Buku Tutorial AM025 (Sesi 2021-2022)

MATHEMATICS 2 (AM025) – PSPM Questions

(b) Find the minimum sample size n, that should be taken so that P(X  1)  0.95.

(c) If 300 people is selected at random, approximate the probability more than 40
people read at least one book in a month.
[PSPM 12/13]

13. (a) The mean number of typing errors per page throughout a document is three.
Find the probability that there are less than three typing errors on any three
pages of the document.

(b) The probability that a randomly chosen youth will contract influenza like
disease (ILD) during a rainy season is 0.4. Suppose that during one rainy
season, 15 youths were randomly chosen and tested for the presence of the
virus causing ILD.
(i) What is the probability that between nine and twelve of the youths will
contract ILD?
(ii) If the probability that more than k youths will contract ILD is 0.095,
determine the value of k.
[PSPM 13/14]

14. The lifetime of a type of hand phone battery is found to be normally distributed with
mean 2.5 years and standard deviation 0.5 year. If a battery is randomly chosen, show
that the probability the battery will last less than two years is 0.1587.
(a) If a customer buys 5 batteries, what is the probability that 3 of the batteries
will last less than two years?
(b) Suppose a dealer wishes to buy 100 such batteries.
(i) Approximate the probability that less than 20 of the batteries bought
will last less than two years.
(ii) If the probability that at most m of the batteries bought will last less
than two years is 0.9772, determine the value of m.
[PSPM 13/14]

15. (a) It was found that 60% of the arrows shot by Ahmad hit the target board. Let X
denote the number of arrows that hit the target board. If Ahmad shots seven

arrows, find (ii) P( X  2).
(i) the mean and variance of X.

(b) At a factory, on average five workers were laid off in one-month period.
Calculate the probability

(i) exactly one worker will be laid off in one-month period.
(ii) between one and six workers will be laid off in a two-months period.

[PSPM 14/15]

16. The monthly sales for a supermarket is found to be normally distributed with mean
RM 485000 and standard deviation RM 30,000.
(a) Calculate the percentage for the monthly sales between RM 425000 and
RM545000.
(b) If only 16.85% of the monthly sales are not more than RM k, find the values of
k.
(c) The operating cost of the supermarket monthly sales is 6.38% less from the
monthly sales mean. Find the probability that the monthly sale are less than
the operating cost.
[PSPM 14/15]

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MATHEMATICS 2 (AM025) – PSPM Questions

17. A parking lot at Teguh Shopping Mall has two entrances A and B. The mean number
of cars that arrive per hour at entrances A and B are three and five respectively.
(a) Find the probability that less than three cars will arrive at entrance A in one
hour.
(b) Determine the probability that at least three cars will arrive at entrance B in 30
minutes.
[PSPM 15/16]

18. The daily expenditure for 500 customers of a supermarket is normally distributed with
the mean RM165 and standard deviation RM50.
(a) Find the minimum number of customers that their daily expenditure will not
exceed RM100 a day.
(b) If 83 customers spent at most RM y, obtain the value of y.
[PSPM 15/16]

19. According to a survey, 25% of the government staff overspent their monthly salary.
(a) A random sample of 25 staff was selected. Find the probability that at least
two of staff overspent their monthly salary.
(b) A random sample of 20 staff was selected. Find the probability,
(i) Not more than 5 staff overspent their monthly salary.
(ii) Between 5 and 10 staff overspent their monthly salary.
(c) A random sample of 200 staff is taken. Use the normal approximation to find
the percentage that not more than forty staff overspent their monthly salary.
[PSPM 15/16]

20. Suppose that 15 percent of the population is left-handed.
(a) Find the probability that in a group of 10 individuals, there will be at most 3
left-handers.
(b) In a group of 20 individuals, how many is expected to be left-handed?
(c) If 500 individuals of the population is selected at random, approximate the
probability that the number of left-handers is between 60 and 80.
[PSPM 16/17]

21. A production manager for a worker’s agency is worried about its elderly employees’
ability to keep up with the minimum work pace. These elderly employees will be on
medical leave for an average of m days per month. Let X be the number of days that
an elderly employee will be on medical leave with the probability distribution

P( X = x) = mxe−m .

x!

