8/13/2019 SEAFIELD 2013 M2(A)

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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)

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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)

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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)

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A1

8/13/2019 SEAFIELD 2013 M2(A)

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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