project work for additional

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PROJECT WORK FOR ADDITIONALMATHEMATHICS 2010

CURRICULUM DEVELOPMENT DIVISIONMINISTRY OF EDUCATION MALAYSIA

PROJECT WORK 4STATISTICS

SEKOLAH MENENGAH

KEBANGSAAN KOTA MASAI

NAME : AUFA FAQIHA BINTI AHMADCLASS : 5 CEKALIC NUMBER : 930920-01-7050SUBJECT TEACHER : PN. MAIZAN BINTI ABDULWAHAB


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INTRODUCTIONINTRODUCTIONWe 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

by groups. 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.


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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

Realize 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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CONTENTCONTENT APPRECIATION

OBJECTIVE

HISTORY

. PART1.

PART2.

PART3.

FUTHEREXPLORATIONS..

CONCLUSION


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REFLECTIONS....


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APPRECIATIONAPPRECIATION

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 Kebangsaan Kota Masai, Tuan Haji Nasuha

bin Paiman for giving me the permission to do my this Additional

Mathematics Project Work.

I also like to thank my Additional Mathematics teacher, Puan Maizan

bin Abdul Wahab for the guide and giving useful and important information

for me to complete this project work.

Not forgotten to my parents for providing everything, such as money,

to buy anything that are related to this project work, their advise, which is

the most needed for this project and facilities such as internet, books,

computers and all that. They also supported me and encouraged me tocomplete this task so that I will not procrastinate in doing it.

Besides that, my friends who always supporting me. Even this project

is individually but we are cooperated doing this project especially in

disscussion and sharing ideas to ensure our task will finish completely.

Last but not least, any party which involved either directly or indirect incompleting this project work. Thank you everyone.


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OBJECTIVEOBJECTIVEThe aims of carrying out this project work are:i. To apply and adapt a variety of problem-solving strategies tosolve problems.

ii. To improve thinking skills.

iii. To promote effective mathematical communication.

iv. To develop mathematical knowledge through problem solving ina way that increases students interest and confidence.

v. To use the language of mathematics to express mathematical

ideas precisely.

vi. To provide learning environment that stimulates and enhanceseffective learning.

vii. To develop positive attitude towards mathematics.


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A BRIEF HISTORY OFA BRIEF HISTORY OFSTATISTICSSTATISTICS

By the 18th century, the term "statistics" designed 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 18thcenturies, 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.


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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.


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STATISTICSSTATISTICS

TODAYTODAYDuring 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 butrather 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.


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PART 1PART 1The prices of goods sold in shops vary from one shop to another.Shoppers tend to buy goods which are not only reasonably pricedbut also give value for their money.You are required to carry out a survey on four different items basedon the following categories i.e. food, detergent and stationery.Thesurvey should be done in three different shops.

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

Answer:

Foods :

Detergent :


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Stationary :


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

Since items maybe differently packed, be sure to use consistent


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0

1

2

3

4

5

6

7

JUSCO

SELF-RAISING FLOUR(1000 g)

SUGAR (1000g)

BUTTER (250g)

EGGS (GRADE A) 1DOZEN


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0

1

2

3

4

5

6

KIPMART

SELF-RAISING FLOUR(1000 g)

SUGAR (1000g)

BUTTER (250g)


0

1

2

3

4

5

6

TESCO

SELF-RAISING FLOUR

(1000 g)SUGAR (1000g)

BUTTER (250g)



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2)Detergents :


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3)STATIONERY


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(d) Based on the graphical representation that you have constructed in Part1(c), interpret, discuss and draw conclusions. Comments on your findings.

Answer:

Based on the graphical representation that I have constructed in Part 1(c), itis 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 doesnt have any obvious price difference. The graph

also show that most of the items that are high priced comes from the JUSCO,

while the lowest price items come from the TESCO .

The graph 1(d) will shows the conclusion of the difference among the shopsbased upon the shops grand total.


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(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:

Clothes detergent

Mean :

=

=

Standard Deviation

=

=

=

Item that has a large price difference among the shops is clothes

detergent maybe because of the standard of the shop. A high standardshop 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.


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

QUESTION

(a ) Suggest a shop from Part 1 which you would go to purchase theingredients for the butter cakes. State and discuss your reasons for

purchasing from the shop you suggested.

Answer:The TESCO supermarket. This is because the total price of the ingredientsfrom this shop is the lowest from the three shops.

