Transcript

CONTENT

1.Introduction.........................................................................2.Appreciation........................................................................3.A Brief History Of Statistic...................................................4.Problem Solving & Finding...................................................

Part 1............................................................................Part 2............................................................................Part 3............................................................................Futher Exploration........................................................Reflection.....................................................................

5.Conclusion...........................................................................6.References..........................................................................7.Rubric..................................................................................

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.This project can be done in groups or individually, and I gladly

choose to do this individually.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

APPRECIATION

Alhamdullilah,thank you to Allah for giving the will to me to complete this

Additional Mathematics project.Secondly, I would like to thank the principle

of Sekolah Menengah Teknik Dungun, Mr. Hj. Alwi for giving me the

permission to do my this Additional Mathematics Project Work. I also like to

thank my Additional Mathematics teacher, for the guide and giving useful

and important information for me to complete this project work. Besides

that, I would like to thank my parents for their support and encouragement.

Lastly, a special thanks to all my friends for their help and cooperation in

searching for information and completing this project work.

A BRIEF HISTORY OF STATISTICSBy 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 is

widely employed in government, business, and all the sciences.

Electronic computers have expedited statistical computation,

and have allowed statisticians to develop "computer-intensive"

methods.

The term "mathematical statistics" designates the mathematical

theories of probability and statistical inference, 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 has close 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 vary from one shop to another.Shoppers tend to buy goods which are not only reasonably priced 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 different shops.

QUESTION

a) Collect pictures,newspaper cuttings or photos on items that you have chosen.Design a collage to illustrate the chosen items Answer:

FOODS :

DETERGENTS :

STATIONARY :

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

Answer:

CATEGORY ITEMPRICE(RM)

TESCO GIANT KEDAI TONG

FOOD 1.SELF-RAISING FLOUR (1000 g)

7.50 7.20 7.50

2.SUGAR (1000g) 3.00 2.25 2.803.BUTTER (250g) 6.00 5.00 5.204.EGGS (GRADE A) 1 DOZEN

9.60 9.30 9.30

TOTAL PRICE 26.10 23.75 24.80DETERGENT 1.SOAP (3 KG) 12.00 10.90 11.00

2.LIQUID DISHWASHER (3 KG)

14.50 11.90 12.90

3.CLOTHES DETERGENT (3KG)

12.00 11.20 11.80

4.TROJAN (3 KG) 12.60 11.50 12.00TOTAL PRICE 51.10 45.50 47.70

STATIONERY 1.SHARPENER 2.00 1.50 1.702.PENCIL (2B) 1 DOZEN 9.00 8.60 8.403.Dupling paper (100 sheet)

4.50 4.00 3.80

4.ERASER 1.50 1.20 1.40TOTAL PRICE 17.00 18.50 15.70

GRAND TOTAL 94.20 84.55 88.20

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

Answer:

1)FOODS

2)DETERGENT

3)STATIONERY

(d) Based on the graphical representation that you have constructed in Part 1(c), interpret,discuss and draw conclusions.Comments on your findings.

Answer:

Based on the graphical representation that I have constructed in Part 1(c), it is shown that there are large and small differences among the pries of items in each category between the shops.In the food 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 is the price of liquid dishwasher and clothes detergent.On the other hand, stationery items doesn;t have any obvious price difference.

(e) Identify an item that has a large price difference among the shops. Calculate the mean and standard deviation of that particular item. Hence, suggest and discuss possible reasons for the price difference.

Answer:

Liquid Dishwasher

Mean=(14.5+11.9+12.9)/3

= 13.1

Standard Deviation

= √(∑x²)/N – ( )²x�

= √[(14.5)²+(11.9)²+(12.9)²/3] – (13.1)²

= 1.0708

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

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

QUESTION

(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:

The Giant Supermarket.This is because the total price of the ingredients from this shop is the lowest from the three shops.

(b) Complete Table 2 with the prices of the items found in the Shop/supermarket that you have chosen

Answer: INGREDIENT QUANTITY

PER CAKEPRICE IN THE

YEAR 2009(RM)

PRICE IN THE YEAR

2010(RM)Self-Raising Flour 250g 0.90 1.80Sugar 200g 0.35 0.45Butter 250g 3.30 5.00Eggs (Grade A) 5 eggs (300g) 1.25 1.55

Table 2

• Calculate the price index for each of the ingredients in Table 2

for the year 2010 based on the year 2009

Answer :

INGREDIENT QUANTITY PER CAKE

PRICE IN THE YEAR 2009(RM)

PRICE IN THE YEAR 2010(RM)

PRICE INDEX FOR THE

YEAR2010 BASED ON THE YEAR 2009(I)

Self-Raising Flour

250g 0.90 1.80 200

Sugar 200g 0.35 0.45 128.57

Butter 250g 3.30 5.00 151.52

Eggs(Grade A)

5 eggs

(300g)

1.25 1.55 124

1.Self-Raising Flour

2.Sugar

3.Butter

4.Eggs (Grade A)

124

• Calculate the composite index for making a butter cake in the

year 2010 based on the year 2009.Discuss how you obtained

your answers.

