33096170 Additional Mathematics Project 4 2010 Microsoft Word

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PROJECT WORK FOR

ADDITIONALMATHEMATHICS 2010

CURRICULUM DEVELOPMENT DIVISIONMINISTRY OF EDUCATION MALAYSIA

PROJECT WORK 4STATISTICS

NAME : ABDUL MAJID BIN ABDAZIZCLASS : 5 SCIENCE 1IC NUMBER : 930206-08-5689SUBJECT TEACHER : SIR RAFHAN BIN

AHMAD

SEKOLAH MENENGAH RAJA DR NAZRINSHAHKG GAJAH



INTRODUCTION

We students taking Additional Mathematics arerequired to carry out a project work while we are inForm 5.This year the Curriculum Development Division,Ministry of Education has prepared four tasks for us.Weare to choose and complete only ONE task based onour area of interest.This project can be done in groupsor individually, and I gladly choose to do this

individually.Upon completion of the AdditionalMathematics Project Work,we are to gain valuableexperiences and able to :

• Apply and adapt a variety of problem solvingstrategies to solve routine and non-routineproblems• Experience classroom environments which arechallenging, interesting and meaningful and henceimprove their thinking skills• Experience classroom environments whereknowledge and skills are applied in meaningfulways in solving real-life problems.• Experience classroom environments whereexpressing ones mathematical thinking,reasoningand communication are highly encouraged and

expected• Experience classroom environments thatstimulates and enhances effective learning.• Acquire effective mathematicalcommunication through oral and writing,and to usethe language of mathematics to expressmathematical 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 ourfuture undertakings and in workplace• Realise that mathematics is an important andpowerful tool in solving real-life problems andhence develop positive attitude towardsmathematics

• Train ourselves not only to be independentlearners but also to collaborate, to cooperate, andto share knowledge in an engaging and healthyenvironment• Use technology especially the ICT

appropriately and effectively• Train ourselves to appreciate the intrinsicvalues of mathematics and to become morecreative and innovative• Realize the importance and the beauty of mathematics



APPRECIATIONAlhamdullilah,thank you to Allah for giving the will to meto complete this Additional Mathematics

project.Secondly, I would like to thank the principle of Sekolah Menengah Raja Dr. Nazrin Shah, Mr. Hj. Omar BinBakar A.M.P,P.P.T for giving me the permission to do mythis Additional Mathematics Project Work. I also like tothank my Additional Mathematics teacher, Sir Rafhan forthe guide and giving useful and important informationfor me to complete this project work. Besides that, Iwould like to thank my parents for their support and

encouragement. Lastly, a special thanks to all my friendsfor their help and cooperation in searching forinformation and completing this project work.



A BRIEF HISTORY OFSTATISTICSBy the 18th century, the term "statistics"

designated the

systematic collection of demographic and

economic data by states. In the early 19th

century, the meaning of "statistics" broadened,

then including the discipline concerned with the

collection, summary, and analysis of data. Today

statistics iswidely employed in government, business, andall the sciences. Electronic computers haveexpedited statistical computation, and haveallowed statisticians to develop "computer-intensive" methods.

The term "mathematical statistics" designates the

mathematical theories of probability and statisticalinference, which are used in statistical practice. The

relation between statistics and probability theory

developed rather late, however. In the 19th century,

statistics increasingly used probability theory, whose

initial results were found in the17th and 18th

centuries, particularly in the analysis of games of



chance (gambling). By 1800, astronomy used

probability models and statistical theories, particularly

the method of least squares, which was invented by

Legendre and Gauss. Early probability theory and

statistics was systematized and extended by Laplace;

following Laplace, probability and statistics have been

in continual development. In the 19th century, social

scientists used statistical reasoning and probability

models to advance the new sciences of experimental

psychology and sociology; physical scientists used

statistical reasoning and probability models to

advance the new sciences of thermodynamics and

statistical mechanics. The development of statistical

reasoning was closely associated with the

development of inductive logic and the scientific

method.

