PROJECT

ADDITIONAL MATHEMATIC

2010

INDEX NUMBER

NAMA : MUHAMMAD ASHRAF BIN SHAHARUDIN

KELAS : 5 SCIENCE 1

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TEACHER : PN. ONG YOKE BEE

OBJECTIVES

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.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:

Apply and adapt a variety of problem solving strategies to solve routine and non-routine problems;

Experience classroom environments 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 environments 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 problems

and hence develop positive attitude towards mathematics. Train ourselves not only to be independent learners but also to collaborate, to

cooperate, 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 more

creative and innovative Realize the importance and the beauty of mathematics

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FOREWARD

First of all, I would like to say Alhamdulillah, for giving me the strength and health to do this

project work. Not forgotten my parents for providing everything, such as money, to buy anything

that are related to this project work and their advise, which is the most needed for this project.

Internet, books, computers, and etc. They also supported me and encouraged me to complete this

task so that I will not procrastinate in doing it. Then I would like to thank my teacher,Pn. Ong

Yoke Bee 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 projectwork.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.

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HISTORY OF INDEX NUMBERPrice index

A price index (plural: “price indices” or “price indexes”) is a normalized average (typically

a weighted average) of prices for a given class ofgoods 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 indices 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.

Some notable price indices include:

Consumer price index

Producer price index

GDP deflator

History of early price indices

No clear consensus has emerged on who created the first price index. The earliest reported

research in this area came from Welshman Rice Vaughan who examined price level change in

his 1675 book A Discourse of Coin and Coinage. Vaughan wanted to separate the inflationary

impact of the influx of precious metals brought by Spain from the New World from the effect

due to currency debasement. Vaughan compared labor statutes from his own time to similar

statutes dating back to Edward III. These statutes set wages for certain tasks and provided a good

record of the change in wage levels. Vaughan reasoned that the market for basic labor did not

fluctuate much with time and that a basic laborers salary would probably buy the same amount of

goods in different time periods, so that a laborer's salary acted as a basket of goods. Vaughan's

analysis indicated that price levels in England had risen six to eightfold over the preceding

century

While Vaughan can be considered a forerunner of price index research, his analysis did not

actually involve calculating an index. In 1707 Englishman William Fleetwood created perhaps

the first true price index. An Oxford student asked Fleetwood to help show how prices had

changed. The student stood to lose his fellowship since a fifteenth century stipulation barred

students with annual incomes over five pounds from receiving a fellowship. Fleetwood, who

already had an interest in price change, had collected a large amount of price data going back

hundreds of years. Fleetwood proposed an index consisting of averaged price relatives and used

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his methods to show that the value of five pounds had changed greatly over the course of 260

years. He argued on behalf of the Oxford students and published his findings anonymously in a

volume entitled Chronicon Preciosum.

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Add Maths : Projek Work 4/2010

Part 1(a)

The price of goods sold in shop vary from one shop to another. Shoppers tend to buy goods which are not only reasonably price but also give value for their money.

You are required to carry out a survey on four different items based on the following categories i.e. food,detergent and stationery. The survey should be done in three differnt shop.

(a) Collect picture,newspaper cuttings or photos on item that you have chosen. Design a collage to illustrate the chosen item.

Answer :

Sationery

6

Detergent

7

Food

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Part 1(b):

Record the item and their prices systematically as such in Table 1. Since item may be differently packed, be sure to use consistent measurements for each item selected so that comparison can be done easily and accurately

Answer :

Category Item Tesco Giant The StoreFood Self-rising flour

(500 gram)2.80 3.80 3.40

Sugar( 1 Kilogram )

1.40 1.40 1.40

Butter( 250 gram )

3.70 3.90 4.60

Eggs (Gred A)( 10 unit )

3.70 3.00 3.10

Total Price 11.60 12.10 12.50Detergent Washing Powder

( 3 Kilogram )20.00 22.00 21.50

Dish Washer( 1000 ml )

5.00 4.20 4.10

Liquid Bleach( 1000 ml )

7.00 6.50 5.90

Tile Cleaner( 1000 ml )

11.20 10.80 10.50

Total Price 43.20 43.50 42.00Stationery Pencil(Shaker) 9.10 9.40 8.40

Highlighter 3.70 3.60 3.30Permanent Marker

3.70 3.10 4.00

Card Indexing 14.90 15.20 16.20Total Price 31.40 31.30 31.90Grand Total 86.20 86.90 86.40

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Part 1(c):

Create at least two suitable graphical representations (the use of ICT is encouraged) to compare contrast the price of the item chosen.

Answer :

Food Detergent Stationery0

5

10

15

20

25

30

35

40

45

50

TescoGiantThe Store

Food Detergent Stationery0

5

10

15

20

25

30

35

40

45

TescoGiantThe Store

10

Grand Total

TescoGiantThe Store

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Part 1 (d):

Based on the graphical representations that you have constructed in part 1(c), interpret, discuss and draw consclusion. Comment on your findings.

