math s paper 2 stpm 2011 trial sabah

8/4/2019 Math s Paper 2 Stpm 2011 Trial Sabah

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Mathematics S

Paper 2

Ogos 2011

JABATAN PELAJARAN NEGERI SABAH

PROGRAM EXCEL STPM TAHUN 2011

MATHEMATICS S (MATKEMATIK S)

PAPER 2 (KERTAS 2)

Three hours (Tiga jam)

___________________________________________________________________________

Instructions to candidates:

Answerallquestions. Answers may be written in either English or Malay.

All necessary working should be shown clearly.

Non-exact numerical answers may be given correct to three significant figures, or one

decimal place in the case of angles in degrees, unless a different level of accuracy is

specified in the question.

Mathematical tables, a list of mathematical formulae and graph paper are provided.

This question paper consists of 5 printed pages.

Jabatan Pelajaran Negeri Sabah 2011

STPM 950/2 [Turn over* This question paper is CONFIDENTIAL until the examination is over. CONFIDENTIAL *


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1. A school has 120 Form Six students. 40% of them are males and the rest are females. 20

of the male students are wearing spectacles. From all of the female students, 30 of them

without glasses. A student is selected at random from the school.

(a) If it is known that the student selected is wearing spectacles.

What is the probability that the student is a male? [2 marks]

(b) LetA be the event that a student who wears spectacles is selected andB be the event

that a female student is selected.

Are eventsA andB independent? Give a reason for your answer. [3 marks]

2. The following table shows the heights (in inch) X, YandZrespectively of a sample of

12 fathers, mothers and their youngest sons.

x 68 65 67 64 68 66 70 66 71 67 69 71

y 66 63 61 64 68 66 65 61 63 64 63 64

z 68 66 68 65 69 66 69 65 71 67 68 70

(a) Plot scatter diagrams to show the relationship between

(i) Sons height and his fathers height, [2 marks](ii) Sons height and his mothers height. [2 marks]

(b) Based on the scatter diagram in (a), which variable has a strong linear relationship

with the sons height? Give a reason for your answer. [2 marks]

3. A normal population has mean and standard deviation 5. An independent randomsample is taken from the population. Determine the size of the sample needed so that the

sample mean lies within a range of 0.4 from with a probability of 0.95. [5 marks]

4. Data below shows the maximum temperature ( for each day from 8th

September to

30th

September in a town.

65 63 64 64 76 59

68 69 67 72 51 64

64 62 70 72 68 77

69 64 73 63 68

(a) Draw a draw a stem plot for data above and find the median. [3 marks]

(b) Draw a box plot to represent the data and identify possible outliers [4 marks]

5. There are 8 telephones in an office. The probability that a telephone reminds free at

11 a.m. on a particular Monday is

.

(a) Find the most likely number of free telephones at that time. [5 marks]

(b) Find, correct to 3 decimal places, the probability that at 11 a.m. that Monday

(i) exactly 6 telephones are used, [2 marks](ii) at least 2 telephones are free. [2 marks]


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6. A company has a total of 400 workers with a mean age of 32.5 years and a standard

deviation of 9.2 years. If a sample of 50 workers is chosen at random from these

workers, what is the probability that this sample will yield an average age less than 35

years? [5 marks]

7. The weekly advertising expense,x (in thousand RM) and the sales,y (in thousand RM)

per week for 6 consecutive weeks are recorded. The results obtained are summarised as

below.

x = 47, y = 550, 2

x = 433, 2

y = 50 764, xy = 4454

(a) Calculate the Pearson correlation coefficient between the weekly advertising expense

and the sales. Interpret your answer. [4 marks]

(b) Find the equation of the least squares regression line of the sales on the weeklyadvertising expense. Interpret the slope of the regression line. [6 marks]

8. The following table shows the heights (in cm) of 400 students chosen at random.

Height (cm) Frequency

100 27

110 58

120 130

130 105

140 50

150 25

160 5

(a) Plot the cumulative frequency curve for the data. [3 marks]

(b) Hence, estimate the median and semi-interquartile range of the height of the

students. [5 marks]

(c) Calculate the mean and standard deviation of the height of the students. [4 marks]


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9. The following table shows the activities for a project and their preceding activities and

duration.

Activity Preceding activities Duration (weeks)

A 4

B 3

C A 5

D A 2

E B, D 1

F B, D 7

G B, C, D 6

H F 2

I E, H 2

(a) Draw an activity network for the project showing the earliest start time and the latest

start time for each activity. [5 marks]

(b) Determine the critical path. [1 mark]

(c) Find the minimum time required to complete the project. [1 mark]

(d) Calculate the independent float of each activity. [2 marks]

10. An electrical company produces three type of refrigerators, A,B and C. The prices and

quantities for each type of refrigerator in the years 2008, 2009 and 2010 are shown in

the table below.

Type

Price

(RM per unit)

Quantity

(thousands

unit)2008 2009 2010

A 1300 1400 1500 50

B 1200 1300 1400 30

C 1000 1200 1300 40

(a) By using the quantity as the weight and the year 2008 as the base year, calculate the

Laspeyres price indices for the years 2009 and 2010. [4 marks]

(b) Comment on the changes in the prices of refrigerators from 2009 to 2010. [2 marks]


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11. The following table shows the fixed deposits in a finance company in the years 2007 to

2010.

Quarter Fixed Deposits (RM 000)

Year 1 2 3 4

2007 13 20 35 22

2008 14 24 55 24

2009 16 28 43 32

2010 18 30 50 20

(a) Plot the data as a time series. [3 marks]

(b) Comment on the data as a time series. [1 mark]

(c) Calculate the centered four-quarter moving averages. [3 marks]

(d) Calculate the adjusted seasonal variation for each quarter using a additive model.[6 marks]

12. Company A produces two kind of products, Alpha and Beta, each of which requires two

stages of production: assembling and packaging. The company spends at most RM 8000

as assembling cost each week. The assembling cost for each unit of Alpha and Beta are

RM16.00 and RM8.00 respectively. The machine time required 4 minutes to assemble a

unit of Alpha and 12 minutes for a unit of Beta. The capacity of the machine is 80 hours

per week. Each unit of Alpha or Beta required 6 minutes of packaging time. The total

amount of packaging time used per week cannot exceed 60 hours. Profits per unit

obtained from the sale of Alpha and Beta are RM 5 and RM8 respectively.

(a) Formulate the above problem as a linear program to maximize profits. [5 marks]

(b) By using a graphical method, determine the weekly quantities of products Alpha and

Beta to be produce to maximize profits. What is the amount of the maximum profit?

[8 marks]

math s paper 2 stpm 2011 trial sabah

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