Statistics is not a field of mathematics but an

autonomous mathematical science, like computer

science or operations research. Unlike mathematics,

statistics had its origins in public administration and

maintains a special concern with demography and

economics. Being concerned with the scientific

method and inductive logic, statistical theory hasclose association with the philosophy of science; with

its emphasis on learning from data and making best

predictions, statistics has great overlap with the

decision science and microeconomics. With its

concerns with data, statistics has overlap with

information science and computer science.



STATISTICS TODAY

During the 20th century, the creation of precise

instruments for agricultural research, public health

concerns (epidemiology, biostatistics, etc.), industrial

quality control, and economic and social purposes

(unemployment rate,econometry, etc.) necessitated

substantial advances in statistical practices.

Today the use of statistics has broadened far beyond its

origins. Individuals and organizations use statistics to



understand data and make informed decisions

throughout the natural and social sciences, medicine,

business, and other areas.

Statistics is generally regarded not as a subfield of

mathematics but rather as a distinct, albeit allied, field.

Many universities maintain separate mathematics and

statistics departments. Statistics is also taught in

departments as diverse as psychology, education, and

public health.

PART 1

The prices of goods sold in shops varyfrom one shop to

another.Shoppers tend to buy goods which arenot only reasonably priced but also give valuefor their money.

You are required to carry out a survey on fourdifferent items based on the followingcategories i.e. food, detergent andstationery.The survey should be done in threedifferent shops.



QUESTION

a) Collect pictures,newspaper cuttings or photos onitems that you have chosen.Design a collage toillustrate the chosen items

Answer:

FOODS :

DETERGENTS :



STATIONARY :



(b) Record the items and their prices systematicallyas in Table 1.Since items maybe differently packed,besure to use consistent measurements for each itemselected so that comparison can be done easily andaccurately.

Answer:

CATEGOR Y ITEM

PRICE(RM)KOOP

SARJANA

KOOPIUI

KIOSK PUM

FOOD 1.SELF-RAISINGFLOUR (1000 g) 4.00 3.70 3.60

2.SUGAR (1000g) 2.00 1.90 1.80

3.BUTTER (250g) 4.70 4.50 4.30



4.EGGS (GRADE A)1 DOZEN 5.90 5.50 5.00

TOTAL PRICE 16.60 15.60 14.70DETERGEN

T1.SOAP (3 BARS) 3.20 3.00 2.802.LIQUIDDISHWASHER(1000ml)

4.29 3.90 3.20

3.CLOTHESDETERGENT (3KG) 18.90 17.00 16.504.TOILET CLEANER(500ml) 5.50 5.50 5.50

TOTAL PRICE 31.89 29.40 28.00STATIONER

Y1.SHARPENER 1.50 1.30 1.002.PENCIL (2B) 1DOZEN 5.00 4.80 4.50

3.PEN 1.30 1.20 1.004.ERASER 1.30 1.20 1.10

TOTAL PRICE 9.10 8.50 7.60GRAND TOTAL 57.59 53.50 50.30

(c) Create at least two suitable graphicalrepresentations (the use of ICT is encouraged) tocompare and contrast the price of the items chosen.

Answer:



1)FOODS



2)DETERGENT



3)STATIONERY



(d) Based on the graphical representation thatyou have constructed in Part 1(c), interpret,discussand draw conclusions.Comments on your findings.

Answer:

Based on the graphical representation that I haveconstructed in Part 1(c), it is shown that there arelarge and small differences among the pries of items in each category between the shops.In thefood category, the smallest price difference are of those sugar, while the highest is the price of

eggs.Besides food, detergent also shows a large



price difference between its items.Among them isthe price of liquid dishwasher and clothesdetergent.On the other hand, stationery itemsdoesn;t have any obvious price difference.Thegraph also show that most of the items that arehigh priced comes from the KOOP SARJANA, while

the lowest price items come frm the KIOSK PUM.the graph 1(d) will show the conclusion of thedifference among the shops based upon the shopsgrand total.

Graph 1(d)

(e) Identify an item that has a large price differenceamong the shops. Calculate the mean and standarddeviation of that particular item. Hence, suggest anddiscuss possible reasons for the price difference.