Answer :

Based on the graphical representations that I have constructed in Part 1(c), it is shown that there are large and small differences among the prices of items in each category between the shops.In the food category, the smallest price difference are of those of sugar, while the highest is the price of eggs. Besides food, detergent also shows a large price difference between its items. Among them is the price of liquid dishwasher and clothes detergent. On the other hand,stationery items doesn’t have any obvious price difference. The graph also show that most of the items that are high priced comes from the Boulevard Supermarket, while the lowest price items come from the Discount Store.The graph 1(d) will show the conclusion of the difference among the shops based upon the shops grand total.

Food Detergent Stationery0

5

10

15

20

25

30

35

40

45

50

TescoGiantThe Store

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Part 1(e):

The item that has a large price difference = washing powder

Mean , X = ∑ x

N =

20+22+21 .53

= 63.5

3 = 21.17 (2dp)

Standard deviation = √∑ x2

N−(mean)2

= √ 202+222+20.21 .52

3−( 63.5

3)

2

=√ 1346.253

−( 633

)2

=20.678( 3 dp )

Reason of difference in price : Sales and discount offer by the supermarket. Supermarket own brand are much cheaper thean the top brands

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Part 2(a):Every year SMK Indah organises a carnival to raise funds for the school. This year the school plans to install air conditioners in school libary. Last year, during the carnival, your class made and sold butter cakes. Because of the popularity of butter cakes, your class has decided to carry out the same project for this yera carnival.

(a)Suggest a shop from Part 1 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 :

Tesco will be the choice.offer the cheapest pricer and has more discount.

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Part 2(b) :

I. Complete Table 2 with the prices of items found in the shop/supermarket that you have chosen.

Answer :

Ingredient Quantity per cake Price in 2009(Rm)

Price in 2010(RM)

Price index 2010 based 2009

P20102009

=

p 2010p 2009

×100

Self-raising flour 250g 0.90 1.40 1.40.9

× 100=155.56

Sugar 200g 0.35 0.28 0.280.35

×100=80.00

Butter 250g 3.30 3.70 3.73.3

× 100=112.12

Eggs (Grade A) 5eggs(300g) 1.25 1.85 1.851.25

×100=14 8

II. Composite index = ∑ p i . wi

∑ wi

= 155.56 (250 )+80 (200 )+112.12 (250 )+148 (300)

250+200+250+300

= 10979127320

1000= 127.32

III. 109.797 = Price of butter cake∈2010Price of butter cake∈2009

× 100

= P 2010

15×100

Thus, p 2010=127.32× 15100

=RM 19.10 (2 d . p )

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Part 2(c) :i. Find out from reliable sources how to determine suitable capacity of air-conditioner to be

installed based on volume/size of a room.ii. Work in group to estimate the volume of yout school libary. Explain how you arrive at your

answer. Hence, determine the number of air conditioners with the appropriate capacity required for your libary.

iii. If your class intends to sponsor one air conditioner for the school libary, how many butter cakes must your class sell in order to buy the air conditioner?

Answer :

How to Calculate : Reliable sources from the internet

from the technician (electrical/home suppliance) Volume = Area of the libary × Height of the libary

determine the shape of the libary from plan of the libary determine how to find the area according to yhe shape of the libary. determine the height. determine the average number of student enter the libary at yhe peak hour check with the data from (a), estimate the number of air conditioner needed

The price of the air conditionerThe unit price of the butter cake

=thenumber of butter cakethat are required ¿ sell

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Part 3As a commite member for the carnivel, you are required to prepared an estimate budget to organise this year’s carnival. The commite has take into consideration the increase in expenditure from the privious year due to inflation. The price of food, trasportation and tents has increased by 15%. The cost of games, prizes and decorations remains the same, where as the cost of miscellaneous items has increased by 30%.

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

Answer:

Expenditure Amount in 2009(RM)

Amount in 2010 (RM)

PriceIndex

Weight

Food 1200.00 1.15 × 1200 = 1380 115 12Games 500.00 1 × 500 = 500 100 5

Transportation 300.00 1.15 × 300 = 345 115 9Decorations 200.00 1 × 200 = 200 100 2

Prizes 600.00 1 × 600 = 600 100 6Tents 800.00 1.15 × 800 = 920 115 8Miscellaneous 400.00 1.3 × 400 = 520 130 4

b) Calculate the composite index for the estimated budget of the carnival in the year 2010 based on the year 2009. Comment on your answer.

Answer :

composite index= εIWiεWi

¿ 446540

¿111.625

c) 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 the budget for the year 2011 based on the year 2009.