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

Answer:

INGREDIENT QUANTITY PERCAKE

PRICE IN THEYEAR 2009(RM)

PRICE IN THEYEAR 2010(RM)

Self-Raising Flour 250g 0.90 0.90

Sugar 200g 0.35 0.36

Butter 250g 3.30 4.30

Eggs (Grade A) 5 eggs (300g) 1.25 2.10

Table 2

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


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INGREDIENT QUANTITYPER CAKE

PRICE IN THEYEAR2009(RM)

PRICE IN THEYEAR2010(RM)

PRICE INDEXFOR THEYEAR2010BASED ONTHE YEAR

2009(I)

Self-RaisingFlour

250g 0.90 0.90 100

Sugar 200g 0.35 0.36 102.86

Butter 250g 3.30 4.30 130.30

Eggs(Grade A)

5 eggs(300g)

1.25 2.10 168

1.Self-Raising Flour

2.Sugar

3.Butter

4.Eggs (Grade A)

(ii) 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.


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INGREDIENT WEIGHTAGE (W)

Self-Raising Flour 250 / 1000 = 1 / 4

Sugar 200 / 1000 = 1 / 5

Butter 250 / 1000 = 1 / 4

Eggs (Grade A) 330 / 1000 = 3 / 10

Composite Index

=

=

(iii) In the year 2009, the butter cake was sold at RM15.00 each. Suggest asuitable selling price for the butter cake in the year 2010.Give reasons foryour answer.

Answer:

On 2009, RM 15.00


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On 2010, price =

Thus, the suitable price for the butter cake for the year 2010 is

RM19.30.The increase in price is also suitable because of the rise in

the price of the ingredients.

(c) (i) Find out from reliable source how to determine suitable Capacity of airconditioner 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 aroom size 1000ft which is around 27m of volume. If we buy an air

conditioner with 3HP, it is suitable for a room around 81m.


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(ii) Work in group to estimate the volume of your school Library. Explain howyou arrive at your answer. Hence, determine the number of air conditionerswith the appropriate capacity required for your library.

Answer:

By using a measuring tape, the dimension for the library is:

Height = 3.6m

Width = 9.17m

Length = 20.12m

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

1 unit of air conditioner with 3HP is for 81mFor 664.20m

=

=

That means our school library needs 8 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 3HP air conditioner = RM2100

Cost for a cake = 0.9 + 0.36 + 4.3 + 2.1= RM 7.66

Selling price = RM19.30


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Profit = 19.30 7.66

= RM 11.64

Number of cakes = 2100to buy 1 unit of 11.64air conditioner

= 180.41

= 180 cakes

PART 3PART 3As a committee member for the carnival, you are required toprepare an estimated budget to organize this years carnival. Thecommittee has to take into the consideration the increase inexpenditure from the previous year due to inflation. The price offood, transportation and tents has increased by 15%. The cost ofgames, prizes and decorations remains the same, whereas the costof miscellaneous items has increase by 30%.

QUESTION:

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

Answer:

EXPENDITURE AMOUNT IN 2009(RM)

AMOUNT IN 2010(RM)

FOOD 1200.00 1380.00


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GAMES 500.00 500.00 TRANSPORTATION 300.00 345.0DECORATIONS 200.00 200.00PRIZES 600.00 600.00 TENTS 800.00

MISCELLANEOUS 400.00 520.00

Table 3

(b) Calculate the composite index for the estimated budget of thecarnival in the year 2010 based on the year 2009. Comment onyour answer

.Answer:

EXPENDITURE AMOUNT IN2009 (RM)

AMOUNT IN2010 (RM)

PRICEINDEX, I

WEIGHTAGE , W

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

Composite Index


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=

=

=

The total price for the year 2010 increase by 11.625%. This is becausesome price in the year 2009 increased in the year 2010.

(c) The change in the composite index for the estimate budget for thecarnival from the year 2009 to the year 2010 is the same as the change fromthe year 2010 to the year 2011. Determine the composite index of thebudget for the year 2011 based on the year 2009.

Answer:

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

Composite index for the year 2010 to the year 2011

= 111.625


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FURTHERFURTHEREXPLORATIONEXPLORATION

Index numbers are being used in many different daily situations, for exampleair pollution index, stock market index, gold index and property index.

Obtain information from the internet or other reliable sources on theimportance of two different types of index number of your choice. Elaboratethe use and the importance of these index numbers in daily life.


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AIR POLLUTION INDEXAIR POLLUTION INDEXAir pollution is the introduction of chemicals, particulate matter,or biological materials that cause harm or discomfort to humans orother living organisms, or damages the natural environment 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 as a threat tohuman health as well as to the Earth's ecosystems.

