TRIAL STPM MATHEMATICS M 2 (SELANGOR) SMK Seafield Answer
Transcript of TRIAL STPM MATHEMATICS M 2 (SELANGOR) SMK Seafield Answer
Answer Scheme for Mathematics (M) SMK SEAFIELD SUBANG Trial STPM 950/2
1
No. Answer scheme Marks Total
1(a)
(b)
Mean, 87.1895
5.1792==x minutes
Median, 78.151032
295.4710 =×
−+=m
Standard deviation,
25.508312 =∑ fx
38.1395
5.1792
95
25.508312
=
−=s
Pearson’s 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 boy|the 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
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
B1
9 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
3
7(a)
(b)
(c)
(d)
( )
27
1
1033
=
=−
k
k
( ) ( )31327
11 −=>XP
27
8=
( ) ( )
−−=
,1
,327
11
,0
3xxF
3
30
0
>
≤<
≤
x
x
x
Let X = 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~ɺX .
( ) ( )5.229229 >=> XPXP
( )1368.0
095.1
152
2165.229
=
>=
−>=
ZP
ZP
M1
M1
A1
B1
D2
B1
B1
M1
A1
B1
B1
B1
M1
A1
15 marks
2
1.5
1
0.5
-0.5
-1 1 2 3 4
0 3
1
( )xFy =
y
x
4
8(a)
(b)
Year
Quarter
Sales
(×RM100,000),
Y
4-pt
moving
average
Centred
moving
average,
T
S=Y/T
1 5.3
2 4.1
3 6.8 5.725 5.6625 1.2009 2009
4 6.7 5.600 5.5625 1.2045
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 2010
4 6.8 5.125 5.1250 1.3268
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 2011
4 6.2 5.325 5.4250 1.1429
1 5.6 5.525 5.5750 1.0045
2 4.6 5.625 5.5125 0.8345
3 6.1 5.400 2012
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 1.1429
2012 1.0045 0.8345
Mean
Seasonal
Variation
0.9115 0.7696 1.1282 1.2247
Adjusting
factor 0.9916 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
5
(c)
(d)
t Y S Deseasonalised
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 5.0952
12 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
( ) ( )( )( ) ( )2136149616
7076.851366733.71916
−
−=b
02600.0−=
( )
−−
=16
13602600.0
16
7076.85a
58.5=
Least squares regression equation is ty 0260.058.5 −= .
4th quarter of 2013, t = 20.
( )200260.058.5 −=y
= 5.06
2144.106.5ˆ ×=Y
= 6.145
Forecast sales = RM6.145 (×100,000)
M1A1
(column
4)
B1
M1
M1
A1
M1
M1
A1
15 marks