Additional Mathematics Project 4 2010 Ayam

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CURRICULUM DEVELOPMENT DIVISION MINISTRY

OF EDUCATION MALAYSIA

ADDITIONAL MATHEMATICS PROJECT WORK 4/2010

NAME :MUHAMAD FADHLI BIN ZAHARITEACHER :PUAN SUHAILA BINTI MASPOR

TITLE :INDEX IN OUR DAILY LIFE

CLASS :5 IT 1

IC NUMBER:930803-04-5351

SEKOLAH MENENGAH KEBANGSAAN

PASIR GUDANG 3,PASIR GUDANG,JOHOR



INTRODUCTION

We students taking Additional Mathematics are required to carry out a project

work while we are in Form 5. This year the Curriculum Development Division,

Ministry of Education has prepared four tasks for us. We are to choose and

complete only ONE task based on our area of interest, and I choose to do

project work 4. This project can be done in groups or individually, but each of

us are expected to submit an individually written report. Upon completion of

the Additional Mathematics Project Work, we are to gain valuable experiences

and able to:

y To know the advantage of additional math in our daily life. y To prepare our self for the future. y Enhance acquisition of mathematical knowledge and skills

through problem-solving in ways that increase interest and

confidence.

y to learn not only in classroom but in our daily life after school. y Use technology especially the ICT appropriately and effectively



APPRECIATION

First of all, I want to give my thanks to Allah because give me chance to

do this assessment. Secondly, I want to thank to all the people that help me

done this assessment, especially to my Additional Mathematics teacher, Puan

Norsuhaila Binti Maspor and not forget to all my friend. Special thanks to my

parent to allow me to do this work.

HISTORY OF INDEX

Index numbers are meant to study the change in the effects of such

factors which cannot be measured directly. According to Bowley, Indexnumbers 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 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 number.

Index numbers are statistical measures designed to show changes in avariable 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

The prices of goods sold in shops vary from one shop to another. Shoppers

tend to buy good which are not only reasonably priced but also give value for

their money.

You are requited to out a survey on four different items based on following

categories i.e. food, detergent, and stationary. The survey should be done in

three different shops.

Question :

(a)Collect pictures, newspaper cuttings and photos on items that you have

chosen.

Answer :

Food:



Detergent:

Stationary :



Question:

(b)Record the items and their prices systematically as in table 1. Since items

may be differently packed, be sure to use consistent measurements for each

item selected so that comparison can be done easily and accuarately.

Answer:

Items Price (RM)Category Kip Mart Tesco BNJ mart Foods Self rising

flour2.80 3.00 3.50

Sugar 2.00 2.30 2.50

Butter 4.50 4.70 5.10

Egg (Grade A) 8.90 9.00 9.30

Total price 18.20 19.00 20.40

Detergent Clothdetergent (3 kg)

15.60 16.50 17.00

Fabricsoftener(200ml)

6.00 6.30 6.50

Toilet cleaner(1000ml)

9.80 10.70 11.20

Body soap(3 bars)

3.20 3.90 4.30

Total price 34.60 37.40 39.00Stationary Sharpener 1.00 1.20 1.50

Pencil (HB)1 dozen

3.80 4.60 5.10

Pen 1.10 1.30 1.50

Eraser 1.00 1.20 1.30Total price 6.90 8.30 9.40Grand total 59.70 64.70 68.80

Table 1



(c)Created at least two suitable graphical representations (the use ICT is

encouraged) to compare and contrast the prices of items chosen.

Answer:

1)Foods:

2)Detergent

17

17.5

18

18.5

19

19.5

20

20.5

21

Kip Mart Tesco BNJ Mart

total prices

total prices

32

33

34

35

36

37

38

39

40


total prices

total prices



3)Stationary:

Question:

(d)Based from the graph that I have constructed in Part 1(Task 2), we can see

small difference of prices between the three shops in food stuff, but we cansee big difference in detergent and stationary items.BNJ Mart is selling the

most expensive detergent between the three shops. You can see the total

money that spend on each shops in the graph below.

