Additional Mathematics Project 4

8/9/2019 Additional Mathematics Project 4

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SMK TAMAN PELANGIPROJECT WORK FORADDITIONAL MATHEMATICS 2010Index in our daily life

NAME : CHITRAN A/L TAMIL CHELVANI/C : 930629-08-5381

CLASS : 5 BESTARITEACHERS NAME : PN. HANIZAH MAFOZ


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CONTENTIntroduction.......................................................1-3Part 1............................................................4-8Part 2............................................................9-10

Part 3...........................................................11Further Explorations..............................................12-16

Conclusion........................................................17Reflections........................................................18

Questions.........................................................19-23Rubric...........................................................24End.............................................................25


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IntroductionWe 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 hasprepared 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 is expected to submit an individually

written report. Upon completion of the Additional Mathematics

Project Work, we are to gain valuable experiences and able to:

Apply and adapt a variety of problem solving strategies to solveroutine and non-routine problems;

Experience classroom environments which are challenging,interesting and meaningful and hence improve their thinking

skills.

Experience classroom environments where knowledge and skillsare applied in meaningful ways in solving real-life problems

Experience classroom environments where expressing onesmathematical thinking, reasoning and communication are highly

encouraged and expected Experience classroom environments that stimulate and enhance

effective learning.

Acquire effective mathematical communication through oral andwriting, and to use the language of mathematics to express

mathematical ideas correctly and precisely

Enhance acquisition of mathematical knowledge and skillsthrough 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 insolving real-life problems and hence develop positive attitude

towards mathematics.

Train ourselves not only to be independent learners but also tocollaborate, to cooperate, and to share knowledge in an engaging

and healthy environment Use technology especially the ICT appropriately and effectively


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Train ourselves to appreciate the intrinsic values of mathematicsand to become more creative and innovative

Realize the importance and the beauty of mathematicsWe 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.

AppreciationThank you to God for giving the will to do my additional

mathematics project. Secondly, I would like to thank the principle of

Sekolah Menengah Kebangsaan Taman Pelangi, Pn Hajah Maznah btOthman for giving the permission to do my Additional Mathematics

Project Work. I also like to thank my Additional Mathematics teacher,

Pn. Hanizah Mafoz 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.

History of indicesNo clear consensus has emerged on who created the first price

index. The earliest reported research in this area came from

Welshman Rice Vaughan who examined price level change in his

1675 book A Discourse of Coin and Coinage. Vaughan wanted to

separate the inflationary impact of the influx of precious metalsbrought bySpainfrom theNew Worldfrom the effect due tocurrency

debasement. Vaughan compared labor statutes from his own time to

similar statutesdating back toEdward III. These statutes set wages for

certain tasks and provided a good record of the change in wage levels.

Vaughan reasoned that the market for basic labor did not fluctuate

much with time and that a basic laborers salary would probably buy

the same amount of goods in different time periods, so that a laborer's

salary acted as a basket of goods. Vaughan's analysis indicated that
http://en.wikipedia.org/wiki/Waleshttp://en.wikipedia.org/wiki/Waleshttp://socserv2.socsci.mcmaster.ca/~econ/ugcm/3ll3/vaughan/coinhttp://socserv2.socsci.mcmaster.ca/~econ/ugcm/3ll3/vaughan/coinhttp://socserv2.socsci.mcmaster.ca/~econ/ugcm/3ll3/vaughan/coinhttp://en.wikipedia.org/wiki/Spainhttp://en.wikipedia.org/wiki/Spainhttp://en.wikipedia.org/wiki/Spainhttp://en.wikipedia.org/wiki/New_Worldhttp://en.wikipedia.org/wiki/New_Worldhttp://en.wikipedia.org/wiki/New_Worldhttp://en.wikipedia.org/wiki/Debasementhttp://en.wikipedia.org/wiki/Debasementhttp://en.wikipedia.org/wiki/Debasementhttp://en.wikipedia.org/wiki/Debasementhttp://en.wikipedia.org/wiki/Statute_of_Labourers_of_1351http://en.wikipedia.org/wiki/Statute_of_Labourers_of_1351http://en.wikipedia.org/wiki/Edward_IIIhttp://en.wikipedia.org/wiki/Edward_IIIhttp://en.wikipedia.org/wiki/Edward_IIIhttp://en.wikipedia.org/wiki/Edward_IIIhttp://en.wikipedia.org/wiki/Statute_of_Labourers_of_1351http://en.wikipedia.org/wiki/Debasementhttp://en.wikipedia.org/wiki/Debasementhttp://en.wikipedia.org/wiki/New_Worldhttp://en.wikipedia.org/wiki/Spainhttp://socserv2.socsci.mcmaster.ca/~econ/ugcm/3ll3/vaughan/coinhttp://en.wikipedia.org/wiki/Wales


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price levels in England had risen six to eightfold over the preceding

century.

