Project Work for Additional

Mathematics 2012

Name : Hanna Nawwarah bt Ismailjee

Class : 5 Edison

Teacher : En Mohd Azrin bin Rahim

Content

No Contents Page

1 Objectives2 Foreward3 Introduction4 Part 15 Part 26 Further Exploration7 Conclusion

8 Reflection

ObjectivesWe students taking 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 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.

We are expected to submit the project work within three weeks from the first day the task is being administered to us. Failure to submit the written report will result in us not receiving certificate.

Foreward

Feeling blessed by Allah s.w.t because give me the willingness to perform this project completely. Secondly, I

want to thank my principle Ayahanda Karim bin Bayok because give me permission to complete this project during school holidays. Then, I want to thank my Additional Mathematics teacher, En. Mohd Azrin bin Rahim because give me the best guidance and support to do this Additional Mathematics Project. By the way, I want to thank my lovely parent En. Ismailjee Mohamed Kassim and Pn. Mimi Farina Ya’acob because give me support and encouragement to complete this Additional Mathematics project. Last but not least, thanks to all my friend and everybody that helped me in order to complete this Additional Mathematics Project because without all of you I cannot done this work individually successly.

Introduction 

History of   Statistic

By 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 the 17th and18th 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.

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 different categories. The survey should be done in three different shops.

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

Food

Detergent

Stationery

Electronics

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

Category Item Price (RM)Econsave Giant Jusco

Food

1. Self-Raising Flour (1000g)

4.00 3.70 3.60

2. Sugar (1000g)2.05 1.75 1.75

3. Butter (250g) 3.95 3.99 4.50

4. Eggs (Grade A)30 eggs

10.00 9.99 9.50

Total Price 20.00 18.00 25.00

1. Kiwi Cleen 6.90 5.49 5.50

2. Softlan Softener 6.29 9.99 6.99

Detergent

(3 litre)3. Daia (1kg) 4.69 5.49 5.50

4. Breeze Liquid Colour (1.8kg)

10.30 10.99 10.70

Total Price 28.18 31.96 28.69

Stationery

1. Highlighter Faber Castell

3.50 3.49 3.70

2. Staedler Water Colour

13.50 10.00 13.50

Stabilo Liquid Paper 3.50 3.90 3.90

Faber Castell Pencil Tri Grip Pencil

7.20 8.00 7.50

Total Price 27.70 25.39 28.60

Electronics

1. Sony Walkman MP3 Player

149.00 139.00 149.00

2. Toshiba DVD Player

129.00 128.99 125.99

3. Samsung LCD 275.00 280.00 295.00

4. Monster Beats Headphones

193.00 180.00 215.00

Total Price 746.00 727.99 784.99

(c) Create a suitable graphical represantations to compare and contrast the price of the items chosen.

Food Detergent Stationery Electronics0

100

200

300

400

500

600

700

800

EconsaveGiantJusco

(d) Based on the graphical in (c), interpret and discuss your findings.

Based on the graph we could see the small and large diferrence among the items. We could see from food price the lowest price is sugar because sugar is now known as controlled goods so there are no such difference among them and the highest price is eggs grade A. All of us know the difference among eggs and another item is because the controlled standard to this eggs which caused the price so high than another food items. More over, when we look to detergent the lower price is Daia that have quantity about 1 kg and the higher price is Breeze Liquid Colour. This is because the difference detergent bring the difference price. On the other hand, the lowest price among stationery items is highlighter Faber Castell and the highest price among them is Staedler Water Colour. I think it is because the standard and quality that given by Staedler to users. All of this can be concluded with the grand total.

(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.

Softlan Softener (3 litre)

Mean = (6.29+9.99+6.99)/3

= 7.756

Standard deviation = √(∑х²)/N – ( х N)²

= √6.29²+9.99²+6.99²3 - (7.756)²

= 1.965536

 The large difference among the price is because the standard of the shop. So, the more standard of the supermarket, the higher the price given to the users. The higher the price the higher quality you can get from that product.

Every year SMK Tun Abdul Razak organizes a carnival to raise funds for the school. Last year, during the carnival, your class made and sold cakes. Because of the popularity of the cakes, your class has decided to carry out the same project for this year’s carnival.

