project add math 2013 index number

7/27/2019 Project Add Math 2013 Index Number

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OBJECTIVES

We, the students who took Additional Mathematics are required to

carry out a project 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 solveroutine and non-routine problems;

Experience classroom environment which are challenging,

interesting and meaningful and hence improve their thinking skills;

Experience classroom environment 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 highlyencouraged 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.


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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 tocollaborate, 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.

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, Cik Nor Afiza binti

Abdul Rahman 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 ourideas. They were helpful that when we combines and discussed together,

we had this task done.


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HISTORY OF INDEX NUMBER

Price index

A price index (plural: price indices or price indexes) is anormalized average (typically a weightedaverage) 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 indices have several potential uses. For particularly broad indices,

the index can be said to measure the economys price level or a cost of

living. More narrow price indices can help producers with business plansand 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 emerges 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 Spainfrom the New World from the effect due to currency debasement.

Vaughan compared labour statutes from his own time to similar statues

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 labour did not fluctuate much with time and


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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 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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ADDITIONAL MATHEMATICS : PROJECT WORK

2013

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:

Stationery


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Detergent

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 andaccurately.

Answer:


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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:


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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 doesnt

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.


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Part 1(e):

The item that has a large price difference = washing powder

Mean , X = =

=

= 21.17 (2dp)

Standard deviation = = =

=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 year 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. Because they offer the cheapest price and has

more discount.

Part 2(b):

I.Complete Table 2 with the prices of items found in the

shop/supermarket that you have chosen.

Answer :


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II.Composite index =

=

= = 127.32

III. 109.797 =

=

Thus,

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 schoollibary, how many butter cakes must your class sell in order to buy the

air conditioner?


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Answer :

How to Calculate :

Reliable sources

from the internet

from the technician (electrical/home)

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

Part 3

As a commite member for the carnivel, you are required to prepared an

estimate budget to organise this years 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%.


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

Answer:

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 :


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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 :

Given that

Thus,

=

= 124.61 (2 d.p)


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FURTHER EXPLAINATION

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

TheAir 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

51-100Moderate 101-200Unhealthy 201-300Very unhealthy >300HazardousIf 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.
http://en.wikipedia.org/wiki/Air_Pollution_Index#Malaysiahttp://en.wikipedia.org/wiki/Air_Pollution_Index#Malaysiahttp://en.wikipedia.org/wiki/Air_Pollution_Index#Malaysiahttp://en.wikipedia.org/wiki/Air_Pollution_Index#Malaysia


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Body Mass Index


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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 onWorld Health Organizationdatahere.The body mass index (BMI), orQuetelet index, is a statistical measure

of body weight based on a person's weight and height. Though it does

not actually measure thepercentage of body fat, it is used to estimate a

healthybody weightbased 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 areunderweight,overweightorobese. It was invented

between 1830 and 1850 by theBelgianpolymathAdolphe

Queteletduring 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

aunit of measureof 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.
http://en.wikipedia.org/wiki/World_Health_Organizationhttp://en.wikipedia.org/wiki/World_Health_Organizationhttp://en.wikipedia.org/wiki/World_Health_Organizationhttp://www.who.int/bmi/index.jsp?introPage=intro_3.htmlhttp://www.who.int/bmi/index.jsp?introPage=intro_3.htmlhttp://www.who.int/bmi/index.jsp?introPage=intro_3.htmlhttp://en.wikipedia.org/wiki/Body_fat_percentagehttp://en.wikipedia.org/wiki/Body_fat_percentagehttp://en.wikipedia.org/wiki/Body_fat_percentagehttp://en.wikipedia.org/wiki/Body_weighthttp://en.wikipedia.org/wiki/Body_weighthttp://en.wikipedia.org/wiki/Body_weighthttp://en.wikipedia.org/wiki/Underweighthttp://en.wikipedia.org/wiki/Underweighthttp://en.wikipedia.org/wiki/Underweighthttp://en.wikipedia.org/wiki/Overweighthttp://en.wikipedia.org/wiki/Overweighthttp://en.wikipedia.org/wiki/Overweighthttp://en.wikipedia.org/wiki/Obesehttp://en.wikipedia.org/wiki/Obesehttp://en.wikipedia.org/wiki/Obesehttp://en.wikipedia.org/wiki/Belgiumhttp://en.wikipedia.org/wiki/Belgiumhttp://en.wikipedia.org/wiki/Adolphe_Quetelethttp://en.wikipedia.org/wiki/Adolphe_Quetelethttp://en.wikipedia.org/wiki/Adolphe_Quetelethttp://en.wikipedia.org/wiki/Adolphe_Quetelethttp://en.wikipedia.org/wiki/Units_of_measurementhttp://en.wikipedia.org/wiki/Units_of_measurementhttp://en.wikipedia.org/wiki/Units_of_measurementhttp://en.wikipedia.org/wiki/Units_of_measurementhttp://en.wikipedia.org/wiki/Adolphe_Quetelethttp://en.wikipedia.org/wiki/Adolphe_Quetelethttp://en.wikipedia.org/wiki/Belgiumhttp://en.wikipedia.org/wiki/Belgiumhttp://en.wikipedia.org/wiki/Obesehttp://en.wikipedia.org/wiki/Overweighthttp://en.wikipedia.org/wiki/Underweighthttp://en.wikipedia.org/wiki/Body_weighthttp://en.wikipedia.org/wiki/Body_fat_percentagehttp://www.who.int/bmi/index.jsp?introPage=intro_3.htmlhttp://en.wikipedia.org/wiki/World_Health_Organization


