trial stpm mathematics m 2 (sarawak) smk paku

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  • 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

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    *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

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    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

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    *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

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    8

    5.

    2M

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

    3M

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    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

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    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