63743526 Math s Paper 2 Stpm 2011 Trial Sabah

8/4/2019 63743526 Math s Paper 2 Stpm 2011 Trial Sabah

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CONFIDENTIAL*/SULIT*

950/2Mathematics S

Paper 2Ogos 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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A school has 120 Form Si st d ts. 40% ofthem are males andthe rest are females. 20

ofthe male st dents are wearing spectacles. From all ofthe female st dents, 30 ofthem

without glasses. A studentis selected at random from the school.

(a) Ifitis known thatthe student selectedis wearing spectacles.

Whatis the probabilitythatthe studentis a male? [2 marks]

(b) LetA be the eventthat a student who wears spectacles is selected andB be the eventthat a female studentis selected.

Are eventsA andBindependent? Give a reason foryour answer. [3 marks]

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

12 fathers, mothers andtheiryoungest 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 scatterdiagrams 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 scatterdiagram in (a), which variable has a strong linear relationship

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

3. A normal population has mean and standard deviation 5. An independent random

sample is taken from the population. Determine the size ofthe sample needed so thatthe

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

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

30th

Septemberin a town.

65 63 64 64 76 59

68 69 67 72 51 6464 62 70 72 68 77

69 64 73 63 68

(a) Draw a draw a stem plot fordata above and findthe median. [3 marks]

(b) Draw a box plotto representthe data andidentify possible outliers [4 marks]

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

11 a.m. on a particular Mondayis

.

(a) Findthe mostlikely number of free telephones atthattime. [5marks]

(b) Find, correctto 3 decimal places, the probabilitythat at 11 a.m. that Monday(i) exactly6telephones are used, [2 marks]

(ii) atleast 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 theseworkers, whatis the probability thatthis sample willyield an average age less than 35

years? [5marks]

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

per week for6 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

andthe sales. Interpretyour answer. [4 marks]

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

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

Hei (cm) Frequency

100 27

110 58

120 130

130 105

140 50

150 25

160 5

(a) Plotthe cumulative frequency curve forthe data. [3 marks]

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

students. [5marks]

(c) Calculate the mean and standarddeviation ofthe height ofthe students. [4 marks]


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9. The following table shows the activities for a project andtheir preceding activities andduration.

Acti ity Preceding acti ities Durati n (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 forthe project showing the earliest starttime andthe latest

starttime for each activity. [5marks]

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

(c) Findthe minimum time requiredto 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 andC. The prices and

quantities for each type of refrigerator in the years 2008, 2009 and 2010 are shown inthe 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 andthe year 2008 as the base year, calculate the

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

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


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11. The following table shows the fixeddeposits in a finance companyin the years 2007to2010.

Quarter Fixed Deposits (RM 000)

Year 1 2 3 4

2007 13 20 35 222008 14 24 55 24

2009 16 28 43 32

2010 18 30 50 20

(a) Plotthe 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.[6marks]

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 ofthe machine is 80 hours

per week. Each unit of Alpha or Beta required6 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. [5marks]

(b) By using a graphical method, determine the weekly quantities of products Alpha andBeta to be produce to maximize profits. Whatis the amount ofthe maximum profit?

[8marks]

63743526 Math s Paper 2 Stpm 2011 Trial Sabah

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