(a) Find m if P ( X = 5) = 1 P ( X = 4) . Hence, calculate Var (3X +1) .

2
(b) In a particular month, calculate the probability that an elderly employee will

be on medical leave between 1 and 5 days.
(c) The agency is planning to suggest elderly employees to retire if the percentage

of them taking medical leave for 5 days or more per month is greater than
50%. Should the company do so?
(d) What is expected number of days that an elderly employee will be on medical
leave for a year period?

[PSPM 16/17]

100

MATHEMATICS 2 (AM025) – PSPM Questions

22. The inner diameter of a pipe for domestic use is normally distributed with a mean of 5
cm and a standard deviation of 0.03 cm.
(a) Find the percentage of pipe that has inner diameter exceeding 5.075 cm.
(b) If 10% of the pipes have inner diameters less than W cm, find the value of W.
(c) Calculate the range which is symmetrical about the mean, within 80% of the
inner diameters of the pipe lies.
[PSPM 17/18]

23. (a) A telephonist receives an average of 3 calls for every 15 minutes.
(i) Find the probability that the telephonist will receive at most two calls
from 10.00 am to 10.20 am.
(ii) Find the average numbers of calls received by the telephonist in a day.
Assume one working day is 8 hours.

(b) In a shooting competition, the probability of Halim hitting the target is 14.5%.
(i) If Halim fires 7 times, what is the probability that he will hit the target
in less than 3 times?
(ii) How many times should Halim fire if the probability of him hitting the
target at least once, is more than 80%?
[PSPM 17/18]

24. (a) 4 out of 10 lecturers in a college own a Malaysian made car. If 20 lecturers are
selected at random, calculate the expected value and variance of the number of
lecturers in the college who do not own a Malaysian made car.

(b) The average number of typing errors per page throughout a document is five.
Find the probability that
(i) there are no typing errors on any page of the document.
(ii) there are less than three typing errors on any half-page of the
document.
[PSPM 18/19]

ANSWERS TOPIC 9 (PSPM)

1.  2 = 19.874  = 59.23
2. (a) (i) n = 10
(ii) P(X = 5) = 0.1536 , P( X  3) = 0.2616
(b) (i) 132
3.  = 3 (ii) r = 107.08
4. (a)  = 8
P( X  3) = 0.6472
5. (a) 0.5169
6. (a) (i) 12 (b) (i) P(X  1) = 1 (ii) 469 patients
7. (a) (i)  = 4
(b) 0.7358
8. (a) 0.3576
9. (b) 0.4456 (ii) 0.4123 (b) 0.8686
10. 8.4, 2.52  2 = 3.2 (ii) 0.4114 (b) 0.2676
11. (a) 134
12. (a) 0.9327 (b) (i) 185 (ii) RM 359
13. (a)0.0062
14. (a)0.0283 (c) (i) 0.023 (ii) 0.9984

(b) 41 (c) 0.7673
(ii)k=8
(b) n = 19 (ii) 23
(b)(i)0.0319
(b)(i)0.8389

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MATHEMATICS 2 (AM025) – PSPM Questions

15. (a) (i) 4.2 , 1.68 (ii) 0.9812

(b) (i) 0.0337 (ii) 0.0666

16. (a) 95.44% (b) k = RM 456200 (c) 0.1515

17. (a) 0.4232 (b) 0.4562

18. (a) 49 customers (b) RM116.50

19. (a) 0.993

(b) (i) 0.6172

(ii) 0.3689

(c) 6.06%

20. (a) 0.95

(b) 3

(c) 0.6779

21. (a) m = 2.5 , Var (3X +1) = 22.5

(b) 0.6039

(c) 10.88% , the company should not suggest elderly employees to retire.