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

I choose Giant Supermarket because it offers me the lowest price among the food items. So my class will be able to sell the cakes at the lowest price and get some profits from the sale. Furthermore, Giant Supermarket is located not far from my school. So it is easier for my friends and I to go there.

(b) Construct a Table which four main ingredients that you use with the quantity, price in year before and price this year.

Ingredient Quantity per cake

Price in the year

2011 (RM)

Price in the year

2012 (RM)

Price index for the year

2012 based on the year 2011 (I)

Self-raising flour

250g 0.90 0.90 100

Sugar 200g 0.35 0.35 100Butter 250g 3.30 4.50 136.33Eggs (Grade A)

5 eggs (300g)

1.25 1.58 126.4

(c) Calculate the price index for each of the ingredients in Table in (b) for the year 2012 based on the year 2011.

Price Index Self-raising flour

I = 0.900.90

×100

= 100

Price Index Sugar

I = 0.350.35

×100

= 100

Price Index Butter

I = 4.503.30

×100

= 136.33

Price Index Eggs (Grade A)

I = 1.581.25

×100

= 126.4

(d) Calculate the composite index for making a cake in the year 2012 based on the year 2011. Discuss your findings.

Composite index

= ∑WI

∑W

= (14×100 )+(15×100 )+(14×136.33 )+(310×126.4)

14+14+14+310

=117.5745

(e) In the year 2011, the cakes was sold at

RM 12.00 each. Suggest a suitable selling for the cakes in the year 2012. Give reasons for your answer.

On 2011, RM 12.00

On 2012, price

12×× 100 = 117.5745 %

×× 100 = 117.5745 ×12

× = 14.10

Thus, the suitable price for the cake for the year 2012 is RM 14.10. The increase in price is also suitable because of the rise in the priceof the ingredients.

Further Exploration

Index number 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 important 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.

CAI Description Health Implications

0 - 50Good

A level that will not impact patients suffering from diseases related to air pollution.

51 - 100 Moderate

A level which may have a meager impact on patients in case of chronic exposure.

101 - 150

Unhealthy for sensitive groups

A level that may have harmful impacts on patients and members of sensitive groups.

151 - 250

Unhealthy

A level that may have harmful impacts on patients and members of sensitive groups (children, aged or weak people), and also cause the general public unpleasant feelings.

251 - 350 Very

unhealthy

A level which may have a serious impact on patients and members of sensitive group in case of acute exposure.

351 - 500 Hazardous

A level which may need to take emergency measures for patients and members of sensitive groups and have harmful impacts on the general public.

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 PM 10

¿¿ particulate

matter is reported in μg/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.

Index Values*

Levels of Health

Concern

Cautionary Statements

0 - 50 Good None51 - 100 Moderate None

101 - 150 Unhealthy for sensitive groups

People with respiratory diseases such as asthma, should limit outdoor exertion.

151 - 200 Unhealthy People with respiratory diseases such as asthma, should avoid outdoor exertion; everyone else. Especially the elderly and children, should limit prolonged outdoor exertion.

201 - 300 Very unhealthy People with respiratory diseases such as asthma, should avoid outdoor exertion; everyone else. Especially the elderly and children, should limit outdoor exertion.

301 - 500 Hazardous Everyone should avoid any outdoor exertion; people with respiratory disease such as asthma, should remain indoors.

*An AQI of 100 for PM 10¿

¿ correspondsto a PM 10¿

¿level of 150 micrograms per cubic meter (averaged over 24 hours).

Stock Market Index

A comparison of three major U.S. stock indices: the NASDAQ Composite ,Dow Jones Industrial Average, and S&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 technology 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 nation—and 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.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 air quality index and to detect any pollutants in our country’s 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 interpretations of the air pollution 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.

Conclusion

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 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.

Reflection

After spending countless hours, day and night to finish this Additional Mathematics Project, here is what I got to say:

Doing this project makes me realize how important Additional Mathematics is. Also, completing this project makes me realize how fun it is and likable is Additional Mathematics.