Additonal Mathematics Project Work 2013 Selangor

7/27/2019 Additonal Mathematics Project Work 2013 Selangor

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The aim of carrying out this project work are:

-to apply and adapt a variety of problem-solving strategies to solve problems

-to improve thinking skills

-to promote effective mathematical communication

-to develop mathematical knowledge through problem solving in a way that increase

students interest and confidence

-to use the language of mathematics to express mathematical ideas precisely

-to provide learning environment that stimulates and enhances effective learning

-to develop positive attitude towards mathematics


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First and foremost, I would like to thank my Additional Mathematic teacher, Pn

Lee Wee Leng as she gives us important guidance and commitment during this project

work. She has been a very supportive figure throughout the whole project.

I also would like to give thanks to all my friends for helping me and always

supporting me to help complete this project work. The have done a great job at

surveying various shops and sharing information with other people including me.

Without them this project would never have had its conclusion.

For their strong support, I would like to express my gratitude to my beloved

mother also for supplying the equipments and money needed for the resources to

complete this project. They have always been by my side and I hope they will still be

there in the future.

Last but not least, I would also like to thank all the nice shop keepers, stuff and

citizens for helping me collect the much needed data and statistic for this. Not forgetting

too all the other people who were involve directly or indirectly towards making this

project a reality.

I really appreciate all the help I have got. Again, thank you very much!


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NO. Content Page

1 Objectives

2 Acknowledgement

3 Introduction

4 Part 1

Part 1(a)(i) Part 1(a)(ii) Part 1(a)(iii) Part 1(b)5 Part 2 Part 2(a) Part 2(b)(i) Part 2(b)(ii) Part 2(c)(i) Part 2(c)(ii) Part 2(d)

6 Part 3

Part 3(a) Part 3(b) Part 3(c)

7 Part 4

Part 4(a) Part 4(b)

8 Reflection

9 Reference


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H istory of I ndex Number

Index numbers are meant to study the change in the effects of such factorswhich cannot be

measured directly. According to Bowley, Index numbers are usedto measure the changes in

some quantity which we cannot observe directly. For example, changes in business activity

in a country are not capable of directmeasurement but it is possible to study relative changes

in business activity bystudying the variations in the values of some such factors which affect

businessactivity, and which are capable of direct measurement.Index numbers are commonly

used statistical device for measuring thecombined fluctuations in a group related variables. If

we wish to compare the pricelevel of consumer items today with that prevalent ten years ago,

we are notinterested in comparing the prices of only one item, but in comparing some sort of

average price levels. We may wish to compare the present agricultural productionor industrial

production with that at the time of independence. Here again, we haveto consider all items of

production and each item may have undergone a differentfractional increase (or even a

decrease). How do we obtain a composite measure This composite measure is provided by

index numbers which may be defined as advice for combining the variations that have come

in group of related variablesover a period of time, with a view to obtain a figure that

represents the result of the change in the constitute variables.Index numbers may be classifiedin terms of the variables that they areintended to measure. In business, different groups of

variables in themeasurement of which index number techniques are commonly used are

(i)price, (ii) quantity, (iii) value and (iv) business activity. Thus, we have index of wholesale

prices, index of consumer prices, index of industrial output, index of value of exports and

index of business activity, etc. Here we shall be mainlyinterested in index numbers of prices

showing changes with respect to time,although methods described can be applied to other

cases. In general, thepresent level of prices is compared with the level of prices in the past.

The present period is called the current period and some period in the past iscalled the base

period.

I ndex Numbers

Index numbers are statistical measures designed to show changes ina variable or group of

related variables with respect to time, geographiclocation or other characteristics such as

income, profession, etc. A collectionof index numbers for different years, locations, etc., is

sometimes called anindex series.

Simple Index Number

A simple index number is a number that measures a relative change ina single variable withrespect to a base.


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Composite I ndex Number

A composite index number is a number that measures an averagerelative changes in a group

of relative variables with respect to a base.

PART 1

(a) Describe in brief

(i) price index,

(ii) weightage,

(iii) composite index.

Answer :

(i) Price index : an index number expressing the level of a group ofcommodity prices relative tothe level of the prices of the same commodities during an arbitrarily chosen base

period and used to indicate changes in the level of prices from one period to

another.

(ii) Weightage : the assignment of a quota (as of members ofa legislature) to a particular

segment of the population as a special favour or concession in a proportion above

that allowable on a strictly numerical basis

(iii) Composite index : A grouping of equities, indexes or other factors combined in a standardized way,

providing a useful statistical measure of overall market or sector performance over

time.