(d) 30

22. (a) 6.21% (b) 4.9616cm (c) 0.076

23. (a) (i) 0.2381 (ii) 96 calls

(b) (i) 0.9322 (ii) Halim should fire 11 times.

24. (a) E ( X ) = 12,Var ( X ) = 4.8

(b) (i) 0.0067
(ii) 0.5438

102

MATHEMATICS 2 (AM025) – PSPM Questions

T 10 C ROPIC : ORRELATION AND EGRESSION

PSPM QUESTIONS

1. A survey is conducted to determine the quality standard of workers at a production
factory. The result is as follows, where

X : represents the quality standard of workers and
Y : represent the number of defects produced by each worker.

Worker A B C D E FG
X -3 -2 -1 0 1 23
Y 45 33 20 16 9 63

(a) Find the least squares regression line, Y = a + bX and interpret the value of b.
(b) Hence, estimate the value of Y when X = −1.

[PSPM 05/06]

2. The following table shows the values of the variables X and Y obtained from an
experiment.

X -3 -2 -1 0 1 2 3
Y 33 23 21 15 9 7 3

(a) Evaluate  x,  x2,  y,  y2 and  xy .

(b) Find the regression line Y=a + bX and interpret the value of b.
(c) Calculate Pearson’s correlation coefficient and interpret the value.

[PSPM 06/07]

3. The following table shows the annual profit obtained by eight small industries for a
particular state versus the amount invested.

Investment (RM ‘000) 20 35 42 37 28 46 31 24

Profit (RM ‘000) 30 50 58 51 47 60 48 42

(a) Calculate the Pearsons’s correlation coefficient. Hence, calculate the
coefficient of determination and interpret your answer.

(b) Obtain the regression line between profit made on amount invested using the
least square method. Hence, interpret the slope of the regression line.

(c) Estimate the amount of profits made if RM45,000 is invested.
[PSPM 07/08]

4. The summary of annual expenditures, Y (in RM’000), for eight towns consisting of
different number of families, X (in hundreds) is as follows.

x = 112.5,  x2 = 126550, y = 228.625,  y2 = 515241,  xy = 255150

(a) Obtain the equation of regression line, Y = a + bX and interpret the value of b.

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MATHEMATICS 2 (AM025) – PSPM Questions

(b) Estimate the annual expenditure for the family living in a town consisting of
6000 families.

(c) Calculate and interpret the
(i) Pearson’s correlation coefficient.
(ii) Coefficient of determination.
[PSPM 08/09]

5. A Mathematics lecturer states that there is a linear relationship between the quiz
marks (y) obtained by the students and the number of hours (x) spent on doing
Mathematics exercises in a week. The summary of information for a sample of 8
students is given below.

 x = 68,  y = 225,  xy = 2032,  x2 = 620,  y2 = 6683

(a) Calculate and interpret the Pearson correlation coefficient and the coefficient
of determination.

(b) Obtain the equation of linear regression line.
(c) Interpret the value of the slope of the regression line obtained in part (b).
(d) If a student spent 9 hours 30 minutes doing Mathematics exercises in a week,

what is the quiz marks obtained?
[PSPM 09/10]

6. The summary statistics of the turnover (Y in RM million) and number of stores (X) in
six regions are as follows.

 x = 952,  x2 = 159728, y = 95,  y 2 = 1597,  xy = 15957

(a) Obtain a least squares regression line of turnover on stores.
(b) Find the Pearson’s correlation coefficient.

(c) For a region of 200 stores, predict the turnover. Comment on the accuracy of

the prediction.

[PSPM 10/11]

7. A researcher wants to investigate the relationship between annual income and annual

expenditure of workers at a company. A sample of annual income (x) and annual

expenditure (y) for 10 workers are as follows.

Worker(s) Income (RM’000), x Expenditure (RM’000), y

1 24.3 22.5

2 27.4 28.7

3 29.3 30.1

4 32.4 31.3

5 37.8 36.6

6 42.7 41.0

7 43.5 44.6

8 45.2 44.8

9 49.3 51.2

10 54.5 52.7

104

MATHEMATICS 2 (AM025) – PSPM Questions

(a) Calculate x2 and  xy

(b) Obtain the least squares regression line for the data above by using the
regression formula given in the List Of Mathematical Formulae. Given your
answer correct to 4 decimal places.

