Ujian Penilaian Pra Pentaksiran 2013

950 STPM

UNIT PENILAIAN & PEPERIKSAANSMK DATO’ JAAFAR, JOHOR BAHRU

UJIAN PENILAIAN PRA PENTAKSIRANSIJIL TINGGI PERSEKOLAHAN MALAYSIA

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MATHEMATICS M

(One and a half hours)

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Instruction to candidates:

DO NOT OPEN THIS QUESTIONS PAPER UNTIL YOU ARE TOLD TO DO SO.Answer all questions in Section A and any one question in Section B. Answers may be written in either English or Bahasa Malaysia.All necessary working should be shown clearly.Scientific calculators may be used. Programmable and graphic display calculators are prohibited. A list of mathematical formulae is provided on page 3 of this question paper.

_____________________________________________________________________________________This question paper consists of 4 printed pages.

Prepared by:

…………………......(MASYATI KARIM)

Checked by:

......................................(TING )

Verified by:

...................................

CONFIDENTIAL*/SULIT*

STPM 950Section A [45 marks]

Answer all questions in this section.

1. A man has a choice of two routes to go to work. The probability of him choosing the first route to work on any day is 0.6. The probability of being delayed on the journey is 0.1 for the first route and 0.2 for the second route. Calculate the probability that(a) he gets to work without being delayed, . [2 marks](b) he is being delayed exactly once in 3 days. [3 marks]

2. The table given shows the number of visitors to a park over a period of 80 days.Number of visitors Number of days

1000 - 1499 3

1500 - 1999 8

2000 - 2499 13

2500 - 2999 22

3000 - 3499 16

3500 - 3999 9

4000 - 4499 7

4500 - 4999 2(a) Draw an ogive to represent the above data. . [3 marks](b) Using your ogive, find the median, lower quartile, upper quartile and interquartile range. [4 marks](c) Calculate the percentages of days where there are more than 2750 visitors to the park. [2 marks]

3. The diagram given shows a sketch graph of the probability density function of the random continuous variable x. Find

a 4

(a) the value of a, hence define . [3 marks]

(b) . [5

marks]

950/2* This question paper is CONFIDENTIAL until the examination is over. CONFIDENTIAL** Kertas soalan ini SULIT sehingga peperiksaan kertas soalan ini tamat . SULIT*

1

f(x)

1/3

CONFIDENTIAL*/SULIT*(c) . [3 marks]

4. The below table shows the prices and quantities sold for three types of pen for the year 2007 and 2008 in a hypermarket.

Types of pen2007 2008

Price per unit (RM)

QuantityPrice per unit

(RM)Quantity

Opal 2.80 400 3.50 300

Firas 3.10 320 4.00 250

Kama 2.50 480 3.00 450

Find(a) the simple aggregate price index for the year 2008 and interpret. [3 marks](b) the Laspeyres price index for the year 2008. [2 marks](c) the Paasche quantity index for the year 2008. [2 marks]

5. A study was conducted to investigate the influence of the quality and fair price of products on preference to shop at a hypermarket. A random sample of 14 customers were asked to rate the hypermarket in terms of preference to shop, Y, quality of product, and fair price of product, . The ratings were based on an 11-point scale with higher numbers indicating higher ratings. The data collected are given in the below.

Customer Preference to shop (Y) Quality of product ( ) Fair price of product ( )

1 6 5 4

2 9 6 10

3 8 6 5

4 3 2 2

5 10 6 11

6 4 3 1

7 5 4 7

8 2 1 4

9 11 9 9

10 9 5 10

11 10 8 8

12 3 1 5

13 8 8 5


2


14 5 3 2(a) Calculate the Pearson correlation coefficient between preference to shop and fair pricing. [4

marks](b) Given that the value of Pearson correlation coefficient between preference to shop and

quality of product is 0.924, state whether quality of product or fair price of product has a greater influence on preference to shop. [1 mark]

(c) Calculate the Spearman's coefficient correlation between preference to shop and quality of product and interpret. [4

marks]

6. The daily closing prices (in RM per share) of a company stock for the month of March in the year 2010 are as follows:

Date Price (RM) Date Price (RM)

1 8.13 11 8.10

2 8.11 12 8.10

3 8.04 15 8.08

4 8.13 16 8.14

5 8.05 17 8.15

8 8.06 18 8.08

9 7.95 19 8.05

10 7.95 22 8.00(a) Plot the data as a time series. [3

marks](b) Comment on the pattern of the time series that you have plotted in (a).

[1 mark]

Section B [15 marks]

Answer any one question in this section.

7. The number of luxury cars sold for each quarter by a local company for a duration of four years are shown in table below.

Year Quarter Number of cars

2007

1 15

2 19

3 16

4 26

2008

1 16

2 21

3 15

4 27


3


2009

1 19

2 23

3 18

4 27(a) Plot the data as a time series. [3

marks](b) Comment on the pattern of the times series that you plotted in (a).

[1 mark](c) Given that the equation of the trend line is . Using an additive model, find the

adjusted seasonal variation for each of the four quarters. Write down your answers correct to three decimal places. [5

marks](d) Hence, predict the number of luxury cars sold for the second and fourth quarter of 2010.

[6 marks]

8. The stemplot shows the diameter of 15 different cylinders.Stem Leaf

3 0 0 1 1 1

3 2 2 2 2 3 3 3

3 4 4 4Key : 3|0 means 3.0 cm

(a) Calculate the mean and standard deviation of the diameter of the cylinder. [5 marks]

(b) Find the median and third quartile of the diameter of the cylinder. [2 marks]

(c) Draw a boxplot and give your comment. [2 marks]

(d) (i) Hence, in the production of cylinders, it is known that 3 out of 15 cylinders produced are faulty. If 20 cylinders are selected, find the probability that exactly 16 cylinders are not faulty.

[2 marks]

(ii) In a consignment of 1500 cylinders, use a suitable approximation to find the value of n such that the probability of obtaining the number of defective cylinders exceeding n is 0.1469.

[4 marks]

END OF EXAMINATION QUESTIONS


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Ujian Penilaian Pra Pentaksiran 2013