Answer:

To calculate the composite index,weightage is needed

(W),

CompoComposite Index ,

INGREDIENT WEIGHTAGE (W)

Self-Raising Flour1.80 X 40.9 = 74

Sugar 0.45 X 40.9 = 18

Butter 5 X 40.9 = 205

Eggs (Grade A) 1.55 X 40.9 = 63

= 155.52

( get the answer by using the formula)

• In the year 2009,the butter cake was sold at RM15.00

each.Suggest a suitable selling price for the butter cake in the

year 2010.Give reasons for your answer.

Answer:

On 2009,RM 15.00Cost on 2009 = RM 5.80 ( refer table 2)Let say,

5.8x = 15

x = 15 5.8

x = 2.59Cost on 2010 = RM 8.80 (refer table 2)The price on 2010 = RM 8.80 X 2.59

= RM 22.80

(c)(i) Find out from reliable source how to determine suitable

Capacity of air conditioner to be installed based on the

volume/size of a room.

Answer:

For common usage, air conditioner is rated according to horse

power (1HP), which is approximately 700W to 1000W of

electrical power. It is suitable for a room size 1000ft³ which is

around 27m³ of volume.

(ii) Work in group 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:

By using a measuring tape,the dimension

for the library is:

Height = 3.6mWidth = 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 = 664.20 m³

= 24.6 (round off)

That means our school library needs 25 unit of air conditioner(iii) If your class intends to sponsor one air conditioner for the School library, how many butter cakes must you sell in order to buy the air conditioner

Answer:

1 unit of 1HP air conditioner =RM700Cost for a cake = RM 8.80

Selling price = RM 22.80Profit = RM 22.80 – RM 8.80

= RM 14.00

Number of cakes = RM 700 RM 22.80

to buy 1 unit of = 31 cakes need to sold air conditioner

PART 3

As a committee member for the carnival, you are required to prepare an estimated budget to organize this year’s carnival. The committee has to take into the consideration the increase in expenditure from the previous year due to inflation. The price of food, transportation and tents has increased by 15%. The cost of games, prizes and decorations remains the same, whereas the cost of miscellaneous items has increase by 30%.

QUESTION

• Complete Table 3 based on the information given above

Answer:

EXPENDITURE AMOUNT IN 2009 (RM)

AMOUNT IN 2010 (RM)

FOOD 1200.00 1380.00GAMES 500.00 500.00TRANSPORTATION 300.00 345.00DECORATIONS 200.00 200.00PRIZES 600.00 600.00TENTS 800.00 920.00MISCELLANEOUS 400.00 520.00

Table 3

• 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:

EXPENDITURE AMOUN

T IN

2009

(RM)

AMOUN

T IN

2010

(RM)

PRICE

INDEX

, I

I = X

100%

WEIGHTAGE

, W

FOOD 1200.00 1380.00 115 12

GAMES 500.00 500.00 100 5

TRANSPORTATIO

N

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 400.00 520.00 130 4

Composite Index

I =

= 111.63

112

The total price for the year 2010 increase by 11.625%.This is

because some price in the year 2009 increased in the year 2010.

• The change in the composite index for the estimate 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:

I =

FURTHER EXPLORATION

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 number of your choice. Elaborate the use and the importance of these index numbers in daily life.

AIR POLLUTION INDEX

Air pollution is the introduction of chemicals, particulate matter,

or biological materials that cause harm or discomfort to humans or

other living organisms, or damages the natural environment into

the atmosphere.

The atmosphere is a complex dynamic natural gaseous system that is

essential to support life on planet Earth. Stratospheric ozone

depletion due to air pollution has long been recognized as a threat to

human health as well as to the Earth's ecosystems.

The Air Quality Index (AQI) (also known as the Air Pollution

Index (API) or Pollutant Standard Index (PSI) is a number used by

government agencies to characterize the quality of the air at a given location.

As the AQI increases, an increasingly large percentage of

the population is likely to experience increasingly severe adverse

health effects. To compute the AQI requires an air pollutant

concentration from a monitor or model. The function used to convert

from air pollutant concentration to AQI varies by pollutant, and is

different in different countries. Air quality index values are divided

into ranges, and each range is assigned a descriptor and a color code.