(c) If the annual income is RM 72,932.00, predict the annual expenditure value.

(d) Given y2 = 15631.13, calculate the Pearson’s correlation coefficient and

hence, interpret the value.

[PSPM 11/12]

8. A student wants to measure the relationship between the monthly income x (RM’00),
and monthly telephone bills y (RM), among a college stuff. The information for a
sample of 10 staffs is summarized as below.

 x = 421,  y = 1165,  x2 = 19915
 y2 = 173025,  xy = 57525

(a) Obtain the equation of linear regression line y = a + bx, with the values a and b

correct to 4 decimal places. Hence, interpret the value of b.
(b) Estimate the monthly telephone bills for a staff who earns RM 5700 in a

month.
(c) Calculate the coefficient of determination, correct to 4 decimal places and

interpret its value.
[PSPM 12/13]

9. A marketing agency states that there is a linear relationship between advertising
expenditure, X (RM’000) and sales generated, Y (RM’000,000). The summarized

information obtained from a survey participating outlets is as follows.

88 88 8
    Xi = 91.00;
X 2 = 1067.0; Yi = 82.8; Yi2 = 828.6; X iYi = 966.8
i

i=1 i=1 i=1 i=1 i =1

(a) Calculate the coefficient of determination and interpret its value.

(b) Obtain the linear regression line by using the least squares method, giving

your answer corrects to three decimal places. Hence, interpret the slope value.

(c) Estimate the sales generated if an outlet invested RM 7500 in advertising a

new product.

[PSPM 13/14]

10. The marketing division of a company wants to study the relationship between the
numbers of pamphlets distributed (X) and the total sales (Y) of a new product
introduced to ten residential areas. The data collected from area as follows

Residential 1 2 3 4 5 6 7 8 9 10
X(‘000) 10 14 20 12 20 16 22 16 18 15
Y(‘000) 8 10 18 9 16 14 20 12 16 10

(a) Obtain the linear regression line by using the least squares method. Hence,
interpret the slope value.

(b) Estimate the total sales if 18500 pamphlets are distributed.
(c) Calculate and interpret the value of the coefficient of determination.

[PSPM 14/15]

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MATHEMATICS 2 (AM025) – PSPM Questions

11. A researcher wants to measure the relationship between the advertising expenditures

and sales. The following table shows the data collected randomly from eight

companies in a certain town.

Advertising Sales
(RM’000) (RM’000)

3 70

4 120

3 110

5 100

6 140

5 120

4 100

5 130

(a) Calculate the coefficient of determination and interpret its value.
(b) Obtain the equation of linear regression line y = a + bx , with the values a and

b correct to three decimal places.
(c) Estimate the sales if the company invests RM5300 in an advertising

expenditure.
[PSPM 15/16]

12. A Mathematics lecturer is interested to find out the relationship between the grades
obtained by his students taking the Mathematics I and Mathematics II subjects. The
following table shows the final examination marks obtained.

Student 1 2 3 4 5 6 7 8 9 10 11
Mathematics I, x 80 78 68 84 65 76 90 56 88 66 79
Mathematics II, y 84 82 72 90 60 72 88 65 84 70 82

(a) Evaluate  x,  x2,  y,  y2 and  xy .

(b) Calculate the coefficient of correlation. Hence, calculate the coefficient of
determination and interpret your answer.

(c) Find the regression line equation y = a + bx and interpret the value of b

obtained.
(d) Estimate the final examination marks for Mathematics II that will be obtained

by a student if his final examination marks for Mathematics I is 75.
[PSPM 16/17]

106

MATHEMATICS 2 (AM025) – PSPM Questions

13. A test of 100 questions related to the importance of manners was given to 10
respondents of different ages. The results are shown in the following table.