The Air Quality Index (AQI) (also known as the Air PollutionIndex (API) or Pollutant Standard Index (PSI) is a number used bygovernment agencies to characterize the quality of the air at a givenlocation. As the AQI increases, an increasingly large percentage of thepopulation is likely to experience increasingly severe adverse health effects.To compute the AQI requires an air pollutant concentration from a monitor ormodel. The function used to convert from air pollutant concentration to AQIvaries by pollutant, and is different in different countries. Air quality indexvalues are divided into ranges, and each range is assigned a descriptor and acolor code.Standardized public health advisories are associated with each AQIrange. An agency might also encourage members of the public to take publictransportation or work from home when AQI levels are high.

Limitations of the AQIMost air contaminants do not have an associated AQI. Many countriesmonitor ground-level ozone, particulates, sulphur dioxide, carbon monoxideand nitrogen dioxide and calculate air quality indices for these pollutants.

Causes of Poor Air QualityThe AQI can worsen (go up) due to lack of dilution of air emissions by freshair. Stagnant air, often caused by an anticyclone or temperature inversion, orother lack of winds lets air pollution remain in a local area.


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Indices by locationSouth KoreaThe Ministry of Environment of South Korea uses the ComprehensiceAir-quality Index (CAI) to describe the ambient air quality based onhealth risk of air pollution. The index aims to help the public easily

understand air quality level and protect the health of people from airpollution. - The CAI has values of 0 through 500, which are divided into sixcategories. The higher the CAI value, the greater the level ofair pollution. - Of values of the five air pollutants, the highest is the CAIvalue.

MalaysiaThe air quality in Malaysia is reported as the API or Air PollutionIndex. Four of the index's pollutant components (i.e., carbonmonoxide, ozone, nitrogen dioxide and sulfur dioxide) are reportedin PM10 particulate matter is reported in g/m.

Unlike the American AQI, the index number can exceed 500. Above500, a state of emergency is declared in the reporting area. Usually,this means that non-essential government services are suspended, andall ports in the affected area closed. There may also be a prohibitionon private sector commercial and industrial activities in the reportingarea excluding the food sector.

STOCK MARKET INDEXSTOCK MARKET INDEX


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

A stock market index is a method of measuring a section of the stockmarket. Many indices are cited by news or financial services firms and areused as benchmarks, to measure the performance of portfolios such asmutual 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 forwhere they are domiciled or traded. Two examples are MSCI World and S&PGlobal 100.

A national index represents the performance of the stock market of a givennationand by proxy, reflects investor sentiment on the state of its economy.The most regularly quoted market indices are national indices composed ofthe 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 FTSE100.

The concept may be extended well beyond an exchange. The Dow Jones

Total Stock Market Index, as its name implies, represents the stocks ofnearly every publicly traded company in the United States, including all U.S.stocks traded on the New York Stock Exchange (but not ADRs) and mosttraded on the NASDAQ and American Stock Exchange. Russell InvestmentGroup added to the family of indices by launching the Russell Global Index.


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More specialised indices exist tracking the performance of specific sectors ofthe market. The Morgan Stanley Biotech Index, for example, consists of 36American firms in the biotechnology industry. Other indices may trackcompanies of a certain size, a certain type of management, or even morespecialized criteria one index published by Linux Weekly News tracks stocks

of companies that sell products and services based on the Linux operatingenvironment.

Index versions

Some indices, such as the S&P 500, have multiple versions.[1] Theseversions can differ based on how the index components are weighted and onhow dividends are accounted for. For example, there are three versions ofthe S&P 500 index: price return, which only considers the price of thecomponents, total return, which accounts for dividend reinvestment, and nettotal return, which accounts for dividend reinvestment after the deduction of

a withholding tax. As another example, the Wilshire 4500 and Wilshire 5000indices have five versions each: full capitalization total return, fullcapitalization price, float-adjusted total return, float-adjusted price, andequal weight. The difference between the full capitalization, float-adjusted,and equal weight versions is in how index components are weighted.


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USES AND IMPORTANCE OFUSES AND IMPORTANCE OFAIR POLLUTION INDEX ANDAIR POLLUTION INDEX AND

STOCK MARKET INDEXSTOCK 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

countrys air. This is to ensure the air is clean and safe for us to 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 countrys economical state sometimes depend

on it.


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CONCLUSIONCONCLUSION

After 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 necessities. Without it,

surveys cant be conducted, the stock market cant be interpret and many

more. So, we should be thankful of the people who contribute in the idea of

statistics.

REFLECTIONREFLECTION


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After spending countless hours, days and night to finish this project and alsosacrifice my bedtime to finish this project, what I learn that most preciousthan my dreams is,..

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