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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

theJournal of Chronic Diseases byAncel 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 explicitlycited by Keys as being appropriate forpopulation 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
http://en.wikipedia.org/wiki/Ancel_Keyshttp://en.wikipedia.org/wiki/Ancel_Keyshttp://en.wikipedia.org/wiki/Ancel_Keyshttp://en.wikipedia.org/wiki/Ancel_Keys


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optimal weight; a BMI lower than 18.5 suggests the person

isunderweightwhile a number above 25 may indicate the person

isoverweight; a BMI below 17.5 may indicate the person hasanorexia

nervosaor a related disorder; a number above 30 suggests the person

isobese(over 40, morbidly obese).

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

weight, BMI is inversely proportional to thesquare 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

indexis based on this natural scaling of weight with the third power of

the height. However, many taller people are not just "scaled up" shortpeople, 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 thePonderal indexdoes), it would

be more appropriate to use an exponent of between 2.3 and 2.7.
http://en.wikipedia.org/wiki/Underweighthttp://en.wikipedia.org/wiki/Underweighthttp://en.wikipedia.org/wiki/Overweighthttp://en.wikipedia.org/wiki/Overweighthttp://en.wikipedia.org/wiki/Overweighthttp://en.wikipedia.org/wiki/Anorexia_nervosahttp://en.wikipedia.org/wiki/Anorexia_nervosahttp://en.wikipedia.org/wiki/Anorexia_nervosahttp://en.wikipedia.org/wiki/Anorexia_nervosahttp://en.wikipedia.org/wiki/Obesityhttp://en.wikipedia.org/wiki/Obesityhttp://en.wikipedia.org/wiki/Obesityhttp://en.wikipedia.org/wiki/Ponderal_indexhttp://en.wikipedia.org/wiki/Ponderal_indexhttp://en.wikipedia.org/wiki/Ponderal_indexhttp://en.wikipedia.org/wiki/Ponderal_indexhttp://en.wikipedia.org/wiki/Ponderal_indexhttp://en.wikipedia.org/wiki/Ponderal_indexhttp://en.wikipedia.org/wiki/Ponderal_indexhttp://en.wikipedia.org/wiki/Ponderal_indexhttp://en.wikipedia.org/wiki/Ponderal_indexhttp://en.wikipedia.org/wiki/Obesityhttp://en.wikipedia.org/wiki/Anorexia_nervosahttp://en.wikipedia.org/wiki/Anorexia_nervosahttp://en.wikipedia.org/wiki/Overweighthttp://en.wikipedia.org/wiki/Underweight


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CONCLUSION

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

a given weight, BMI is inversely proportional to thesquare of

the height. So, if all body dimensions double, and weight scalesnaturally 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 indexis 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 totheir height. It has been suggested that instead of squaring the

body height (as the BMI does) or cubing the body height (as

thePonderal indexdoes), it would be more appropriate to use an

exponent of between 2.3 and 2.7.
http://en.wikipedia.org/wiki/Ponderal_indexhttp://en.wikipedia.org/wiki/Ponderal_indexhttp://en.wikipedia.org/wiki/Ponderal_indexhttp://en.wikipedia.org/wiki/Ponderal_indexhttp://en.wikipedia.org/wiki/Ponderal_indexhttp://en.wikipedia.org/wiki/Ponderal_indexhttp://en.wikipedia.org/wiki/Ponderal_index


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REFLECTION

After spending countless hours, days and night to finish this project and alsosacrificing 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

project add math 2013 index number

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