Add math project

Index Number

Nalini Ramesh

960926-05-5018

Title Page

Introduction

Foreword

Part 1

(a)

(i) Price Index

(ii) Weightage

(iii) Composite Index

(b) Weightage Representation

Part 2

(a) Family’s Monthly Expenditure

for year 2013

(b)(i)(ii) Calculating Price Indexes

(c)(i)(ii) Composite Index for

Average Monthly Expenditure for

year 2013 Based on year 2012

(d) Conclusion

Part 3

(a) Survey on prices of Televisions

(b) Television That I Want to Buy

(c) Fair Price Shop Award

Part 4

(a) Modified Monthly

Expenditure to Buy New

Television

(b) My Own Monthly Expenditure

Planning

Reflection

INTRODUCTION

As a student who takes Additional Mathematics in SPM, I am required to carry out a project work. This year the Curriculum Development Division, Ministry of Education has prepared two tasks for me. I need to choose one project based on my interest. This project can be done in groups or individually but the students are required to submit an individually written report. Upon completion of the Additional Mathematics Project Work, we are able to gain valuable experiences and able to: -Apply and adapt a variety of problem solving strategies to solve routine and non-routine problems; -Experience classroom environment which are challenging, interesting and meaningful and hence improve their thinking skills. -Experience classroom environments where knowledge and skills are applied in meaningful ways in solving real-life problems -Experience classroom environments where expressing ones mathematical thinking reasoning and communication are highly encouraged and expected -Experience classroom environment that stimulates and enhances effective learning. -Acquire effective mathematical communication through oral and writing; and to use the language of mathematics to express mathematical ideas correctly and precisely -Enhance acquisition of mathematical knowledge and skills through problem-solving in ways that increase interest and confidence -Prepare ourselves for the demand of our future undertakings and in workplace -Realise that mathematics is an important and powerful tool in solving real-life problemsand hence develop positive attitude towards mathematics. -Train ourselves not only to be independent learners but also to collaborate, tocooperate, and to share knowledge in an engaging and healthy environment -Use technology especially the ICT appropriately and effectively -Train ourselves to appreciate the intrinsic values of mathematics and to become morecreative and innovative -Realize the importance and the beauty of mathematics

FOREWORD

First of all, I would like to express my highest gratitude to god for

giving me the strength and health to complete this Additional Mathematics

Project Work for the year of 2013 successfully .Not to forget a special thanks to

my beloved parents for their non-stop support since I started this project till

the end it was finished .They always encourage and advice me not to

procrastinate on this work.

Next I would like to thank to my dedicated teacher, Pn Roimah Basri

for her helpful guides. Without her guidance, I would not be able to complete

this project. Plus, thanks to my fellow friends who did a great work in helping

me to do this project work.

Lastly I would like to say thank you to any individuals or party who

has directly or indirectly involvedin completing this task. Your help is much

appreciated

SELANGOR EDUCATION DEPARTMENT

ADDITIONAL MATHEMATICS PROJECT WORK 2/2013

PART 1

(a)Describe in brief :

(i)price index

A price index (plural: “price indices” or “price indexes”) is a normalized average (typically a weighted averaged) of prices for a given class of goods or services in a given region, during a given interval of time. It is a statistic designed to help to compare how these prices, taken as a whole, differ between time periods or geographical locations.

Price indexes have several potential uses. For particularly broad indices, the index can be said to measure the economy's price level or a cost of living. More narrow price indices can help producers with business plans and pricing. Sometimes, they can be useful in helping to guide investment.

(ii)weightage

Weightage is common word used in Asia. The meaning for weightage is a

weighting factor assigned to compensate for a perceived advantage or ⅟ weight

factor or ratio; weight.

An example for its usage is: “The admission holds 80% weightage while the

interview holds 20% weightage of the admission process”.In a nutshell,

weightage can also be said as stake.

(iii)composite index

Composite index is a grouping of equities, indexes and other factors combined

in ⅟ standardized way, providing a useful statistical measure of overall market

or sector performance over time.

A composite index may also be used in the natural or social sciences to

summarize complex or multidimensional data or redundant measures.

(b)Ways of weightage representations.

Weightage in a set of data can be represented in certain ways.

1.Pie Chart

2.Bar chart

3.Percentage

4.Ratio

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.

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.

(b)(i) In this case, I am going to select 2012 as the base year.

By selecting year 2012 as the base year, we can see the increment of price index from year

2012 to 2013.