While Vaughan can be considered a forerunner of price indexresearch, his analysis did not actually involve calculating an index. In

1707 Englishman William Fleetwood created perhaps the first true

price index. An Oxford student asked Fleetwood to help show how

prices had changed. The student stood to lose his fellowship since a

fifteenth century stipulation barred students with annual incomes over

five pounds from receiving a fellowship. Fleetwood, who already had

an interest in price change, had collected a large amount of price data

going back hundreds of years. Fleetwood proposed an indexconsisting of averaged price relatives and used his methods to show

that the value of five pounds had changed greatly over the course of

260 years. He argued on behalf of the Oxford students and published

his findings anonymously in a volume entitled Chronicon Preciosum.

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 universitiesmaintain

separate mathematics and statistics departments. Statistics is also

taught in departments as diverse aspsychology,education, and public

health.
http://en.wikipedia.org/wiki/William_Fleetwoodhttp://en.wikipedia.org/wiki/William_Fleetwoodhttp://en.wikipedia.org/wiki/Agricultural_researchhttp://en.wikipedia.org/wiki/Agricultural_researchhttp://en.wikipedia.org/wiki/Public_healthhttp://en.wikipedia.org/wiki/Public_healthhttp://en.wikipedia.org/wiki/Epidemiologyhttp://en.wikipedia.org/wiki/Epidemiologyhttp://en.wikipedia.org/wiki/Biostatisticshttp://en.wikipedia.org/wiki/Biostatisticshttp://en.wikipedia.org/wiki/Quality_controlhttp://en.wikipedia.org/wiki/Quality_controlhttp://en.wikipedia.org/wiki/Unemploymenthttp://en.wikipedia.org/wiki/Unemploymenthttp://en.wikipedia.org/wiki/Econometryhttp://en.wikipedia.org/wiki/Econometryhttp://en.wikipedia.org/wiki/Universityhttp://en.wikipedia.org/wiki/Universityhttp://en.wikipedia.org/wiki/Academic_departmenthttp://en.wikipedia.org/wiki/Academic_departmenthttp://en.wikipedia.org/wiki/Psychologyhttp://en.wikipedia.org/wiki/Psychologyhttp://en.wikipedia.org/wiki/Psychologyhttp://en.wikipedia.org/wiki/Educationhttp://en.wikipedia.org/wiki/Educationhttp://en.wikipedia.org/wiki/Educationhttp://en.wikipedia.org/wiki/Public_healthhttp://en.wikipedia.org/wiki/Public_healthhttp://en.wikipedia.org/wiki/Public_healthhttp://en.wikipedia.org/wiki/Public_healthhttp://en.wikipedia.org/wiki/Public_healthhttp://en.wikipedia.org/wiki/Educationhttp://en.wikipedia.org/wiki/Psychologyhttp://en.wikipedia.org/wiki/Academic_departmenthttp://en.wikipedia.org/wiki/Universityhttp://en.wikipedia.org/wiki/Econometryhttp://en.wikipedia.org/wiki/Unemploymenthttp://en.wikipedia.org/wiki/Quality_controlhttp://en.wikipedia.org/wiki/Biostatisticshttp://en.wikipedia.org/wiki/Epidemiologyhttp://en.wikipedia.org/wiki/Public_healthhttp://en.wikipedia.org/wiki/Agricultural_researchhttp://en.wikipedia.org/wiki/William_Fleetwood


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PART 1

(a) After surveying on four different items


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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 measurements for each item selected so that

comparison can be done easily and accurately.