Answer:

Liquid Dishwasher

Mean = 18.9+17+16.53



= 17.47

Standard Deviation= √ (∑x²)/N – (x̃ )²

= √18.9²+17²+16.5²3

= 0.97

The large price difference of clothes detergentamong the shops maybe because of the standard of the shop.A high standard shop or supermarket, theitems sold intend to be much more expensive than aregular shop or supermarket.Also, the pricedifference of the items may also due to the quality of the item present.A better quality means a higherprice.

PART 2

Every year SMK Indah organises a carnival toraise funds for the school. This year the schoolplans to install air conditioners in the schoollibrary. Last year, during the carnival, yourclass made and sold butter cakes. Because of the popularity of the butter cakes,your classhas decided to carry out the same project for



this year’s carnival.

QUESTION

(a ) Suggest a shop from Part 1 which you would goto purchase the ingredients for the buttercakes.State and discuss your reasons forpurchasing from the shop you suggested.

Answer:

The Giant Supermarket.This is because the totalprice of the ingredients from this shop is the lowestfrom the three shops.

(b) Complete Table 2 with the prices of the itemsfound in the

Shop/supermarket that you have chosen

Answer:

INGREDIEN T

QUANTITYPER CAKE

PRICE IN THE YEAR2009(RM)

PRICE IN THE YEAR2010(RM)

Self-RaisingFlour

250g 0.90 0.90

Sugar 200g 0.35 0.36Butter 250g 3.30 4.30Eggs (GradeA)

5 eggs(300g)

1.25 2.10

Table 2

(i) Calculate the price index for each of theingredients in Table 2 for the year 2010 based on theyear 2009

Answer :

INGREDIE QUANTIT PRICE PRICE PRICE INDEX



NT Y PERCAKE

IN THE YEAR2009(R

M)

IN THE YEAR2010(R

M)

FOR THE YEAR2010

BASED ON THE YEAR 2009( I)

Self-RaisingFlour

250g 0.90 0.90 100

Sugar 200g 0.35 0.36 102.86Butter 250g 3.30 4.30 130.30Eggs(Grade A)

5 eggs

(300g)

1.25 2.10 168

1.Self-Raising Flour

I = x 100 = 100

2.Sugar

I = x 100 = 102.86

3.Butter

I = x 100 = 130.30

4.Eggs (Grade A)

I = x 100 = 168

(ii) Calculate the composite index for making abutter cake in the year 2010 based on the year2009.Discuss how you obtained your answers.

Answer:



To calculate the composite index,weightage isneeded(W),

INGREDIENT WEIGHTAGE (W)Self-Raising Flour

=

Sugar =

Butter =

Eggs (Grade A) =

Composite Index

= (100)+ (102.86)+ (130.30)+ (168)1

= 128.54

(iii) In the year 2009,the butter cake was sold atRM15.00 each.Suggest a suitable selling price for thebutter cake in the year 2010.Give reasons for your

answer.



Answer:

On 2009,RM 15.00

On 2010, price = x 100 = 128.54%

x 100 = 128.54 x 15

=

= 19.30

Thus,the suitable price for the butter cake for theyear 2010 is RM19.30.The increase in price isalso suitable because of the rise in the price of the ingredients.

(c)

(i) Find out from reliable source how to determine



suitableCapacity of air conditioner to be installed basedon thevolume/size of a room.

Answer:

For common usage, air conditioner is rated accordingto horse power (1HP), which is approximately700W to 1000W of electrical power. It issuitable for a room size 1000ft³ which is around27m³ of volume.

(ii) Work in group to estimate the volume of yourschoolLibrary.Explain how you arrive at youranswer.Hence,determine the number of air conditioners withtheappropriate capacity required for your library.

Answer:

By using a measuring tape,the dimension for the

library is:

Height = 3.6m

Width = 9.17mLength = 20.12m

Volume of the room = 3.6 x 9.17 x 20.12=664.20m³

1 unit of air conditioner is for 27m³

For 664.20m³ =

= 24.6



That means our school library needs 25 unit of airconditioner

(iii) If your class intends to sponsor one airconditioner for the

School library, how many butter cakes mustyou sell in

order to buy the air conditioner

Answer:

1 unit of 1HP air conditioner =RM700Cost for a cake = 0.9 + 0.36 + 4.3 +

2.1= RM 7.66

Selling price = RM19.30Profit = 19.30 – 7.66

= RM 11.64

Number of cakes =

to buy 1 unit of = 60.13air conditioner = 60 cakes



PART 3

As a committee member for the carnival, you arerequired to prepare an estimated budget to organizethis year’s carnival. The committee has to take into theconsideration the increase in expenditure from theprevious year due to inflation. The price of food,transportation and tents has increased by 15%. The costof games, prizes and decorations remains the same,whereas the cost of miscellaneous items has increase

by 30%.