Age Number of questions answered correctly
29 59
20 71
40 53
30 60
31 56
42 55
28 72
29 75
23 75
35 70

(a) Calculate the coefficient of determination and interpret its value.
(b) Obtain an equation of the linear regression line y = a + bx , with the values of

a and b correct to three decimal places. Hence, interpret the value of the
slope.
(c) Estimate the number of questions likely to be answered correctly by a 24-year
old student.

[PSPM 17/18]

14. The following table shows the number of hours spent on revision per week for

Mathematics and the final examination marks obtained by seven students.

Hours, X 10 15 12 9 17 14 8

Marks, Y 65 85 75 60 90 88 62

(a) Obtain the equation of linear regression line y = a + bx , with the values of a

and b correct to four decimal places. Hence, interpret the slope b obtained.
(b) Estimate the final examination marks of a student who spent 16 hours per

week for revision.
[PSPM 18/19]

15. A researcher wants to determine the relationship between number of shops, X (‘00)
and annual revenue, Y(RM‘000) of 10 towns. The following statistic was obtained:

 x = 1096,  y = 2278.2,  x2 = 125820,  y2 = 608572,  xy = 254987

(i) Obtain the product moment coefficient of correlation. Hence, interpret the
value obtained.

(ii) Calculate the coefficient of determination correct to four decimal places and
interpret its value.
[PSPM 18/19]

107

MATHEMATICS 2 (AM025) – PSPM Questions

ANSWERS TOPIC 10 (PSPM)

1. (a) Y = 18.857 − 6.821X
b = −6.821meaning that every 1 unit increasing in worker quality there is
6.821 unit decrease in number of defect by each worker.

(b) Y = 25.678

2. (a)  x = 0,  x2 = 28,  y = 111,  y2 = 2423,  xy = -134

(b) Y = 15.857 − 4.786X
The slope b = −4.786 means when X increase by 1 unit Y will decrease by
4.786 units.

(c) r = −0.9839
3. (a) r = 0.9537

There is a strong positive linear correlation between the annual profit and the
amount invested.
r2 = 0.9095 , 90.95% of the variation in the profit can be explained by the
variation in the investment. And 9.05% of the variation can be explained by
other factors.
(b) y = 14.98 +1.012x
The slope b = 1.012 means when x increase by 1 unit y will increase by 1.012
units.
(c) RM60520
4. (a) Y = 9.025 +1.952x
b = 1.952 means the annual expenditure of a town increases by RM 1.952 for

each unit increment in the number of families living in the town.
(b) RM 126,145
(c) (i) r = 0.997

There is strong positive relationship between the annual expenditure of
a town and the number of families living in the town.
(ii) r2 = 0.994 , 99.4% of the changes in the annual expenditure is
explained by the number of families in the town and 0.6% explained
by other factors.
5. (a) r = 0.9788 , r2 = 0.9580
r = 0.9788 means that there is strong positive correlation between the quiz
marks obtained by the students and the number of hours spent on doing
Mathematics exercises in a week.
r2 = 0.9580 means that 95.8% of the variation in quiz marks obtained by the
students is accounted for by the variation in the number of hours spent on
doing Mathematics exercises in a week.
(b) y = 3.9408 + 2.8452x

(c) In part (b), the value of slope, b is positive (2.8452) which means that if the
number of hours spent on doing Mathematics exercises in a week is increases,
the quiz marks obtained by the students also increases.

(d) y = 30.9702
6. (a) y = −0.3189 + 0.1018x

(b) r = 0.9846
(c) y = 20.041 , Accuracy of the prediction is good because of high correlation.