0

1

2

3

4

5

6

7

8

9

10


total prices

total prices



Answer:

Total price of all items in each shops

Question:

Identify an item that has a large price different among the shops. Calculate the

mean and standard deviation of that particular item. Hence, suggest and

discuss possible reasons for the price different.

Answer:

Cloth Detergent(3 kg)

Mean:

= 16.40#

54

56

58

60

62

64

66

68

Kip Mart

Tesco BNJ Mart

total price

total price



Standard Deviation:

¥(²)/N ± ( )²

=

- (16.40)2

=0.03#

The large difference between this the three shops might be because some of

the shop were supermarket. It is because supermarket selling items in lower

price than in regular shop. The different might also because many people is go

to supermarket between regular shop.

PART 2

Every year SMK Indah organizes a carnival to raise funds for the school. This

year the school plans to install air conditioner in the school library. Last year,

during the carnival, your class made and sold butter cake. Because of thepopularity of butter cakes, your class has decided to carry out the same

project for this years carnival.

Question:

(a)Suggest a shop from Part 1 from which you would go to purchase the

ingredients for the butter cakes. State and discuss your reasons for purchasing

from the shop you suggested.

Answer:

I will suggest people to buy in shop Kip Mart, it is because the total price of

all the ingredient in Kip Mart is the lowest between the three shops.



Question:

(b)Complete Table 2 with the prices of the items found in the

shop/supermarket that you have chosen.

Ingredient Quantity per cake Price in year 2009 Price in year 2010

Self- raising flour 250 g 0.90 1.00

Sugar 200 g 0.35 0.40

Butter 250 g 3.30 4.50

Eggs 5 eggs 1.25 1.50

Question:

( i )Calculate the price index for each ingredient in Table 2 for the year 2010

based on the year 2009.

Answer:

ingredient Quantity per

cake

Price in year

2009

Price in year

2010

Price index

Self-raising

flour

250 g 0.9 1.00 111.1

Sugar 200 g 0.35 0.40 114.3 Butter 250 g 3.30 4.50 136.4

Eggs 5 eggs(300 g) 1.25 1.50 120.0

1. Self- raising flour :

x 100 : 1.111

2. Sugar :

x 100 : 1.143

3

.

Butter :

x 100 : 136

.4 4. Eggs :

x 100 : 120.0

Question:

(ii)Calculate the composite index for making butter cake in year 2010 based

2009. Discuss how you obtained your answer.



Answer:

To calculate the composite index, weight of the ingredients is needed

Composite Index :

Ingredients Composite index

Self- raising flour 250/1000 : 1/4

Sugar 200/1000 : 1/5

Butter 250/1000 : 1/4

Eggs 300/1000 : 3/10

Composite index :

: 93.24

Question:

(iii) In the year 2009, butter cake was sold at RM 15.00 each. Suggest a

suitable selling price for the butter cake in year 2010. Give reasons foryour answer.

Answer:

On 2010 :

For 2010, the suitable price for butter cakes is RM 13.99, it is because

the increase of the ingredient is not too much.



Question:

(c)(i) Find out from reliable sources how to determine suitable capacity of

air-conditioner to be installed based on volume/size of the room.

Answer:

For common usage, air conditioner is according to the horse power and

I choose 1.5 horse power air-conditioner to be installed in the library,

which is using 1000 watt of electrical power. It is suitable for large

places.

Question:

(ii)Work in groups to estimate the volume of your school library. Explain how

you arrive at your answer. Hence, determine the number of air conditioners

with the appropriate capacity required for your library.

Answer:

Based from trusted source, the dimension of the library is:

Height : 5.5 meter

Width : 13.25 meter

Length : 19.85 meter

Volume of the room : 1447.1meter3

1 unit of air conditioner is for 90meter3

For 1447.1

=16.1

Our school library need 16 of air-conditioner.



Question:

(iii) If your class intends to sponsor one air conditioner for the school library,

how many butter cakes must your class sell in order to buy the air conditioner?

