bukit mertajam 2014(a)
TRANSCRIPT
1
MARKING SCHEME
PEPERIKSAAN PERCUBAAN PENGGAL 2 TAHUN 2014
SMK BUKIT MERTAJAM
MATHEMATICS M ( PAPER 2)
NO SCHEME MARKS
1.
[8]
a)
Time Frequency Width Midpoint Frequency
density
1200 x 1 120 60 0.5
180120 x 9 60 150 9
240180 x 15 60 210 15
300240 x 17 60 270 17
360300 x 13 60 330 13
600360 x 5 240 480 1.25
M1(width)
M1
(frequency
density)
D1(Label &
scale)
D1(All
correct)
2
b) Mean = 60
48053301327017210151509601
= 60
15840
= 264
c) Standard deviation = 226460
4674600
= 90.6
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2.
[6]
a) 5.0)(
1.0
BP
P(B) = 0.2
b) )()( BPABP A and B are not independent
c) 25.0)(
1.0
AP
P(A) = 0.4
)()()( ' BAPAPBAP
= 0.4 – 0.1
= 0.3
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3.
[6]
ai) r measure the strength of the relationship between x and y.
ii) 11 r
r = 1 mean a perfect positive relationship between x and y.
b)
8
)470(29450)(
8
)423(24479(
8
)470(42326520
22
r
= 0.847
There have a strong positive correlation between variable x and y.
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4.
[7]
a) p+0.25+2p+0.3+0.15=1
3p+0.7=1
P=0.1
b) E(x)=5.7
0(0.1)+2(0.25)+5(0.2)+n(0.3)+12(0.15) = 5.7
3.3+0.3n = 5.7
n = 8
c) E(X2) = 0
2(0.1)+2
2(0.25)+5
2(0.2)+8
2(0.3)+12
2(0.15)
= 46.8
Var (X) = 46.8-5.72
= 14.31
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5.
[10]
a)
Year Quarter
Time
column
, t
Number
of tourist
4-quarter
moving
average
Centred
4-quarter
moving
average
Deviation
2011
1 1 22.0
2 2 12.0
3 3 110.0 43.75 43.63 66.38
4 4 31.0 43.5 45.25 -14.25
2012
1 5 21.0 47 52.00 -31.00
2 6 26.0 57 61.88 -35.88
3 7 150.0 66.75 70.38 79.63
4 8 70.0 74 75.25 -5.25
2013
1 9 50.0 76.5 76.00 -26.00
2 10 36.0 75.5 80.50 -44.50
3 11 146.0 85.5
4 12 110.0
b)
Year Q1 Q2 Q3 Q4
2011 66.38 -14.25
2012 -31.00 -35.88 79.63 -5.25
2013 -26.00 -44.50
Unadjusted
seasonal
variation
-28.50 -40.19 73.00 -9.75
Correction
factor -1.359 -1.359 -1.359 -1.359
Seasonal
variation -27.14 -38.83 74.36 -8.39
M1
(4-quarter
moving
average)
A1 (Centred
4-quarter
moving
average)
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c)
Year Quarter Coded
quarter, t
Number
of
tourist, y
Seasonal
variation
, S
Deseaso
nalised,
T=y-S
t^2 tT
2011
1 1 22.0 -27.14 49.14 1 49.14
2 2 12.0 -38.83 50.83 4 101.66
3 3 110.0 74.36 35.64 9 106.92
4 4 31.0 -8.39 39.39 16 157.56
2012
1 5 21.0 -27.14 48.14 25 240.70
2 6 26.0 -38.83 64.83 36 388.97
3 7 150.0 74.36 75.64 49 529.48
4 8 70.0 -8.39 78.39 64 627.13
2013
1 9 50.0 -27.14 77.14 81 694.27
2 10 36.0 -38.83 74.83 100 748.28
3 11 146.0 74.36 71.64 121 788.05
4 12 110.0 -8.39 118.39 144 1420.69
Total 78 784.0 784.00 650 5852.84
12
78650
12
)784)(78(84.5852
2
b
= 5.293
)12
78(293.5
12
784a
= 30.93
tT 293.593.30
)13(293.593.301 T
= 99.74
1F = 99.74+(-27.14)
= 72.6
The predict number of tourist fot 1st quarter 2014=72.6X1000=72600
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6.
[8]
a) Simple aggregate price index
120= 1005126105.2
614123X
a
1005.35
35120 X
a
A=7.60
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b) 100)5(5)15(12)10(6)10(10)20(5.2
)5(6)15(14)10(6.7)10(12)20(3XLp
= 100415
496X
= 119.5
From January to July, the family’s expenditure on daily food has increased by
19.5%
c) 100)6(5)14(15)6.7(10)2(10)3(20
)4(6)10(14)9(6.7)8(12)10(3XPq
= 100496
4.358X
= 72.26
From January to July, there is a drop of 27.74% in the quantity of daily food
bought by the family.
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7.
[15]
a) p=0.6 , q = 0.4
i) )3( XP
53
3
8 )4.0()6.0(C
=0.124
ii) )1()0(1)2( XPXPXP
71
1
880
0
8 )4.0()6.0()4.0()6.0(1 CC
= 1- 0.000655-0.00786
= 0.9914
iii) E(X) = 8X0.4
= 3.2
= 3
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iv) qx
pxn
xXP
xXP
)1(
)(
)(
)1(
If P(X = x+1) > P(X = x)
(n-x)p > (x+1)q
(8-x)(0.6) > (x+1)(0.4)
x < 4.4
Hence, P(X=5) > P(X=4) > …. >P(X=0)
If P(X = x) > P(X = x+1)
Then x > 4.4
Hence, P(X=5) > P(X=6) > …. >P(X=8)
P(X=5) has the highest probability, Hence, number of students that most
likely to pass is 5.
b) 99.0)1( XP
1 – P(X=0) > 0.99
P(X=0) < 0.1
01.0)4.0()6.0( 0
0 nnC
01.04.0 n
01.0log4.0log n
4.0log
01.0logn
02.5n
n = 6
c) 6or 36)4.0)(6.0(150 and 90)6.0(150 npqnpqnp
36) ,90(~ NX
P( X> 85) = )5.85( XP
= )6
905.85(
ZP
= )75.0( ZP
= )75.0(1 ZP
= 1-0.2266
= 0.7734
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8.
[15]
. a)
Boys Stem Girls
0 8
1 6
9 6 2 4 5
9 8 6 6 5 5 5 5 4 4 1 0 3 1 2 4 4
7 5 3 0 0 0 4 0 0 0 2 4 5 7 8 8
5 0
Key: 6 2 means hours
Key: 0│8 means 8 hours
b) The distribution for the boys is almost symmetrical while the girls is
negatively skewed.
c) Boys: IQR Girls: IQR
d)
Boys:
mean hours
number of hours
Girls:
mean hours
number of hours
e) The dispersion of distribution is larger for the girls.
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