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MATHEMATICS 2 (AM025) – PSPM Questions

7. (a) 15837.66 , 15724.73
(b) yˆ = −0.2514 + 0.999x

(c) RM72607.67
(d) 0.9899, Strong positive correlation
8. (a) y = 3.8699x − 46.4216

(b) y = 3.8699x − 46.4216

(c) 0.9379 , r2 = 0.8797
9. (a) 0.9504

(b) b = 0.783 , a = 1.443 , y = 1.443 + 0.783x

(c) If investment is RM 7,500 in advertising the new product, then the expected
sales generated is = 1.443 + 0.783(7.5) = 7.3155 or RM 7,315,500

10. (a) yˆ = −3.7628 +1.0468x
For every 1 unit (‘000) increase in pamphlet distributed the total sales of the
new product increase by RM 1.4068 (‘000)

(b) RM 15603

(c) r2 = 0.923

92.3% of the total variation in total sales of the new product is due to a
number of pamphlet distributed.
11. (a) 0.522
52.2% Variation in sale can be explained by the variation in advertising

expenditure
(b) y = 46.666 +14.762x

(c) RM124905
12. (a)
 x = 830,  x2 = 63742,  y = 849,  y2 = 66497,  xy = 64994

(b) r = 0.8975 , r2 = 0.8055, 80.55% of the variation in grades of Mathematics

II subject can be explained by the variation in grades of Mathematics I subject.
(c) y = 14.026 + 0.837x

(d) 76.801
13. (a) r2 = 0.4673

(b) b = −0.879 , a = 91.585
(c) 70

14. (a) y = 29.9573 + 3.7094x

If the students increase 1 hour for revision, the marks increase by 3.7094
(b) 89.3077
15. (i) r = 0.2345

There exist a weak positive correlation between number of shops and annual
revenue.
(ii) r2 = 0.0550
This means that 5.5% of the variation in annual revenue is explained by the
variation in number of shops and 94.5% are caused by other factors.

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MATHEMATICS 2 (AM025) – PSPM Questions

TOPIC 11 : INDEX NUMBER

PSPM QUESTIONS

1. The following table shows the price for three type of food in year 2003 and 2004.

Type of Food Price per Kilogram (RM)

2003 2004

Fish 4.00 5.00

Meat 6.00 6.80

Prawn 3.60 3.00

Using 2003 as the base year, calculate and explain the

(a) Simple relative price index for year 2004

(b) Simple aggregate price index for year 2004

[PSPM 05/06]

2. The table below shows the average price and sales quantity for three types of fruit at a
supermarket in Kuala Lumpur for the years 2004 and 2005.

Types of 2004 2005
Fruits
Average Price Quantity Average Price Quantity

(RM/kg) (100 kg) (RM/kg) (100 kg)

Mango 2.50 450 3.20 750

Orange 3.00 300 4.10 360

Apple 2.30 500 3.00 800

Calculate the value of

(a) Simple aggregate price index for the year 2005 and interpret the value.

(b) Paashe price index for the year 2005.

(c) Laspeyres quantity index for the year 2005.

[PSPM 06/07]

3. Table below shows the average price (RM per kilogramme) and price indices for three

items in year 2006 and 2007.

Item 2006 2008 Price Index

A x 4.55 130

B 5.00 6.00 120

C 7.00 8.40 y

2006:100

(a) Find the values of x and y

(b) Find the average relatives price index and the answer obtained.

(c) Given the quantity (in metrics tonnes) for the three items are 30, 50 and 80

respectively.

(i) Obtained the weighted price index

(ii) State the name of the above weighted price index.

[PSPM 07/08]

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MATHEMATICS 2 (AM025) – PSPM Questions

4. The price and quantity of kitchen utensils used in a restraint for the years 2007 and

2008 are shown in the following table.

Kitchen 2007 2008
Utensils
Price Quantity Price Quantity

(RM per unit) (unit) (RM per unit) (unit)

A 17.90 20 18.80 28

B 10.00 55 11.90 60

C 12.10 45 13.50 52

D 8.00 38 9.60 45

By using 2007 as the base year, find

(a) the average relative quantity index and explain the answer obtained.

(b) the Laspyres price index.

(c) the Paasche quantity index.

[PSPM 08/09]

5. The table below shoes the price per unit (RM) and the number of units sold for each brand
of handphones in a shop for year 2007 and 2008.

2007 2008

Brand Price per unit No. of units Price per unit No. of units
(RM) sold (RM) sold

A 700 q 680 40

B 480 60 450 30

C 680 50 650 60

D 600 27 580 60

The simple aggregate price index based on the prices in 2007 is 114.5. Show that
q = 30 .

Hence, calculate and interpret

(a) Laspeyres quantity index.

(b) Paasche quantity index.

State the difference between the Laspeyres and Paasche index.

[PSPM 09/10]

6. The selling price and quantity for several grocery items are given below.

2009 2010

Item Price Quantity Price Quantity

(RM/kg) (kg) (RM/kg) (kg)

A 0.25 210 0.40 210

B 0.85 180 1.15 210

C 10.00 40 8.00 60

D 0.35 35 0.60 40

2009 : 100

Calculate

(a) the simple aggregate price index. Explain the value obtained.

(b) the Laspeyres quantity index.

(c) the Paasche price index.

[PSPM 10/11]

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MATHEMATICS 2 (AM025) – PSPM Questions

7. The following table indicates the price and quantity for three brands of personal
computer sold for the year 2010 and 2011 by company A.

Brand 2010 2011

X Price (RM) Quantity Price (RM) Quantity
Y
Z 2500 100 2200 130

2100 145 q 150

1800 185 1600 195

By using 2010 as the base year,
(a) find q, if given the simple aggregate price index is 89.0625
(b) Hence, calculate

(i) the Laspeyres price index.
(ii) the Paasche price index.
(iii) Interpret your answer for the Paasche price index calculated in part

(b)(ii).
[PSPM 11/12]

8. Table below shows the price per unit and quantity sold for three electrical appliances at
a shop in year 2010 and 2012.

Electrical 2010 2012
Appliances Price (RM) Quantity Price (RM) Quantity

A 77 50 89 55
B 185 26 184 20
C 88 102 101 130

By using 2010 as the base year, calculate
(a) the simple aggregate quantity index.
(b) The Laspeyres price index and Paasche price index. Explain why is there a

difference between the two values obtained.
[PSPM 12/13]

9. The following table shows the average prices and quantities of three types of shoes
sold by a shoe store for the year 2010 and 2011.

2010 2011
Average price
Shoe type Average price Quantity Quantity
(RM)
A (RM) 160.00 4000
B 140.00 3000
C 140.00 4200 120.00 2400

120.00 3500

90.00 3000

By using 2010 as the base year, calculate the Paasche price index and Laspeyres
quantity index. Interpret each of the result.

[PSPM 13/14]

112

MATHEMATICS 2 (AM025) – PSPM Questions

10. The following table shows the average price and quantity for three types of vegetables
sold at a hypermarket in year 2013 and 2014.

2013 2014

Types of Average Price Quantity Average Quantity sold
vegetables (per kg) sold (in kg) Price (per (in kg)

Spinach RM 5.40 4000 kg) 4500
Tomato RM 3.50 3200 RM 4.40 3000
Cucumber RM 2.70 2400 RM 2.50 3000
RM 3.40

By using 2013 as the base year, calculate and interpret the
(a) average relative price index.
(b) Laspeyres price index.
(c) Paasche quantity index.

[PSPM 14/15]

11. The price of three items and the quantity sold for a company in 2014 and 2015 are as
follows:

Item 2014 2015

Price (RM) Quantity Price (RM) Quantity

A 4000 100 3850 120

B 3300 92 2900 85

C 2500 160 2300 175

Using 2014 as the base year,
(a) calculate and interpret the Laspeyres price index.
(b) calculate the Paasche quantity index.

[PSPM 15/16]

12. The following table shows the average price and quantity of four type of building
materials that has been bought by a building company for the year 2015 and 2016.

Building Material Price (RM per unit) Quantity (unit)

A 2015 2016 2015 2016
B
C 25.60 24.00 115 130
D
2.50 4.80 450 400

18.65 17.80 205 250

15.00 19.50 90 100

By using 2015 as the base year, calculate
(a) the Laspeyres price index.
(b) the Paasche quantity index and interpret the value obtained.

[PSPM 16/17]

113

MATHEMATICS 2 (AM025) – PSPM Questions

13. A construction company requires four main raw materials for its construction project.

The following table shows the prices of the materials and the quantities used in 2016

and 2017.

Raw material Price (RM per kg) Quantity (kg)

2016 2017 2016 2017

A 4.00 5.00 4000 3500

B 6.00 7.00 3750 3000

C 5.00 4.00 5000 3000

D 8.00 9.00 1000 2000

By using 2016 as the base year, calculate and interpret the

(a) average relative price index.

(b) Laspeyres price index.

(c) Paasche quantity index.

[PSPM 17/18]

14. The following table shows the average price per kilogram, (RM), and the quantity for

four types of vegetable, (kg), for the year 2017 and 2018.

2017 2018

Vegetable Average Price Quantity Average Price Quantity

Per Kilogram Per Kilogram

Chilli m 1200 13.00 1000

Long bean 10.00 950 12.00 1200

Cucumber 9.00 800 8.00 1300

Cabbage 8.00 950 7.00 800

2017:100

(a) Given that the average relative price index is 101.1806, find the value of m.

(b) Find and interpret simple aggregate quantity index.

(c) Calculate the Paasche price index. Interpret your answer.

[PSPM 18/19]

15. Company XYZ produces three models of washing machines AA, BB and CC. The

selling price per unit (RM) and the quantity sold in the year 2017 and 2018 are given

in the following table.

Washing Machine Price per unit (RM) Quantity (unit)

2017 2018 2017 2018

Model AA 800 850 150 200

Model BB 1200 1400 450 490

Model CC 1500 1550 180 220

By using 2017 as the base year, calculate and interpret

(i) the simple aggregate price index of the washing machines in the year

2018 correct to three decimal places.

(ii) the Laspeyres quantity index correct to three decimal places.

[PSPM 18/19]

114

MATHEMATICS 2 (AM025) – PSPM Questions

ANSWERS TOPIC 11 (PSPM)

1. (a) Fish 125 The price increase 25% compared to 2003

Meat 113.33 The price increase 13.33% compared to 2003

Prawn 83.33 The price decrease 16.67% compared to 2003

(b) 108.82

2. (a) 132.05 (b) 130.89 (c) 151.02
(c) 121.148
3. (a) x = 3.5, y = 120 (b) 123.33

4. (a) 120.77 (b) 114.02 (c) 118.55

5. (a) 119.2 (b) 119.8
6. (a) 88.65 The total price has decreased by 11.35%

(b) 136.79 (c) 98.17 (ii) 89.10
7. (a) q = 1900 (b) (i) 89.18

(c) The prices of three brands of personal computer decreased by 10.90%
8. (a) 115.17

(b) 110.77, 112.03.

Laspeyres price index use base year as a weight whereas Paasche price index
use current year as a weight.

9. 118.66, The price of shoes sold in 2011 has increased by 18.66%
88.89 , The quantity of shoes sold in 2011 has decreased by 11.11%

10. (a) 92.9, The prices of the three types of vegetables have decreased by 7.1%.

(b) 85.95 , The total price of the three types of vegetables has decreased by
14.05%.

(c) 111.08 , The total quantity of the three types of vegetables has increased by
11.08%

11. (a) 92.41 , The price is decrease by 7.59% compare to year 2014

(b) 108.94
12. (a) I = 111.7

(b) I = 110.81, The quantity of four type of building materials increased 10.81%

in year 2016 as a comparison to year 2015.

13. (a) 108.54 (b) 105.24 (c) 91.03
14. (a) m = 12

(b) 110.2564

The quantity increased by 10.26% in 2018 compared to 2017.

(c) 103.0879

15. (i) The price increased by 3.09% in 2018 compared to 2017.
108.571

The prices of washing machine in 2018 increased by 8.571% compared to year

2017.

(ii) 115.914

The quantity of washing machine in 2018 increased by 15.914% compared to

year 2017.

115

PSPM
AM025
2019/2020
&
2020/2021