Standardized public health advisories are associated with each AQI

range. An agency might also encourage members of the public to take public

transportation or work from home when AQI levels are high.

Limitations of the AQI

Most air contaminants do not have an associated AQI. Many countries

monitor ground-level ozone, particulates, sulphur dioxide, carbon

monoxide and nitrogen dioxide and calculate air quality indices for

these pollutants.

Causes of Poor Air Quality

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

by fresh air. Stagnant air, often caused by

an anticyclone or temperature inversion, or other lack of winds lets air

pollution remain in a local area.

Indices by location South Korea

The Ministry of Environment of South Korea uses the Comprehensice

Air-quality Index (CAI) to describe the ambient air quality based on

health risk of air pollution. The index aims to help the public easily

understand air quality level and protect the health of people from air

pollution. - The CAI has values of 0 through 500, which are divided into six

categories. The higher the CAI value, the greater the level of

air pollution. - Of values of the five air pollutants, the highest is the CAI value.

Malaysia

The air quality in Malaysia is reported as the API or Air Pollution

Index. Four of the index's pollutant components (i.e., carbon

monoxide, ozone, nitrogen dioxide and sulfur dioxide) are reported

in PM10 particulate matter is reported in g/m³.

Unlike the American AQI, the index number can exceed 500. Above

500, a state of emergency is declared in the reporting area. Usually,

this means that non-essential government services are suspended, and

all ports in the affected area closed. There may also be a prohibition

on private sector commercial and industrial activities in the reporting

area excluding the food sector.

STOCK MARKET INDEX

A comparison of tree major U.S. stock indices: the NASDAQ Composite, Dow Jones Industrial Average, andS&P 500. All three have the same height at March 2007. Notice the large dot com spike on the NASDAQ, a result of the large number of tech. companies on that index.

A stock market index is a method of measuring a section of the stock market. Many indices are cited by news or financial services firms and are used as benchmarks, to measure 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 are domiciled or traded. Two examples are MSCI World and S&P Global 100.

A national index represents the performance of the stock market of a given nation²and by proxy, reflects investor sentiment on the state of its economy. The most regularly quoted 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 Japanese Nikkei 225, and the British FTSE 100.

The concept may be extended well beyond an exchange. The Dow Jones Total Stock Market Index, as its name implies, 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 not ADRs) and most traded on the NASDAQ and American Stock Exchange. Russell Investment Group added to the family of indices by launching the Russell Global Index.

More specialised indices exist tracking the performance of specific sectors of

the market. The Morgan Stanley Biotech Index, for example, consists of 36

American firms in the biotechnology industry. Other indices may track

companies of a certain size, a certain type of management, or even more

specialized criteria one index published by Linux Weekly News tracks stocks

of companies that sell products and services based on the Linux operating

environment.

Index versions

Some indices, such as the S&P 500, have multiple versions.[1] These versions

can differ based on how the index components are weighted and on how

dividends are accounted for. For example, there are three versions of the S&P

500 index: price return, which only considers the price of the components,

total return, which accounts for dividend reinvestment, and net total return,

which accounts for dividend reinvestment after the deduction of a

withholding tax. As another example, the Wilshire 4500 and Wilshire 5000

indices have five versions each: full capitalization total return, full

capitalization price, float-adjusted total return, float-adjusted price, and equal

weight. The difference between the full capitalization, float-adjusted, and

equal weight versions is in how index components are weighted.

USES AND IMPORTANCE OF AIR POLLUTION INDEX AND STOCK MARKET INDEX

As everyone can see,the air pollution index is use by the government to measure the quality of air index and to detect any pollutants in our country’s air.This is to ensure the air is clean and safe for us ti inhale.Besides that,an early warning can be given to us if the air pollution is too high for us to get out of our homes.This warning is given based upon readings and unterpretations of the air index.

As for the stock market index, it is mainly for the business entrepreneurs. This type of index is used to determine the outcome of a stock market and also the conclusion of a stock market. The stock market index is important because a country’s economical state sometimes depend on it.

CONCLUSIONAfter doing research,answering questions,drawing graphs and some problem solving, I saw that the usage of statistics 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 nessecities.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.

REFLECTIONxAdter spending countless hours,days and night to finish this project and also sacrificing my time video games and mangas in this mid year holiday,there are several things that I can say...

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...

REFERENCES• hhtp://www.pelajaranperak.gov.my • hhtp://pelaaranperak.gov.my/v2/modules/news/article.php?

storyid=117• Jabatan Negeri Perak, Kerja Projek Matematik Tambahan 2010