Answer :

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Given that 20112010

∧2010

2009=111.625

Thus, 20102009

=20112010

×20102009

= (111.625 ) (111.625 )

100

= 124.61 (2 d.p)

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FURTHER EXPLONATION

Index numbers are being used in many different daily situations, for example air pollution index, stock market index, gold index and property index.Obtain information from the Internet or other reliable sources on the importance of two different types of index numbers of your choice. Elaborate the use and the importance of these index numbers in daily life situations.

Answer :

Air Polution Index

The Air Pollution Index (API) is used in to measure the quality of air in Malaysia, based on

several sets of air pollution data.

A scale is used to show the health classifications used by the Malaysian government to determine

the API in a specific area:

  0-50  Good

 51-100 Moderate

101-200 Unhealthy

201-300 Very unhealthy

>300 Hazardous

If the API exceeds 500, a state of emergency is declared in the reporting area. This usually

means that non-essential government services are suspended, and all ports in the affected area

are closed. There may also be a prohibition of commercial and industrial activities which are

under the private sector in the reporting area excluding the food sector.

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Body mass index

A graph of body mass index is shown above. The dashed lines represent subdivisions within a

major class. For instance the "Underweight" classification is further divided into "severe",

"moderate", and "mild" subclasses.

Based on World Health Organization data here.

The body mass index (BMI), or Quetelet index, is a statistical measure of body weight based

on a person's weight and height. Though it does not actually measure the percentage of body fat,

it is used to estimate a healthy body weight based on a person's height. Due to its ease of

measurement and calculation, it is the most widely used diagnostic tool to identify weight

problems within a population, usually whether individuals are underweight, overweightor obese.

It was invented between 1830 and 1850 by the Belgian polymath  Adolphe Quetelet during the

course of developing "social physics".Body mass index is defined as the individual's body weight

divided by the square of his or her height. The formulae universally used in medicine produce

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a unit of measure of kg/m2. BMI can also be determined using a BMI chart. which displays BMI

as a function of weight (horizontal axis) and height (vertical axis) using contour lines for

different values of BMI or colours for different BMI categories.

SI units

Imperial units

Usage

While the formula previously called the Quetelet Index for BMI dates to the 19th century, the

new term "body mass index" for the ratio and its popularity date to a paper published in the

July edition of 1972 in the Journal of Chronic Diseases by Ancel Keys, which found the BMI to

be the best proxy for body fat percentage among ratios of weight and height; the interest in

measuring body fat being due to obesity becoming a discernible issue in prosperous Western

societies. BMI was explicitly cited by Keys as being appropriate for population studies, and

inappropriate for individual diagnosis. Nevertheless, due to its simplicity, it came to be widely

used for individual diagnosis, despite its inappropriateness.

BMI provided a simple numeric measure of a person's "fatness" or "thinness", allowing health

professionals to discuss over- and under-weight problems more objectively with their patients.

However, BMI has become controversial because many people, including physicians, have come

to rely on its apparent numerical authority for medical diagnosis, but that was never the BMI's

purpose; it is meant to be used as a simple means of classifying sedentary (physically inactive)

individuals with an average body composition. For these individuals, the current value settings

are as follows: a BMI of 18.5 to 25 may indicate optimal weight; a BMI lower than 18.5 suggests

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the person is underweightwhile a number above 25 may indicate the person is overweight; a BMI

below 17.5 may indicate the person has anorexia nervosa or a related disorder; a number above

30 suggests the person is obese (over 40, morbidly obese).

For a given height, BMI is proportional to weight. However, for a given weight, BMI is inversely

proportional to the square of the height. So, if all body dimensions double, and weight scales

naturally with the cube of the height, then BMI doubles instead of remaining the same. This

results in taller people having a reported BMI that is uncharacteristically high compared to their

actual body fat levels. In comparison, thePonderal index is based on this natural scaling of

weight with the third power of the height. However, many taller people are not just "scaled up"

short people, but tend to have narrower frames in proportion to their height. It has been

suggested that instead of squaring the body height (as the BMI does) or cubing the body height

(as the Ponderal index does), it would be more appropriate to use an exponent of between 2.3

and 2.7.

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CONCLUSION

After doing research, answering questions, drawing graphs and some problem solving, I saw that the usage of index number is important in daily life. It is not just widely used in markets but also in interpreting the condition of the surrounding like the air or the water. Especially in conducting an air-pollution survey. In conclusion, statistics is a daily life essecities. Without it, surveys can’t be conducted, the stock market can’t be interpret and many more. So ,we should be thankful of the people who contribute in the idea of statistics.

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REFLECTION

After spending countless hours, days and night to finish this project and also sacrificing my time video games and magazine in this month , there are several things that I can say...

Additional maths…

You are like a very bright star..

Smiling at me..

Every time teacher teaches me bout you…

Additional maths…

Who says you so difficult?

Who says you kill them off?

Who says you hurt parents’ feeling?

You, one of the greatest creature of God..

You, open my eyes..

Telling me little by little bout The Knower of All

Know, I feel so grateful

That He has given me the chance to get to know you…

Additional Maths, …

I love you

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