(ii)

ITEM AVERAGE MONTHLY EXPENSES FOR THE YEAR 2012 AS THE

BASE YEAR (RM)

AVERAGE MONTHLY EXPENSES FOR THE YEAR 2013

(RM)

Food 250 300

Accomodation (Rental/Loan)

400 400

Transportation (Petrol/Loan/Bus fare etc)

100 150

Clothing 50 50

Education 150 150

Recreation 50 50

Utilities (Water/Electricity/Telephone)

100 200

Medication 100 200

Miscellaneous 50 100

TOTAL 1250 1600

Table 2

(c)(i)

Item Price Indices for the year 2013

Based on the Year 2012

Weightage

Food 120 9

Accomodation (Rental/Loan) 100 8

Transportation

(Petrol/Loan/Bus Fare etc)

150 11

Clothing 100 8

Education 100 8

Recreation 100 8

Utilities

(Water/Electricity/Telephone)

200 16

Medication 200 16

Miscellaneous 200 16

TOTAL 1270 100

Table 3

(ii) The composite index for my family’s average monthly expenditure in the

year 2013 based on the selected base year is :

composite index: 120(9)+100(8)+150(11)+100(8)+100(8)+100(8)+200(16)+200(16)+200(16)

100

=155.3

(d)CONCLUSION

Based on my findings,the composite index for the average monthly

expenditure in year 2013 based onyear 2012 increases.This shows that the

price of goods has increased.Inflation occurs as price of goods increasebut the

valu of money spent remain teh same.

Here we can also conclude that my family’s expenditure has increased.

PART 3

Your family is planning to buy a new television.

(a) I have conducted a survey on the price of the television for two

different brands from three different shops.I would like to make

comparison between the two modes of payment,namely,cash payment

and payment by installment

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

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

Table 4(a)

Brand

Size of

Televisions

(inches)

Price (RM) Mean Price

(RM)

Standard

Deviation

(RM) Shop A Shop B Shop C

Sony

24 759 699 649 702 49.90

32 1349 1299 1199 1282 68.87

40 2549 2249 2149 2315 178.81

Samsung

24 849 749 799 799 40.82

32 1499 1399 1299 1399 81.64

40 2699 2449 2399 2515 143.44

Table 4(b)

(b) Based on my findings from part (a) above, I have decided to buy television Sony from Shop C

by using the cash payment method.

From the data above, we can see that the price of the television that I have chosen which is

RM1199 is below the mean price. This shows that the price is cheaper than the average price

for that kind of television. This gives me advantage and chance to save some money. Apart

from that, the price is affordable accordance to my family average household expenditure.

Other than that, the standard deviation for that television brand, Sony 30 inches is RM68.87

which means the average data value is not extreme. A high standard deviation value means

that the average data value is extreme which will result in insensibility for the consumers to

buy. The television Sony 30 inches has reasonable price as the standard deviation is not too

high.

(c) Fair Price Shop Award

The Ministry of Domestic Trade and Consumer Affairs wishes to present the Fair Price Shop

Award for the shops above. I am one of the panels for this award. Based on my findings, the

shop that deserves this award is Shop C. By considering the value of the mean and the value

of standard deviation, here are my justifications.

Shop C offers prices of television for both brands which are below the mean price which the

average market price. This shows that Shop C is able to offer lower prices for the consumers

compared to other shops. Hence, this will benefit the consumers especially for those who

come from a low income family.

The data of standard deviation for prices of television in Shop C is acceptable and sensible as

the standard deviation values are not too high. This shows that the data does not have

extreme values by both means of payment.

Brand

Size of

Televisions

(inches)

Price (RM) Mean Price

(RM)

Standard

Deviation

(RM) Shop A Shop B Shop C

Sony

24 799 739 689 742 50.16

32 1399 1349 1229 1325 82.80

40 2599 2299 2199 2365 179.00

Samsung

24 899 779 739 805 75.47

32 1539 1439 1339 1439 81.64

40 2759 2529 2439 2575 146.93

PART 4

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

family need to make some adjustment on the various types of

expenditure.

Item Average Monthly Expenditure

for the Year 2013 (to the

nearest RM)

Food 250

Accomodation (Rental/Loan) 300

Transportation

(Petrol/Loan/Bus Fare etc)

100

Clothing 50

Education 100

Recreation 50

Utilities

(Water/Electricity/Telephone)

100

Medication 100

Miscellaneous 50

Savings 500

TOTAL 1600

Revised Monthly Family Expenditure

(b) Assuming that I have just started working with a monthly salary of

RM2500, I intend to save 10% of my salary every month.Besides, I also

plan to contribute some of my salary to my parents every month.

My monthly expenditure budget

Item Average Monthly Expenditure

for the Year 2013 (to the

nearest RM)

Percentage of Monthly

Expenses (to the nearest %)

Food 400 16

Accomodation (Rental/Loan) 500 20

Transportation

(Petrol/Loan/Bus Fare etc)

200 8

Clothing 100 4

Education 50 2

Recreation 100 4

Utilities

(Water/Electricity/Telephone)

200 8

Medication 100 4

Miscellaneous 200 8

Savings 250 10

Contributions to my Parents 400 16

TOTAL 2500 100

REFLECTION

From conducting the project, I have learnt so many things. I have learnt that

money is very important in our daily life hence agreeing with the saying,

“money is not everything but everything is money”. Apart from that, money is

so vital for us to ensure the sustainability of our normal life because without

money, many things that we want to do cannot be done.

Some of the moral values that I practiced during this project are

patience, creative and innovative. To conduct a survey on the prices of the

television indeed spent a lot of time and energy. Without being patient, the

survey might not have been conducted. Other than that, my creativity is

developed as I need to do some calculations on the data and to represent it.

Besides, I also gain the ability to innovate as I needed to do some modifications

on the data in certain circumstances.

Here’s a picture which bear in my mind during the progress of this project: