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TRIAL STPM Mathematics M MethodistKL

Section A

[45 marks]

Answer all questions in this section

1 For a project, a student asked 40 people to draw two straight lines with what they thought was an angle of

75° between them, using just a ruler and a pencil. She then measured the size of the angles that had been

drawn and her data are summarised in this stem and leaf diagram

4 1

4

5 0 2 4

5 5 8 9

6 1 1 3 3 4

6 5 5 7 8 9

7 0 1 1 2 3 3 4 4 4

7 5 6 6 7 7 9 9

8 0 1 1 3 4

8 5 6

Key: 4 | 1 = 41o

(a) Find the median and quartiles of the data. [3 marks]

(b) Draw a box plot representing these data on a graph paper. [3 marks]

(c) Describe this distribution. [1 mark]

2 In a large restaurant, an average of 3 out of every 5 customers ask for water with their meal. A random

sample of 10 customers is selected.

(a) Find the probability that

(i) Exactly 6 ask for water with their meal, [2 marks]

(ii) Less than 9 ask for water with their meal. [3 marks]

A second random sample of 50 customers is selected

(b) Find the smallest value of n such that

P 9.0)( nX

where the random variable X represent the number of these customers who ask for water.

[3 marks]

3 For a geography project a student studied weather records kept by her school since 1993. To see if there

was any evidence of global warming she worked out the mean temperature in degrees Celsius at noon for

the month of June in each year.

Her results are shown in the table below.

Year 1993 1994 1995 1996 1997 1998 1999 2000

Mean

Temperature

(oC)

21.9 24.1 20.7 23.0 24.2 22.1 22.6 23.9

(a) Plot a scatter diagram showing these data. [2 marks]

The student wanted to investigate further whether or not her data provided evidence of an

increase in temperature in June each year. Using Y for the number of years since 1993 and T for

the mean temperature,

(b) Calculate the product moment correlation coefficient for these data. [4 marks]

(c) Comment on your result in relation to the student’s enquiry. [1 mark]

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4 A group of office workers were questioned for a health assurance policy. 5

2were found to take regular

exercise. When questioned about their eating habits 3

2said they always eat breakfast and, of those who

always eat breakfast 25

9also take regular exercise.

Find the probability that a randomly selected worker

(a) always eats breakfast and take regular exercise. [3 marks]

(b) does not always eats breakfast and does not always take regular exercise. [3 marks]

Determine, giving your reason, whether or not always eating breakfast and taking regular exercise are

statistically independent. [2 marks]

5 The wage rates paid and number of employees in each of three categories are shown below for the years

1983 and 1988.

1983 1988

Categories Wage Rate (RM) Number of

employees Wage Rate (RM

Number of

employees

A 3.80 150 4.40 200

B 3.50 250 3.90 300

C 3.00 500 3.30 400

Calculate both base and current weighted index numbers with 1983 as base to show the change in wage

rates. Explain why the results differ. [7 marks]

6 The data below showed the number of unemployed population of a certain country for the year 1988,

1989 and 1990.

Year

Number of Unemployed (Thousand)

Quarter

1 2 3 4

1988 36 24 25 30

1989 32 23 23 27

1990 28 21 20 25

If the seasonal factors based on the additive models are as follows:

Quarter

1 2 3 4

+4 -3 -3 +2

(a) Write the seasonally adjusted number for this data. [3 marks]

(b) Write the equation for the trend line and forecast the number of unemployed population for the first

quarter of the year 1991. [5 marks]

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Section B

(15 marks)

Answer any one question in this section

7 Happyholidays is a travel company which organizes package holidays that are sold through a number of

travel agents. It decides to offer the travel agents a bonus if they can increase the number of holidays sold

by 10% or more.

The number of Happyholidays holidays sold by Ajay, a travel agent is shown in the table below.

2007 2008 2009

Jan-Apr May-Aug Sept-Dec Jan-Apr May-Aug Sept-Dec Jan-Apr May-Aug Sept-Dec

145 98 121 123 85 101 118 76 74

(a) Calculate values of a suitable moving average. [3 marks]

(b) Plot the moving average on the given graph and the determine the appropriate model for this data.

[2 marks]

(c) Estimate the seasonal effects on this data and obtain the equation for the trend line. [8 marks]

(d) Hence calculate how many holidays Ajay needs to sell during January-April 2010 to exceed the

current trends by at least 10%. [2 marks]

8 Alfred and Benny play a game, each starting with cash amounting to RM100. Two dice are thrown. If the

total score is 5 or more then Alfred pays RM x , where 80 x , to Benny. If the total is 4 or less then

Benny pays RM )8( x to Alfred, Show that the expectation of Alfred’s cash after the first game is

RM )2304(3

1x . [6 marks]

(a) Find the expectation of Alfred’s cash after six games. [2 marks]

(b) Find the value of x for the game to be fair. [3 marks]

(c) Given that x = 3, find the variance of Alfred’s cash after the first game. [4 marks]

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