Category ItemPrice

Cold Storage Giant Kedai Runcit Sri Murni

Food

1. Self-Raising Flour RM 9.99 RM 9.65 RM 10.30

2. Sugar RM 1.65 RM 1.65 RM 2.40

3. Butter RM 7.49 RM 6.99 RM 7.80

4. Eggs (Grade A) RM 3.99 RM 3.89 RM 3.80

Total Price RM 23.12 RM 22.18 RM 24.30

Detergent

1. Trojan RM 10.49 RM 17.49 RM 11.20

2. Fab RM 22.99 RM 14.49 RM 15.90

3. Breeze RM 16.94 RM 13.99 RM 10.45

4. Bio Zip RM 9.99 RM 9.49 RM 11.20


Stationery

1. Pen RM 3.29 RM 2.99 RM 1.80

2. Correction Pen RM 5.29 RM 7.99 RM 4.80

3. Stapler Clip RM 2.29 RM 1.65 RM 3.20

4. Marker RM 7.29 RM 5.99 RM4.30


Grand Total RM 101.69 RM 96.26 RM 87.15


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(c) Record the items and their prices systematically as in Table1. Since items maybe differently packed, be sure to use

consistent measurements for each item selected so that

comparison can be done easily and accurately.

FOOD

Detergent

RM0.00RM2.00RM4.00RM6.00RM8.00RM10.00

ColdStorage Giant KedaiRuncitSri Murni

Self-Raising FlourSugarButterEggs (Grade A)

RM0.00RM5.00RM10.00RM15.00RM20.00RM25.00

Cold Storage Giant Kedai RuncitSri Murni

TrojanFabBreezeBio Zip


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Stationery

(d) Based on the graphical representations that I have constructedin Part 1(c), it is shown that there are large and small

differences among the prices of items in each category

between the shops. In the food category, the smallest pricedifference is of those of sugar, while the highest is the price

of eggs. Besides food, detergent also shows a large price

difference between its items. Among them is the price of

detergent. On the other hand, stationery items dont have anyobvious price difference. The graph also show that most of

the items that are high priced comes from the Giant, while the

lowest price items come from the Kedai Runcit Sri Murni.

The graph 1(d) will show the conclusion of the difference

among the shops based upon the shops grand total.

RM0.00RM2.00RM4.00RM6.00RM8.00

ColdStorage Giant KedaiRuncit SriMurni

PenCorrection PenStapler ClipMarker


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(e) Detergent (Fab)Mean = 22.99+14.49+15.9

3= 17.79

Standard deviation

= (2 ( )2

=22.992 + 14.492 + 15.92 - (17.79)23

= 3.74

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. A better quality means a

higher price.

0102030405060708090100

110

Cold Storage Giant Kedai Runcit Sri Murni


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PART 2

(a) I will choose the Giant. This is because the total price of theingredients from this shop is the lowest from the three shops.

(b)Ingredient

Quantity per

cake

Price in the

year 2009

(RM)

Price in the

year 2010

(RM)

Self-raising flour 250 g 0.9 1.1

Sugar 200 g 0.35 0.55Butter 250 g 3.3 3.5

Eggs (Grade A) 5 eggs (300 g) 1.25 1.4

i.

Ingredient Quantity per cakePrice in the year

2009 (RM)

Price in the year

2010 (RM)

Price index for the year 2010

based on the year 2009 (

Self-raising flour 250 g 0.9 1.1 122.22Sugar 200 g 0.35 0.55 157.14

Butter 250 g 3.3 3.5 106.1

Eggs (Grade A) 5 eggs (300 g) 1.25 1.4 112

1.Selfraising flour >I = 1.1/0.9 100=111.222.Sugar >I = 0.55/0.35 100=157.143.Butter >I = 3.5/3.3 100=106.104.Eggs >I = 1.4/1.25 100=112

ii.

=1/4(122.22) + 1/5(157.14) + 1/4(106.10) + 3/10(112)1

Ingredient Weighatge (w)

Self-raising flour 250 / 1000 = 1/4

Sugar 200 / 1000 = 1/5

Butter 250 / 1000 = 1/4

Eggs (Grade A) 300 / 1000 = 3/10


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= 122.108

iii. On 2009, RM 15

On 2010, Price =

100 =122.108

15

100 = 122.108 15

= 1831.62

100

= 18.32

Composite index = 122.108, this means the food items increased byabout increased compared to the year 2009. This means the selling

price of the cake must also increased by the same margin to maintain

competitive pricing.

