33845495 additional mathematics project work 4

8/9/2019 33845495 Additional Mathematics Project Work 4

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ADDITIONAL

MATHEMATICS

PROJECT WORK

4/2010

INDEX NUMBER IN OUR DAILY LIFE

NAME : NOOR WILIA AMIERA BT AFENDY

CLASS : 5 MURNI

TEACHER : PN. RUZI SUZANA

NO. I/C : 930907-03-5836

SEKOLAH : SMK SULTAN SULAIMAN


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Introduction ______________________________

Objectives ______________________________

Appreciation ______________________________

Part 1 ______________________________

Part 2 ______________________________

Part 3 ______________________________

Further Exploration ______________________________

Conclusion ______________________________

Reflection ______________________________


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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 orindividually, 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:

y Apply and adapt a variety of problem solving

strategies to solve routine and non-routine

problems;

y Experience classroom environments which are

challenging, interesting and meaningful and hence

improve their thinking skills.

y Experience classroom environments where

knowledge and skills are applied in meaningful ways

in solving real-life problemsy Experience classroom environments where

expressing ones mathematical thinking, reasoning

and communication are highly encouraged and

expected


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y Experience classroom environments that stimulate

and enhance effective learning.

y Acquire effective mathematical communication

through oral and writing, and to use the language ofmathematics to express mathematical ideas

correctly and precisely

y Enhance acquisition of mathematical knowledge

and skills through problem-solving in ways that

increase interest and confidence

y Prepare ourselves for the demand of our future

undertakings and in workplace

y Realise that mathematics is an important and

powerful tool in solving real-life problems and hence

develop positive attitude towards mathematics.

y Train ourselves not only to be independent learners

but also to collaborate, to cooperate, and to share

knowledge in an engaging and healthy environmenty Use technology especially the ICT appropriately and

effectively

y Train ourselves to appreciate the intrinsic values of

mathematics and to become more creative and

innovative

y Realize the importance and the beauty of

mathematics


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First of all, I would like to say Alhamdulillah, for giving me the strength and

health to do this project work. Not forgotten my parents for providing

everything, such as money, to buy anything that are related to this project work

and their advise, which is the most needed for this project. Internet, books,

computers, and etc. They also supported me and

encouraged me to complete this task so that I will not

procrastinate in doing it. Then I would like to thank my teacher, Mrs. Zainun

Abdullah for guiding me and my friends throughout this project. We had some

difficulties in doing this task, but she taught us

patiently until we knew what to do. She tried and tried to teach us

until we understand what we supposed to do with the project

work. Last but not least, my friends who were doing this project with me and

sharing our ideas. They were helpful that when we combined and discussed

together, we had this task done.


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HISTORY OF INDEX NUMBER

Index numbers are meant to study the change in the effects of such factors

which cannot be measured directly. According to Bowley, Index numbers are usedto measure the changes in some quantity which we cannot observe directly. For

example, changes in business activity in a country are not capable of direct

measurement but it is possible to study relative changes in business activity by

studying the variations in the values of some such factors which affect business

activity, and which are capable of direct measurement.

Index numbers are commonly used statistical device for measuring the

combined fluctuations in a group related variables. If we wish to compare the price

level of consumer items today with that prevalent ten years ago, we are not

interested in comparing the prices of only one item, but in comparing some sort of

average price levels. We may wish to compare the present agricultural production

or industrial production with that at the time of independence. Here again, we have

to consider all items of production and each item may have undergone a different

fractional increase (or even a decrease). How do we obtain a composite measure?

This composite measure is provided by index numbers which may be defined as adevice for combining the variations that have come in group of related variables

over a period of time, with a view to obtain a figure that represe nts the net result of

the change in the constitute variables.


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Index numbers may be classified in terms of the variables that they are

intended to measure. In business, different groups of variables in the

measurement of which index number techniques are commonly used are (i)price, (ii) quantity, (iii) value and (iv) business activity. Thus, we have index of

wholesale prices, index of consumer prices, index of industrial output, index of

value of exports and index of business activity, etc. Here we shall be mainly

interested in index numbers of prices showing changes with respect to time,

although methods described can be applied to other cases. In general, the

present level of prices is compared with the level of prices in the past. The

present period is called the current period and some period in the past is

called the base period.

Index Numbers:

Index numbers are statistical measures designed to show changes in a

variable or group of related variables with respect to time, geographic location

or other characteristics such as income, profession, etc. A collection of index

numbers for different years, locations, etc., is sometimes called an index

series.

Simple Index Number:

A simple index number is a number that measures a relative change in

a single variable with respect to a base.

Composite Index Number:

A composite index number is a number that measures an average

relative changes in a group of relative variables with respect to a base.


