ADDITIONAL

MATHEMATICS

PROJECT WORK 2013

SELANGOR

(PROJECT 2) NAME:Wan Nur Emilly Bt Wan Mohd Ariffin

CLASS:5 Science3

NO I.C:960329105456

TEARCHER NAME:PUAN ROIAMAH BASRI

˅ CONTENT ˅

content page

1. rubric 2

2.

content 3

3. introduction 4

4. objective 5

5. Appreciate 6

6. Part 1 7-9

Part 2 10-13

Part 3 14-16

Part 4 18

Reflection 19

OBJECTIVE

The aims of carrying out project work are :

i) To apply and adapt a variety of problem – solving

strategies to solve problems;

ii) To improve thinking skills

iii) To promote effective mathematical communication

iv) To develop mathematical knowledge through problem

solving in a way that increases students interest and

confidence

v) To use the language of mathematical to express

mathemical ideas precisely

vi) To provide learning environment that stimulates and

enhances effective learning

vii) To develop positive attitude towards mathematics

APPRECIATE

First of all, I wish to express gratitude to Allah s.w.t for his guidance and also giving me the

strength to do this project work. Finally, the additional mathematics project work was

successfully completed with the inspiration, the gift and the instruction were given by Him.

Not forgotten my parents for providing everything, such as money, to buy anything that are

related to this project work and their advise, support which are the most needed for this

project. Internet, books, computers and all that. They also supported me and encouraged me to

complete this task so that I will not procrastinate in doing it. Beside that My father teacher at

SMK taman tasik , ampang, Selangor puan rhoimah for sharing ideas to ensure our task will

finish completely.

Then I would like to thank my teacher, for guiding me and my friends throughout this

project. We had some difficulties in doing this task, but she taught us patiently until we knew

what to do. She tried and tried to teach us until we understand what we supposed to do with

the project work.

Last but not least, my friends who were doing this project with me and sharing our ideas.

They were helpful that when we combined and discussed together, we had this task done.

INTRODUCTION

(source: http://www.scribd.com/doc/33106504/Add-Math-Complete-task4-2010-sample) History of Index Number Index numbers are meant to study the change in the effects of such factors which cannot be measured directly. According to Bowley, Index numbers are used to measure the changes in some quantity which we cannot observe directly´. For example, changes in business activity in a country are not capable of direct measurement but it is possible to study relative changes in business activity by studying the variations in the values of some such factors which affect business activity, and which are capable of direct measurement. Index numbers are commonly used statistical device for measuring the combined fluctuations in a group related variables. If we wish to compare the price level of consumer items today with that prevalentten years ago, we are not interested 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 production or industrial production with that at the time of independence. Here again, we have to consider all items of production and each item may have undergone a different fractional 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 variables over 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 classified in terms of the variables that they are intended to measure. In business, different groups of variables in the measurement 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 mainly interested in index numbers of prices showing changes with respect to time, although methods described can be applied to other cases. In general, the present 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 is called the base period. Index Numbers Index numbers are statistical measures designed to show changes in a variable or group of related variables with respect to time, geographic location or other characteristics such as income, profession, etc. A collection of index numbers for different years, locations, etc., is sometimes called an index series. Simple Index Number A simple index number is a number that measures a relative change in a single variable with respect to a base. Composite Index Number A composite index number is a number that measures an average relative 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

Price index

An index number expressing the level of a group of commodity prices relative to

the 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.

Weightage

The assignment of a quota(as of members of a legislature)to a particular segment

of the population as a special favor or concession in a proportion above that

allowable on a strictly numerical basis.

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.

i) Pie chart

ii) Bar Chart

iii) Percentage

pie chart

1st Qtr 2nd Qtr 3rd Qtr 4th Qtr

0

1

2

3

4

5

6

Category 1 Category 2 Category 3 Category 4

Series 1 Series 2 Series 3

PART2

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 thr year 2013.

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

Accommodation (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

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.

Answer:

Item Average monthly expenses for the base year 2008 (RM)

Food 700 Accommodation

(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

(ii) Hence, complete Table 2 below

Item

Average monthly expenses for the year 2008 as the base year (RM)

Average monthly expenses for the year 2013 (RM)

Food 700 1200 Accommodation

(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

Medication 200 300

Miscellaneous 1000 1500 TOTAL 4000 6000

TABLE 2

(c) (i) Complete Table 3 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(Petro/Loan/Bus fare

etc) 133.33 10.0

Clothing 200.00 4.0

Education 150.00 25.0

Recreation 140.00 3.5 Utilites(Water/Electricity/Telephone) 116.67 3.5

Medication 150.00 5.0 Miscellanous 150.00 25.0

TOTAL 1331.43 100

Table 3

Formula to calculate price index :

ii) Hence, calculate the composite index for the average monthly expenditure in the year 2013 based on the selected base year. Answer : Formula to calculate composite index : Formula ;

=209.97

(d) Make a conclusion about your family's expenditure based on your findings. Answer : The conclusion is the conjecture is correct. Conjecture is average money expenses for year 2012 is to be lower than year 2013.

I = price index/index number

W = weightage

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 two modes of payment, namely, cash payment and payment by installment.

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

Answer:

Brand Size of TV (Inches)

Price (RM) Mean Price(RM)

Standard deviation

(RM) Shop A Shop B Shop C

samsung 24 988 788 888 888.00 81.65

32 1788 1599 1690 1693.33 1685.61 40 2888 2500 2300 562.67 2512.02

penasonic 24 788 699 999 828.67 125.78 32 969 848 1200 1005.67 1010.70

40 1288 1269 1499 1352.00 104.23

TABLE 4(a)

Brand

Price (RM) Mean price (RM)

Standard deviation (RM)

Hup liong Ramli electronics

and hardware

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

Table4(b)

b)

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

member sin 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 m

oreexpensive 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)

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

& Hardwareshop 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

telivisons at the shop isalso the lowest. It shows that the prices of television

offered by the Ramli Electronics& Hardware shop is reasonable and affordable.

Part 4

a)The average monthly expenditure that you have modified in a table

Item Average monthly expenditure (RM)

Modified expenditure (RM)

food 1200 1200

Accomondation (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

Item Average monthly expenditure (RM)

Food 400

Accommodation (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

CONCLUSION Rich countries are able to achieve high level of literacy instead only a few poor countries achieved stable literacy level.

REFLECTION

While I conducting this project, a lot of information that I had

found. I have learnt how index number appear in our daily life.

Apart from that, this project encourages the student to

work together and share their knowledge. It is also encourage

student to gather information from the internet, improve

thinking skills and promote effective mathematical

communication. Not only that, I had learned some moral values

that I practice. This project had taught me to responsible on

the works that are given to me to be completed. This project

also had made me felt more confidence to do works and not to

give easily when we could not find the solution for the

question. I also learned to be more discipline on time, which I

was given about three weeks to complete this project and pass

up to my teacher just in time. I also enjoy doing this project I

spend my time with friends to complete this project and it had

tighten our friendship. Last but not least, I proposed this

project should be continue because it brings a lot of moral

value to the student and also test the students understanding

in Additional Mathematics.

END OF PROJECT…