# trial stpm mathematics m 2 (sarawak) smk paku

Post on 29-Apr-2017

263 views

Embed Size (px)

TRANSCRIPT

CONFIDENTIAL*

STPM 950/2 [Turn over

CONFIDENTIAL*

This question paper is CONFIDENTIAL until the examination is over.

TRIAL STPM MATHEMATICS M (SARAWAK) SMK Paku QA

Section A

[45 marks]

Answer all questions in this section.

1 In a box containing 80 light bulbs, 60 are in good condition. Two bulbs are taken

randomly, one after the other, from the box. Find the probability that only one of

the two bulbs taken is in good condition.

(a) If the first bulb is returned into the box. [3 marks]

(b) If the first bulb is not returned into the box. [3 marks]

2 The table below shows the prices of fish and the quantities of it bought by a

housewife at a market in the year 2011 and 2012.

2011 2012 Fish

Price

(RM per kg)

Quantity

(kg)

Price

(RM per kg)

Quantity

(kg)

Parang 11.00 2 12.00 1

Tenggiri 12.00 2 13.00 2

Bawal Putih 10.00 2 a 1

Kembung 8.00 3 10.00 2

Selar Kuning 4.00 5 5.00 6

(a) If the simple aggregate price index increases by 20 % from 2011 to 2012,

determine the value of a. [3 marks]

(b) Calculate the Laspeyres price index, and comment on the housewifes

change in expenditure on fish. [3 marks]

3. A random sample of 24 people were asked to record the number of kilometres

they travelled by car in a given week. The distances, to the nearest kilometres, are

shown below.

67 66 85 93 63 44 87 57

72 77 67 48 66 50 52 74

70 70 41 108 58 74 62 68

(a) Construct a stem-and-leaf diagram to represent these data. [2 marks]

(b) Determine the median and interquartile range of this distribution.

[3 marks]

(c) Draw a box-and-wisker plot for this data. [3 marks]

CONFIDENTIAL*/SULIT

STPM 950/2

CONFIDENTIAL*

*This question paper is CONFIDENTIAL until the examination is over.

2

4 The probability density function of the time t, in minutes, of a student spends

every morning waiting for bus to school is given by

otherwise

t

t

t

t

tf ,155

,50

0

,75

1

5

175

2

)(

CONFIDENTIAL*/SULIT

STPM 950/2

CONFIDENTIAL*

*This question paper is CONFIDENTIAL until the examination is over.

3

Section B

[15 marks]

Answer any one question in this section.

7. Everyday, a bus leaves town A for town B at 0800 hours. The time taken for this

journey is recorded for a certain period. The result are shown in the following

table.

Time (minutes) Frequency

2825 x 6 2928 x 12 3029 x 27 3130 x 30 3231 x 18 3332 x 14 3433 x 9 3534 x 4 4035 x 5

a) Draw a histogram to represent these data. [3 marks]

b) Calculate the median, mean and standard deviation for this data.

[5 marks]

c) Hence, calculate the Pearson coefficient of skewness and comment the

skewness of the distribution. [2 marks]

d) Plot a cumulative frequency curve of the above data. Hence, find the

number of times a bus arrives at town B between 0830 hours and 0836

hours. [5 marks]

8 (a) On average, the number of books read by an adult is 5 books per year. Using

the Poisson distribution, find the probability that

(i) an adult reads exactly 3 books per year, [2 marks]

(ii) an adult reads more than 2 books in 5 years. [2 marks]

(b) The marks obtained by the candidates for a paper in an examination are

distributed normally with mean of 50 and standard deviation 10.

(i) If a candidate must obtain 70 marks to score a distinction for the paper,

find the percentage of candidates who obtained distinctions for this paper

in the examination. [3 marks]

(ii) If 70% of the candidates pass the paper, determine the minimum marks

required to get a passing grade for the paper. [3 marks]

(c) In a group of teachers, the expected number of teachers who own Proton cars

is 8 and the variance is 1.6. Find the probability that

(i) a teacher chosen at random owns a Proton car, [3 marks]

(ii) exactly 4 teachers from the group own Proton cars. [2 marks]

END OF QUESTION PAPER

CONFIDENTIAL*/SULIT

STPM 950/2

CONFIDENTIAL*

*This question paper is CONFIDENTIAL until the examination is over.

4

CONFIDENTIAL*/SULIT

STPM 950/2

CONFIDENTIAL*

*This question paper is CONFIDENTIAL until the examination is over.

5

CONFIDENTIAL*/SULIT

STPM 950/2

CONFIDENTIAL*

*This question paper is CONFIDENTIAL until the examination is over.

6

ANSWER TRIAL STPM MATHEMATICS M (SARAWAK) SMK Paku QA

1

[2M]

[1M]

[2M]

[1M]

2. a) Simple aggregate price index 1000

=

x

xn

12010048101211

5101312=

++++

++++ a

a =14

b) Laspeyres Price Index 10000

=

qp

qp nn

100)5(4)3(8)2(10)2(12)2(11

)5(5)3(10)2(14)2(13)2(12

++++

++++=

= 120.9

The housewifes expenditure on fish in year 2012 increased by 20.9% when

compared with 2011.

2M

1M

2M

1M

3a)

stem leaf

4 1 4 8

5 0 2 7 8

6 2 3 6 6 7 7 8

7 0 0 2 4 4 7

8 5 7

9 3

10 8

2M

b)

1M

1. a) P(only one of the two bulbs is in good

condition ,replacing the first bulb)

= 280

20

80

60

= 0.375

b) P(only one of the two bulbs is in good

condition, with the first bulb not

returned into the box)

= 279

20

80

60

= 0.3797

[1M]

Key: 4 1 means 41

CONFIDENTIAL*/SULIT

STPM 950/2

CONFIDENTIAL*

*This question paper is CONFIDENTIAL until the examination is over.

7

67

12

)24(2

1Median

=

=

=

th

th

5.57

2

5857

6

)24(4

1Q1

=

+=

=

=

th

th

74

18

)24(4

3Q3

=

=

=

th

th

1M

c.

75.32

)5.5774(2

35.57

)(2

3Qboundary Lower 131

=

=

= QQ

75.106

)5.5774(2

374

)(2

3Qboundary Upper 131

=

=

= QQ

Outlier = 108

1 M

2M

4a)

Interquartile range = 13 QQ

= 74 -57.5 = 16.5

CONFIDENTIAL*/SULIT

STPM 950/2

CONFIDENTIAL*

*This question paper is CONFIDENTIAL until the examination is over.

8

5.

2M

6 a) Graph Year Quarter Unemployed 4-quarter Centred 4-quarter Deviation

3M

CONFIDENTIAL*/SULIT

STPM 950/2

CONFIDENTIAL*

*This question paper is CONFIDENTIAL until the examination is over.

9

school

leavers

moving

average

moving average

(t)

(y-t)

2010 1 22

2 12

43.75

3 110 43.625 66.375

43.50

4 31 45.25 -14.250

47.00

2011 1 21 52.00 -31.000

57.00

2 26 61.875 -35.875

66.75

3 150 70.375 79.625

74.00

4 70 75.250 -5.250

76.50

2012 1 50 76.000 -26.000

75.50

2 36 80.500 -44.500

85.50

3 146

4 110

b) seasonal variation

Year Quarter 1 Quarter 2 Quarter 3 Quarter 4

2010 66.375 -14.250

2011 -31.000 -35.875 79.625 -5.250

2012 -26.000 -44.500

Unadjusted

seasonal

variation

-28.500 -40.188 73.000 -9.750

Correction

factor

-1.3595 -1.3595 -1.3595 -1.3595

Seasonal

Variation

-27.14 -38.83 74.36 -8.39

C) The least square method

4822 = x 66= x 794182 = y 784= y 4627= xy

12

)66(482

12

)784)(66(4629

2

= = 2.664

1M

[1M]

[2M]

CONFIDENTIAL*/SULIT

STPM 950/2

CONFIDENTIAL*

*This question paper is CONFIDENTIAL until the examination is over.

10

=

12

66664.2

12

784a =50.68

Regression line, y = 50.68+2.664x

For the first quarter of the year 2013, eT = 50.68+2.664(13) = 85.312

Unemployed school leavers for the first quarter of the year 2013

=85.312+ (-27.14) = 58.172 59

Or

Average quarterly increment =7

625.435.80 =5.2679

For the first quarter of the year 2013, eT = 80.5 + 3 x 5.2679 = 96.304

Unemployed school leavers for the first quarter of the year 2013

= 96.304 + (-27.14)= 69.164 69

1M

1M

1M

1M

2M

1M

7a Histogram

b) 5.62)125(2

1

2

1==N

minutes58.30)1(30

45)125(2

1

30

2

1

Median,

=

+=

+= cf

FN

LMm

2M

x f fx 2fx Cumulative frequency,F

26.5 6 6

28.5 12 18

29.5 27 45

30.5 30 75

31.5 18 93

32.5 14 107