QUESTION

(a) Complete Table 3 based on the information givenabove

Answer:

EXPENDITURE AMOUNTIN 2009(RM)

AMOUNTIN 2010(RM)

FOOD 1200.00 1380.00GAMES 500.00 500.00

TRANSPORTATION

300.00 345.00

DECORATIONS 200.00 200.00

PRIZES 600.00 600.00 TENTS 800.00 920.00MISCELLANEOUS

400.00 520.00

Table 3



(b) Calculate the composite index for the estimatedbudget of the carnival in the year 2010 based on theyear 2009. Comment on your answer.

Answer:

EXPENDITURE AMOUNT IN2009(RM)

AMOUNT IN2010(RM)

PRICE

INDEX, I

I =

X

100%

WEIGHTAGE, W

FOOD 1200.00 1380.00 115 12GAMES 500.00 500.00 100 5

TRANSPORTA TION

300.00 345.00 115 3

DECORATIONS

200.00 200.00 100 2

PRIZES 600.00 600.00 100 6 TENTS 800.00 920.00 115 8

MISCELLANEOUS

400.00 520.00130 4

Composite Index

Ĩ=

=



=

= 111.625

The total price for the year 2010 increase by11.625%.This is because

some price in the year 2009 increased in the year2010.

(c) The change in the composite index for the

estimate budget for the carnival from the year 2009to the year 2010 is the same as the change fromthe year 2010 to the year 2011. Determine thecomposite index of the budget for the year 2011based on the year 2009.

Answer:

Composite index for the year 2009 to the year 2010= 111.625Composite index for the year 2010 to the year 2011= 111.625

Ĩ X 100 = Ĩ X Ĩ

Ĩ = 111.625 X111.625 XĨ = 124.60



FURTHEREXPLORATION

Index numbers are being used in many differentdaily situations, for example air pollution index,stock market index, gold index and property index.

Obtain information from the internet or otherreliable sources on the importance of two differenttypes of index number of your choice. Elaboratethe use and the importance of these indexnumbers in daily life.



AIR POLLUTION INDEXAir pollution is the introduction of chemicals,particulate matter,or biological materials that cause harm or discomfort tohumans orother living organisms, or damages the naturalenvironment intothe atmosphere.

The atmosphere is a complex dynamic natural gaseous

system that isessential to support life on planet Earth.Stratospheric ozonedepletion due to air pollution has long been recognized asa threat tohuman health as well as to the Earth's

ecosystems.

The Air Quality Index (AQI ) (also known as the AirPollutionIndex (API ) or Pollutant Standard Index (PSI ) i s anumber used bygovernment agencies to characterize the quality of the airat a given location. As the AQI increases, an increasingly

large percentage of



the population is likely to experience increasingly severeadversehealth effects. To compute the AQI requires an airpollutantconcentration from a monitor or model. The function usedto convert

from air pollutant concentration to AQI varies bypollutant, and isdifferent in different countries. Air quality index values aredividedinto ranges, and each range is assigned a descriptor and acolor code.Standardized public health advisories are associated witheach AQIrange. An agency might also encourage members of the

public to take public transportation or work from homewhen AQI levels are high.

Limitations of theAQI

Most air contaminants do not have an associated AQI. Many

countries

monitor ground-level ozone, particulates, sulphurdioxide, carbonmonoxide and nitrogen dioxide and calculate air qualityindices forthese pollutants.Causes of Poor AirQuality

The AQI can worsen (go up) due to lack of dilution of air

emissionsby fresh air. Stagnant air, oftencaused byan anticyclone or temperature inversion, or other lack of winds lets airpollution remain in a local area.



