SEAFIELD 2013 M2(A)
Transcript of SEAFIELD 2013 M2(A)
-
8/13/2019 SEAFIELD 2013 M2(A)
1/5
Answer Scheme for Mathematics (M) Trial STPM 950/2
1
No. Answer scheme Marks Total
1(a)
(b)
Mean, 87.1895
5.1792x minutes
Median, 78.151032
295.47
10
m
Standard deviation,
25.508312 fx
38.1395
5.1792
95
25.50831 2
s
Pearsons coefficient of skewness
6928.0
38.13
78.1587.183
The distribution is positively skewed.
M1A1
M1A1
B1
M1A1
M1
A1
B1 10 marks
2(a)
(b)
(c)
P(the child is a girl who writes using left hand)
= 0.052 0.58
= 0.03016
P(the child writes using left hand)
= 0.03016 + 0.078 0.42
=0.06292
P(the child is a boythe child writes using left hand)
5207.0
06292.0
42.0078.0
M1
A1
M1
A1
M1
A1 6 marks
3(a)
(b)
0.15 + 0.40 + 2k+ k= 1
k = 0.15
15.0230.0140.0015.01 XE = 0.45
15.0230.0140.0015.01 22222 XE = 1.05
245.005.1Var X = 0.8475
M1
A1
M1
A1
B1
M1
A1 7 marks
-
8/13/2019 SEAFIELD 2013 M2(A)
2/5
2
4(a)
(b)
(c)
Negative correlation.
As the mortgage interest rate increases the housing sales index
decreases.
985,1043,99,10 2 yxxn
9355,1005252 xyy Coefficient of determination,
22
2
2
9851005251099104310
98599935510
r
= 0.7136
Hence, 71.36% of the variation in the number of houses sold is
accounted for by the variation in the mortgage interest rate.
D2
B1
B1
B1
M1
M1
A1
B19 marks
5(a)
(b)
Simple aggregate price index for February 2013
44.112
10080.3150.2468.5
40.3530.2899.5
The price of the seafood has increased by 12.44% from January
to February 2013.
Weighted average of price relatives for February 2013
27.111
10080.42400.28365.209
80.42480.31
40.35283
50.24
30.2865.209
68.5
99.5
The price of the seafood has increased by 11.27% from January
to February 2013.
M1
A1
B1
M1
A1
B1
6 marks
6(a)
(b)
(c)(i)
(ii)
The time series has an increasing trend.
The revenue is the highest in the fourth quarter each year but
rather low in the first three quarters.
An additive model is more suitable because the amplitude of
the seasonal variations is almost constant as the trend rises.
7439.0
00761.26427.06895.0
k
k
2.0761 means that the revenue in the fourth quarter is
RM2.0761 million above the trend value.
B1
B1
B1
B1
M1
A1
B1
7 marks
-
8/13/2019 SEAFIELD 2013 M2(A)
3/5
3
7(a)
(b)
(c)
(d)
27
1
103 3
k
k
31327
11 XP
27
8
,1
,327
11
,0
3xxF
3
30
0
x
x
x
LetX= the number of observations greater than 1.
Then,
27
8,3B~X .
011 XPXP
6515.0
27
191
3
27
8,729B~X .
Hence, 152,216N~X . 5.229229 XPXP
1368.0
095.1
152
2165.229
ZP
ZP
M1
M1
A1
B1
D2
B1
B1
M1
A1
B1
B1B1
M1
A1 15 marks
2
1.5
1
0.5
-0.5
-1 1 2 3 4
0 3
1
xFy
y
x
-
8/13/2019 SEAFIELD 2013 M2(A)
4/5
4
8(a)
(b)
Year
Quarter
Sales
(RM100,000),
Y
4-pt
moving
average
Centred
moving
average,
T
S=Y/T
2009
1 5.3
2 4.1
3 6.8 5.725 5.6625 1.2009
4 6.7 5.600 5.5625 1.2045
2010
1 4.8 5.525 5.3750 0.8930
2 3.8 5.225 5.2375 0.7255
3 5.6 5.250 5.1875 1.0795
4 6.8 5.125 5.1250 1.3268
2011
1 4.3 5.125 5.1375 0.8370
2 3.8 5.150 5.0750 0.7488
3 5.7 5.000 5.1625 1.1041
4 6.2 5.325 5.4250 1.1429
2012
1 5.6 5.525 5.5750 1.0045
2 4.6 5.625 5.5125 0.8345
3 6.1 5.400
4 5.3
Q1 Q2 Q3 Q4
2009 1.2009 1.2045
2010 0.8930 0.7255 1.0795 1.3268
2011 0.8370 0.7488 1.1041 1.14292012 1.0045 0.8345
Mean
Seasonal
Variation
0.9115 0.7696 1.1282 1.2247
Adjusting
factor0.9916 0.9916 0.9916 0.9916
Adjusted
Seasonal
Variation
0.9038 0.7631 1.1187 1.2144
Adjusted seasonal variations are:
Q1 Q2 Q3 Q4
0.904 0.763 1.119 1.214
M1A1
(column
5)
B1
(column
6)
B1
M1
A1
-
8/13/2019 SEAFIELD 2013 M2(A)
5/5
5
(c)
(d)
t Y SDeseasonalised
Series, y=Y/S
1 5.3 0.9038 5.8641
2 4.1 0.7631 5.3728
3 6.8 1.1187 6.0785
4 6.7 1.2144 5.5171
5 4.8 0.9038 5.3109
6 3.8 0.7631 4.9797
7 5.6 1.1187 5.0058
8 6.8 1.2144 5.5995
9 4.3 0.9038 4.7577
10 3.8 0.7631 4.9797
11 5.7 1.1187 5.095212 6.2 1.2144 5.1054
13 5.6 0.9038 6.1961
14 4.6 0.7631 6.0280
15 6.1 1.1187 5.4528
16 5.3 1.2144 4.3643
7076.85,1496,136,16 2 yttn 6733.719ty
21361496167076.851366733.71916
b
02600.0
16
13602600.0
16
7076.85a
58.5 Least squares regression equation is ty 0260.058.5 .
4thquarter of 2013, t= 20.
200260.058.5 y = 5.06
2144.106.5 Y = 6.145
Forecast sales = RM6.145 (100,000)
M1A1
(column
4)
B1
M1
M1
A1
M1
M1
A1 15 marks