
Q
= +
=
Interquartile range = 63.28 53
= 10.28
4
6
(a) BCO = 60
= 1.047 rad
AOB = 0.6982 rad
3
(b) 21 (10) (1.047)2
or 52.35
21 (10) (0.6982)
2
or 34.91
2
(c)Area of segmentBC= 52.35 2
1(10) sin1.047
2
r= 9.237
Area of the shaded region = 25.673
3
N1
7
K1
N1
P1
Lower
boundary OR
3(40) 25
549
N1
7
K1
K1
N1
K1
N1
K1
K1
N1
K1
N1
N1
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5
(0.78, 1.94)
(0, 0.30)
x10log
.0
.2
.8
0.2 0.3 0.4 0.5
.2
0
og10y Q7
x10log 0.30 0.48 0.60 0.78 0.85 0.95
y10log 0.93 1.30 1.57 1.94 2.07 2.31
Correct both axes (Uniform scale) K1
All points are plotted correctly N1
Line of best fit N1
0.1 0.6 0.7 0.8
N1
N1
.4
.6
.8
.0
.2
.4
.6
0.9 1.0
(a) Each set of values correct (log10y must be at least
2 decimal places) N1, N1
log 10y = nlog 10x + log 10 (p + 1) K1
where Y= log 10y, X= log 10x,
m = n and c = log 10 (p + 1)
(c) (i)X= log 10 5.6 = 0.748
Y= 1.88 = log 10yy = 75.86 N1n = gradient
n =1.94 0.30
0.78 0
= 2.103 N1
log 10 (p + 1) = Y-interceptlog 10 (p + 1) = 0.30 K1
p = 0.9953 N1
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QUESTION
NO.SOLUTION MARKS
8
(a) (i)
(ii)
(b) (i)
(ii)
2,0
2
82
12
18
2
=>
=
=
=
aa
a
a
aa
3
++=
+
2)2(5,
206
23,
24 yx
D(2, 6)
@
Solving the equationsy = 4x 2 and2
13
4
1+= xy
D(2, 6)
2
0214
5)2()0(
22
22
=++
=++
yyx
yx
Get equation ofBC,y = 4x 19
( )
0544
)264)(17(4136
4
026413617
021)194(4)194(
2
2
2
22
>=
=
=+
=++
acb
xx
xxx
The locus intersects the lineBC.
2
3
K1
K1
K1
N1
N1
N1
K1
N1
K1
K1
N1
K1
10
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QUESTION
NO.SOLUTION MARKS
9(a) 1
2OP x y= +
1
(b)
(i)
(ii)
OQ x y = +
( )1
2
11
2
OQ OL LQ
x LP
x LM MP
x y x
x y
= +
= +
= + +
= +
= +
4
x : = 1 1
2
y : =
= 1 1
2
= =2
3
3
(c)Area of triangle OLM=
3
2 24 = 36
Therefore area of parallelogram OLMN= 72
2
P1
10
K1
K1
N1
K1
K1
N1
K1
N1
N1
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QUESTION
NO.SOLUTION MARKS
10(a)
3 9 3
r h hr= =
2
9
dV h
dh
=
2
0.89
h dh
dt
=
2
0.89h dh
dt=
4
(b)
(i)
(ii)
h = 1 and k= 1
Area of the shaded region
= ( ) ( )1 0
3 3
0 1
y y dy y y dy
+
=
14 2
04 2
y y
+
0
1
24
24
yy
= ( )1 1
0 04 2
+
( )41 10 0
4 2
=2
1
Note: OW 1 once only for correct answer without showing theprocess of intergration.
6
N1
K1
K1
K1
K1
N1
N1
K1
K1
10
N1
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QUESTION
NO.SOLUTION MARKS
11(a)
(i)
(ii)
(b)
(i)
(ii)
0 550( 0) (0.2) (0.8)
0.3277
P X C= =
=
( 2)P X< = 0 5 1 45 50 1(0.2) (0.8) (0.2) (0.8)C C+
= 0.7373
5
( 0.811)P Z> @R(0.811)
= 0.7913 @ 0.79132
P(0.811
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QUESTION
NO.SOLUTION MARKS
12
(a) Initial velocity 8=Av 1
(b)
4
12
42
55
2
5
2
5
052
2
=
+
=
=
=+=
Bv
t
tdt
dv
3
(c) ( 2)( 4) 0
( 1)( 4) 0
4
A
B
v t t
v t t
t
= =
= =
=
3
(d)
3
26
)2(8)2(33
)2(
833
83
23
23
2
=
++=
+=
+= tt
t
dtttsA
3
N1
K1
K1
K1
N1
K1
K1
N1
10
K1
N1
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QUESTION
NO.SOLUTION MARKS
13
(a)
(b)(i)
(ii)
A : 12510060
08 =P
08 RM75P =
2
(125 4) (120 ) (80 5) 150( 3)120
12 2
n n
n
+ + + +=
+
1440 240 1350 270n n+ = +
n = 3
06
RM30100 120
P =
RM25=
3
(c)
18
)6150()580()3138()4125(
138)15.0120(120
06/09
+++=
=+
I
= 123
3
K1
K1
N1
K1
N1
K1
N1
10
N1
K1
K1
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QUESTION
NO.SOLUTION MARKS
14
(a)
(b)
(c)
18 28
sin38 sin QSR=
QSR = 180 7316
= 10644
3
QRS = 3516
2 2 228 18 2(28)(18) cos 35 16
@ Sine Rule
16.88
PS
QS
= +
=
3
2 2 226 11 16.88 2 11 16.88 cos PQS= +
PQS = 13639
Area of triangle PQR = 12
1128sin 17639
= 8.999
2
10
K1
N1
K1
N1
K1
N1
K1
N1
K1
N1
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Answer for question 15
2 4 6 8 10 12 140 16
2
4
14
12
10
16
8
6 (15, 6)
R
(a) I. 4832 + yx
II. 4885 + yx
III. xy 3
(b) Refer to the graph,
1 or 2 graph(s) correct3 graphs correct
Correct area
(c) ii) max point (15, 6)
k= RM(500x + 300y)
Maximum Profit = RM 500(15) + RM 300(6)
= RM 7500
(ii) 8 units
10
N1
N1
N1
N1
N1
N1
K1
N1
K1
N1
x
y