(c)i. For common usage, air conditioner is rated according to horse

power (1 HP), which is approximately 850W to 1100W of

electrical power. It is suitable for a room size 1500ft3 which isaround 30m3 of volume.

ii. 7 bays

iii. 1 unit of 1HP air conditioner = RM 950

Cost for a cake = 1.1+0.55+3.5+1.4

=6.55

Selling Price = RM 23

Profit = 23-6.55=16.45

Number of cakes to buy 1 unit of air conditioner

950 = 57.75 > 58 cakes

16.45


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PART 3(a)

Expenditure Amount in 2009 Amount in 2010 Index Weightage

(RM) (RM)

Food 1200 1.15 x 1200 =1380 115 1380/115 = 12

Games 500 1 x 500 =500 100 500/100 = 5

Transportation 1300 1.15 x 1300 =345 115 345/115 = 3

Decorations 200 1 x 200 =200 100 200/100 = 2

Prizes 600 1 x 600 =600 100 600/100 = 6

Tents 800 1.15 x800 =920 115 920/115 = 8

Miscellaneous 400 1.3 x400 =520 130 520/130 = 4

(b) =

= 115(12) + 100(5) + 115(3) + 100(2) + 100(6) + 115(8) + 130(4)

12+5+3+2+6+8+4

= 4465 = 111.625

40The total price for the year 2010 increase by 11.625%.This is because

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

(c)Composite index for the year 2009 to the year 2010

=111.625

Composite index for the year 2010 to the year 2011

=111.625

2011 100 = 2010 20112009 2009 2010

2011 = 111.625 111.625

2009

2011 = 124.62009


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Fu rther Ex plorationAir Pollution Index

Air pollution is the introduction of chemicals, particulate matter, orbiological 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 ozonedepletion due to airpollution 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 PollutionIndex

(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 AQIincreases, an increasingly large percentage of the population is likely toexperience 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. 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 countriesmonitor ground-level ozone, particulates, sulphurdioxide, 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 ofwinds lets air pollution remain in a local area.


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Indices by location

South KoreaThe Ministry of Environment of South Korea uses the Comprehensice

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

0-50 Good

A level that will not impact patients suffering from

diseases related to air pollution.51-

100 Moderate

A level which may have a meagre 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 patientsand members of sensitive groups 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.

MalaysiaThe 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 sulphur dioxide) are reported in PM10 particulate matter isreported in gm3.

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.


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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 dotcom 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 financialservices firms and are used

as benchmarks, to measure theperformance ofportfolios such as mutual funds.


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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&P

Global 100.

A national index represents the performance of the stock market of a

given nationand by proxy, reflects investor sentiment on the state of itseconomy. 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&P500, 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 UnitedStates, including all U.S. stocks

traded on the New York StockExchange (but not ADRs) and most traded on the

NASDAQ and American Stock Exchange. Russell InvestmentGroup added tothe family of indices by launching the RussellGlobal 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 tracksstocks of companies that sell products and services based on the Linux

operating environment.

Index versionsSome 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 Wilshire4500 and Wilshire 5000 indices have fiveversions 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.


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Uses and importance of air pollution index and stock market index

As everyone can see, the air pollution index is use by the government tomeasure the air quality 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 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

countrys economical state sometimes depend on it.


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Conclusion

After doing research, answering questions, drawing graphs and someproblem solving, I saw that the usage of statistics and index is important in

daily life. It is not just widely used in markets but also in interpreting thecondition of the surrounding likeair. Especially in conducting an air-pollution

survey. Inconclusion, statistics and index is a daily life nessecities.Without it,

surveys cant be conducted, the stock market cant be interpretand many more.So, we should be thankful of the people who contribute in the idea of making

statistics and index.


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ReflectionAfter spending countless hours, days and night to finish this

project and also sacrificing my time on playing video games andreading mangas in this mid year holiday, there are several things that I

can say...

Doing this project makes me realize how important Additional

Mathematics is in our daily life and completing this project makes me

realize how fun it is and likable is Additional Mathematics. Besides, I

had learned many moral values that I practice. This project had taught

me to think rationally on doing something because can effect the

future. Remember...let the mind first before your act. I also learned to

be calm and a lot of patient for solving the problem asked.

Besides, this project prepared me for be more confident on

answering question even thou I got the weird and so on answer but it

give me confident to answer it, I become more brave. I also be

exposure to do assignment when I entering the university soon.

Lastly, not much that I can say about this project but I can

expressed it like the picture below


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Additional Mathematics Project 4

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Transcript of Additional Mathematics Project 4