Answer:

1 unit of 1.5 horse power air-conditioner : RM 999

Cost for a butter cake : 1+0.4+4.5+1.5

:RM 7.40

Profit : 13.99 7.40

: RM 6.59

Number of cakes to buy 1 air-conditioner :

:

: 152 cakes

PART 3

As a committee member for the carnival, you are required to prepare as

estimated budget to organize this years carnival. The committee has to take

into consideration the increase in expenditure from the previous year due toinflation. The price of food, transportation and tent has increase by 15%. The

cost of games, prizes and decorations remains the same, whereas the cost of

miscellaneous items has increased by 30%.

Question:

(a) Complete Table 3 based on the information given above.



Answer:

EXPENDITURE AMOUNT IN 2009 (RM) AMOUNT IN 2010 (RM)FOODS 1200.00 1380.00

GAMES 500.00 500.00

TRANSPORTATION 300.00 345.00

DECORATION 200.00 200.00

PRIZES 600.00 600.00

TENTS 800.00 920.00

MISCELLANEOUS 400.00 520.00

Question:

Calculate the composite index for the estimated budget of the carnivalin the

year 2010 based on the year 2009.Comment on your answer.

Answer:

EXPENDITURE AMOUNT IN

2009(RM)

AMOUNTIN 2010

(RM)

PRICEINDEX, I

I =

WEIGHT,W

FOODS 1200.00 1380.00 115 12GAMES 500.00 500.00 100 5TRANSPORTATIONs 300.00 345.00 115 3DECORATIONS 200.00 200.00 100 2PRIZES 600.00 600.00 100 6TENTS 800.00 920.00 115 8MISCELLANEOUS 400.00 520.00 130 4



Composite index:

I =

=

=

= 111.625

The total price increase from year 2009 to 2010 is 11.625%. This isbecause some price of items increase in 2009.

Question:

The change in the composite index for the estimated budget for the carnival

from the year 2009 to the year 2010 is the same as the change from the year

2010 to the year 2011. Determine the composite index of budget fo the year

2011 based on the year 2009.

Composite index for the year 2009 to 2010 : 111.625

Composite index for the year 2010 to 2011 : 111.625

E

=E

E

E

100=111.625

E

=124.60



FURTHER EXPLORATION

Index is one of the most useful formula in everyday life. You can see the usage

from many situation, such as stock market index, gold index and propertyindex.

STOCK MARKET INDEX

A large number of commodities are offered for sale in every country of the

world. If we study the behavior of the prices of the commodities in any market,

we will soon arrive at a conclusion that they do not move in unison. There is

every possibility that prices of some commodities may be going up and other

falling. Even when the price of all the commodities are changing in onedirection, the rate of change may not be uniform. The prices of some

commodities may be rising or falling faster than other. Index number is a

device or an instrument which measure the average movements of a number

of selected commodities. In the words of Thomas" the index number is a

device that permits the measuring of the average behavior of a number of

individual prices.

INDEX NUMBER OF DIFFERENT TYPE OF WORK

Like a barometer showing fluctuations I the magnitude of a phenomena fromtime to time. One of these index numbers is the index number prices by means

of which one can measure the changes in the value of money. If in a particular

period there is 100 percent increase in the index number of prices it means

100 percent decrease in the purchasing power of money or value of money.

Index number is very useful device for measuring the relative changes in the

value of money. It is equally important for measuring quantitative changes in

any sector of the economy for the guidance and formulation of economic

policies in the country

The government and the people are very much concerned over changes in the

value of money.

The economic effects of the rise or fall in the purchasing power of the money

have a direct bearing on the socio economic structure of the country. The

government therefore, compiles different types of index numbers and

formulates policies on the basis of their result.



Index numbers help in comparing the economic conditions of a group of

people at two periods. If we are to know the true consumption standard of a

class of people in locality we can compute index number for a particular

section of the society only.

CONCLUSION

After doing some research of this project, additional mathematics is very

useful in our daily life. We might even use index number in anything we do.

Without it, surveys cant be conducted, stock market cant be interpret and

many more. So we should thankful to the people found the theory of index

number.

REFLECTION

After spending lots of time to do this assessment, I realize that Im still cant do

a lot about additional math, I should learn more so that I can do the best in my

SPM exam. A lot of thanks to Puan Norsuhaila Binti Maspor because she do her

best to make use understand about this subject.

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Additional Mathematics Project 4 2010 Ayam

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