(b) State four ways of weightage representations. Find the examples of the representations

using internet or any printed materials.


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Answer :

Ways to represent weightage :

1) Pie chart

2) Bar graph


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3) Line graph

4) Histogram


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PART 2

We often hear complaints from the public about inflation. It causes an increase in the

household expenditure in a family. The household expenditure for every family is different.

a) Complete Table 1 for your family's monthly expenditure for the year 2013.

Answer:

Monthly

salary

Number of

family members

Item

Average Monthly

Expenditure for the

year 2013

(to the nearest RM)

Percentage of

monthly expenses

(to the nearest %)

RM 6000 5

Food 1200 20.0

Accomodation

(Rental / Loan) 240 4.0

Transportation

(Petrol/Loan /Bus

fare etc)

600 10.0

Clothing 240 4.0

Education 1500 25.0

Recreation 210 3.5

Utilities(Water / Electricity /

Telephone)

210 3.5

Medication 300 5.0

Miscellaneous 1500 25.0

TOTAL 6000 100

Table 1


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(b) If we want to compare the cost of living from one year to another, we have to

calculate the price index that involves some of the items mentioned above.

(i) In order to calculate the price index of all the items above, we have to consider the

average monthly expenses of any previous year as the base year.

Select the appropriate year as the base year.

Answer:

Item

Average Monthly

Expenditure for the base

year 2008

(RM)

Food 700

Accomodation

(Rental / Loan)

200

Transportation

(Petrol/Loan /Bus fare etc)

450

Clothing 120

Education 1000

Recreation 150

Utilities

(Water / Electricity /

Telephone)

180

Medication 200

Miscellaneous 1000

TOTAL 4000


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(ii) Hence, complete Table 2 below:

Answer:

Item

Average monthly

expenses for the year 2008as the base year

(RM)

Average monthly

expenses for the year2013

(RM)

Food 700 1200

Accomodation

(Rental / Loan) 200 240

Transportation

(Petrol /Loan /Bus fare etc) 450 600

Clothing 120 240

Education 1000 1500

Recreation 150 210

Utilities

(Water / Electricity / Telephone) 180 210

Medication200

300

Miscellaneous1000

1500

TOTAL 4000 6000

Table 2


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(c) (i) Complete Table 3 based on the above information.

Item Price indices for the year 2013

based on the year 2008

Weightage

Food 171.43 20.0

Accomodation

(Rental / Loan) 120.00 4.0

Transportation

(Petrol /Loan /Bus fare etc) 133.33 10.0

Clothing 200.00 4.0

Education 150.00 25.0

Recreation 140.00 3.5

Utilities

(Water / Electricity / Telephone) 116.67 3.5

Medication 150.00 5.0

Miscellaneous 150.00 25.0

TOTAL 1331.43 100

Table 3

Formula to calculate price index :


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( ii) Hence, calculate the composite index for the average monthly expenditure

inthe year 2013 based on the selected base year.

Answer :

Formula to calculate composite index :

= (171.43 X 20) + (120 X 4) + (133.33 X 10) + (200 X 4) + (150 X 25) + (140 X 3.5) +

(116.67 X 3.5) +(150 X 5) + (150 X 25)

(20 + 4 + 10 + 4 + 25 + 3.5 + 3.5 + 5 + 25)

= 151.90

(d) Make a conclusion about your family's expenditure based on your findings.

Answer :

Based on the findings, I found that the average expenses for current year is higher than the

base year 2008. We spent a total of RM1200 for food in 2013 compared to only RM700 in2008. Other expenses such as accommodation, utilities, transportation, clothing, education,

recreation, and medications also increase compared to the year 2008. This is due to the high

inflation rate in 2008. After the year 2008, daily expenses for our family had increased due to

the increasing of the prices of raw materials.


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PART 3

Your family is planning to buy a new television set.

(a) You have conducted a survey on the price of the television for two different brands

from three different shops. You would like to make a comparison between twomodes of payment, namely, cash payment and payment by instalment .

Table 4 (a) shows the prices of televisions by cash payment in three different shops

whereas Table 4(b) shows the prices of televisions by instalment.

Complete Table 4 (a) and 4(b) using the data you obtained.