Indices by location

South Korea The Ministry of Environment of South Korea uses theComprehensiceAir-quality Index (CAI) to describe the ambient air quality

based onhealth risk of air pollution. The index aims to help thepublic easilyunderstand air quality level and protect the health of people from air pollution. - The CAI has values of 0 through500, which are divided into six categories. The higher theCAI value, the greater the level of air pollution. - Of values of the five air pollutants, thehighest is the CAI value.

Malaysia The air quality in Malaysia is reported as the API or AirPollutionIndex. Four of the index's pollutant components (i.e.,carbonmonoxide, ozone, nitrogen dioxide and sulfur dioxide) arereported

in PM 10 particulate matter is reported ing/m³.Unlike the American AQI, the index number can exceed500. Above500, a state of emergency is declared in the reportingarea. Usually,this means that non-essential government services aresuspended, and

all ports in the affected area closed. There may also be aprohibitionon private sector commercial and industrial activities in thereportingarea excluding the food sector.



STOCK MARKET INDEXA comparison of tree major U.S. stock indices: theNASDAQ Composite, Dow Jones Industrial Average,andS&P 500. All three have the same height at March2007. Notice the large dot com spike on the NASDAQ,a result of the large number of tech. companies on thatindex.

A stock market index is a method of measuring a sectionof the stock market. Many indices are cited by news orfinancial services firms and are used as benchmarks, tomeasure the performance of portfolios such as mutual funds.

Types of indices

Stock market indices may be classed in many ways. A'world' or 'global' stock market index includes (typically

large) companies without regard for where they aredomiciled or traded. Two examples are MSCI World andS&P Global 100.

A national index represents the performance of the stockmarket of a given nation²and by proxy, reflects investorsentiment on the state of its economy. The most regularlyquoted market indices are national indices composed of the

stocks of large companies listed on a nation's largest stock



exchanges, such as the American S&P 500, the JapaneseNikkei 225, and the British FTSE 100.

The concept may be extended well beyond an exchange. The Dow Jones Total Stock Market Index, as its nameimplies, represents the stocks of nearly every publicly

traded company in the United States, including all U.S.stocks traded on the New York Stock Exchange (but notADRs) and most traded on the NASDAQ and AmericanStock Exchange. Russell Investment Group added to thefamily of indices by launching the Russell Global Index.





USES AND IMPORTANCE OF AIRPOLLUTION INDEX AND STOCK MARKET INDEX

As everyone can see,the air pollution index is use by thegovernment to measure the quality of air index and to detectany pollutants in our country’s air.This is to ensure the air is

clean and safe for us ti inhale.Besides that,an early warningcan be given to us if the air pollution is too high for us to getout of our homes.This warning is given based upon readingsand unterpretations of the air index.

As for the stock market index, it is mainly for the businessentrepreneurs. This type of index is used to determine theoutcome of a stock market and also the conclusion of a stockmarket. The stock market index is important because a

country’s economical state sometimes depend on it.



CONCLUSION

After doing research,answering questions,drawing graphs andsome problem solving, I saw that the usage of statistics isimportant in daily life.It is not just widely used in markets butalso in interpreting the condition of the surrounding like the air

or the water.Especially in conducting an air-pollution survey.Inconclusion,statistics is a daily life nessecities.Withoutit,surveys can’t be conducted,the stock market can’t beinterpret and many more.So,we should be thankful of thepeople who contribute in the idea of statistics.



REFLECTION

Adter spending countless hours,days and night to finish thisproject and also sacrificing my time video games and mangasin this mid year holiday,there are several things that I cansay...

Additional Mathematics...From the day I born...From the day I was able to holding pencil...From the day I start learning...And...From the day I heard your name...

I always thought that you will be my greatest obstacle and

rival in excelling in my life...But after countless of hours...Countless of days...Countless of nights...

After sacrificing my precious time just for you...Sacrificing my Computer Games...Sacrificing my Video Games...Sacrificing my Facebook...Sacrificing my Internet...Sacrifing my Anime...Sacrificing my Manga...I realized something really important in you...

I really love you... You are my real friend... You my partner... You are my soulmate...I LOVE U ADDITIONAL MATHEMATICS...

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33096170 Additional Mathematics Project 4 2010 Microsoft Word

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