Answer:

Brand

Size of

Television

(inches)

Price (RM)

Mean

Price

(RM)

Standard

Deviation

(RM)Hup

Liong

Shop

Ramli

Electonics

&

Hardware

Kedai

Elektrik

Chong

TS

24 988 788 888 888.00 81.65

32 1788 1599 1690 1693.33 1685.61

40 2888 2500 2300 562.67 2512.02

SH 24 788 699 999 828.67 125.7832 969 848 1200 1005.67 1010.70

40 1288 1269 1499 1352.00 104.23

Table 4(a)

Brand

Size of

Television

(inches)

Price (RM)

Mean

Price

(RM)

Standard

Deviation

(RM)

Hup Seng

Ramli

Electronics&

Hardware

Kedai

Elektrik

Chong

TS

24 1383.2 945.6 1154.4 1161.07 178.69

32 2503.2 1918.8 2197.0 2206.33 238.70

40 4043.2 3000.0 2990.0 3344.40 494.14

SH

24 1103.2 838.8 1298.7 1080.23 188.47

32 1356.6 1017.6 1560.0 1311.40 223.73

40 1803.2 1522.8 1948.7 1758.23 176.79

Table 4(b)


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The mean and standard deviation of the data can be calculated using formula :


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(b) Determine the brand and size of the television that you have decided to buy. Give

your reasons based on the findings from part (a) above.

Answer:

I want to buy a size 32 inch TS television. This is because there are only five

members in my family and only requires medium-sized television for our living room.

I choose this brand because I am confident of its quality as our family has long been

using this brand for other electrical appliances in our home. Although the brand TS is

more expensive than the brand SH, our family still can afford to buy it. I plan to buy

from Ramli Electronics & Hardware store because they offer 2 years of warranty. In

addition, they also offer the lowest price of televisions compared to the other two

shops.

(c) The Ministry of Domestic Trade and Consumer Affairs wishes to present the Fair PriceShop Award for one of the above shops. If you are one of the panels for this award,

determine the shop that deserve the award. Do you consider the value of the mean and

the value of standard deviation in making your decision? Give your justifications.

Answer:

If I am one of the panel for the award, I would prefer Ramli Electronics & Hardware

shop because the mean price of all types of television for both brands is the lowest

compared to the other two shops. Standard deviation for the telivisonsat the shop is

also the lowest. It shows that the prices of television offered by the Ramli Electronics

& Hardware shop is reasonable and affordable.


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PART 4

(a) Your family has a fixed monthly income. In order to buy the television, your

family needs to make some adjustment on the various types of expenditure.

[You can choose to pay by cash or by instalment]

Show the average monthly expenditure that you have modified in a table.

ItemAverage Monthly

Expenditure (RM)

Modified expenditure

(RM)

Food 1200 1200

Accomodation(Rental / Loan) 240 240

Transportation

(Petrol/Loan /Bus

fare etc)

600 500

Clothing 240 50

Education 1500 1300

Recreation 210 100

Utilities

(Water / Electricity

/ Telephone)

210 210

Medication 300 150

Miscellaneous 1500 750

Television - 1500

TOTAL 6000 6000


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(b) Assuming you have just started working with a monthly salary of RM2 500. You

intend to save 10% of your salary every month.

Plan your monthly expenditure as in Table 1 above and add other items such as

savings and contributions to your parents.

Item Average Monthly Expenditure (RM)

Food 400

Accomodation

(Rental / Loan) 300

Transportation

(Petrol/Loan /Bus fare etc) 200

Clothing 100

Education 100

Recreation 50

Utilities

(Water / Electricity / Telephone) 100

Medication 100

Savings 250

Parents 600

Miscellaneous 300

TOTAL 2500


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In the process of conducting this project, I have learnt that perseverance pays off,

especially when you obtain a just reward for all your hard work. For me, succeeding in

completing this project work has been reward enough. I have also learnt that mathematics is

used everywhere in daily life, from the most simple things like daily expenses and choosing

size of electronic devices, prediction and estimation of price of products in the market.

Besides that, I get to communicate with friends by discussing this project. We used the time

wisely and finished up the project in time.

The co-operation among everyone made our relationship getting closer. And also

parents who helped me while Im having problem with the project. I get to build relationships

with my parents. While I was conducting the project, I had learned many moral values that I

practice. This project work had taught me to be more confident when doing something

especially the homework given by the teacher. I also learned to be a disciplined type of

student which is always sharp on time while doing some work, complete the work by myself

and my friends and researching the information from the internet. I also felt very enjoy when

making this project.

Additonal Mathematics Project Work 2013 Selangor

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