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Part 1

The prices of goods sold in shops vary from one shop toanother. 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 itemsbased on the following categories i.e. food, detergent andstationery. The survey should be done in three different shops.

a) Collect pictures, newspaper cuttings or photos on itemsthat you have chosen. Design a collage to illustrate thechosen items


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Answer:

Food:


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Detergent:


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Stationery:


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Question

(b) Record the items and their prices systematically as inTable 1.Since items maybe differently packed, be sure to use

consistent measurements for each item selected so thatcomparison can be done easily and accurately.

Answer:

Category Item Price(RM)Mydin Mall Giant Astaka

Food1.Self-RaisingFlour (1000g)

RM3.65 RM3.99 RM3.80

2.Sugar (1000g) RM1.65 RM1.65 RM1.653.Butter (250g) RM3.89 RM4.29 RM3.904.Eggs (Grade A)1 dozen

RM3.89 RM4.69 RM4.20

Total Price RM13.08 RM14.64 RM13.55

Detergent

1.Attack Softener

(1L)

RM7.50 RM8.49 RM7.90

2.Top (1L) RM8.90 RM10.89 RM9.903.Downy (1L) RM8.65 RM11.69 RM9.954.Softlan (1000ml) RM3.90 RM4.50 RM4.20

Total Price RM28.95 RM35.57 RM31.95

Stationery1.HighlighterStabilo

RM3.50 RM3.79 RM3.50

2.Ruler (2pcs) RM1.80 RM1.99 RM1.503.Colour PencilsFaber-Castell

RM18.90 RM25.99 RM22.90

4.Pen Power GelFaber-Castell

RM2.20 RM2.99 RM2.30

Total Price RM26.40 RM34.76 RM30.20Grand

TotalRM68.43 RM90.96 RM75.70


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Question:

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

the items chosen.Answer:

1) Food

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Giant Mydin Mall Astaka

Self-raising flour

Sugar

Butter

Eggs(Grade A)


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2) Detergent

0

2

4

6

8

10

12

14


Attack Softener

Top

Downy

Softlan


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3) Stationery

0

5

10

15

20

25

30


R

ler

Colo

r Pencil

Pen Po

er Gel Faber -Castell

Highlighter Stabilo


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self-raising flour

Giant

Mydin Mall

staka

sugar

Giant

Mydin Mall

staka


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butter

Giant

Mydin Mall

staka

Eggs

Giant

Mydin Mall

staka


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Attack S fte er

Gia

t

Mydi

Mall

Astaka

Top

Gia t

Mydi

Mall

Astaka


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Downy

Giant

Mydin Mall

staka

Softlan

Giant

Mydin Mall

staka


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Ruler

Gia

t

Mydi

Mall

Astaka

Colour Pencils

Gia t

Mydi

Mall

Astaka


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PenPower Gel Faber-Castell

Giant

Mydin Mall

staka

Highlighter Stabilo

Giant

Mydin Mall

staka


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Question

(d) Based on the graphical representation that you have constructed inPart 1(c), interpret,discuss and draw conclusions. Comments on yourfindings.

Answer:

Based on the graphical representations that I have constructed in Part1(c), it is shown that there are large and small differences among theprices of items in each category between the shops.In the food category,the smallest price difference are of those of sugar, while the highest isthe price of eggs. Besides food, detergent also shows a large price

difference between its items. Among them is the price of downy andtop.On the other hand,stationery items doesnt have any obvious pricedifference. The graph also show that most of the items that are highpriced comes from the Giant, while the lowest price items come from theMydin Mall.The graph 1(d) will show the conclusion of the differenceamong the shops based upon the shops grand total.

0

10

20

30

40

50

60

70

80

90

100

Grand total

Giant

Astaka

Mydin Mall


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Question

(e) Identify an item that has a large price differenceamong the shops. Calculate the mean and standard deviation

of that particular item. Hence, suggest and discuss possiblereasons for the price difference.

Answer:

Top:

Mean=

=22.60

Standard deviation

= ()/N ( )

=

- (22.60)

=2.88

The large price difference of clothes detergent (Top) among theshops maybe because of the standard of the shop.A highstandard shop or supermarket, the items sold intend to be muchmore expensive than a regular shop or supermarket.Also, theprice difference of the items may also due to the quality of theitem present. A better quality means a higher price.


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Part 2

Every year SMK Indah organises a carnival to raise fundsfor the school. This year the school plans to install air

conditioners in the school library. Last year, during thecarnival, your class made and sold butter cakes. Because ofthe popularity of the butter cakes,your class has decided tocarry out the same project for this years carnival.

Question

(a) Suggest a shop from Part 1 which you would go topurchase the ingredients for the butter cakes.Stateand discuss your reasons for purchasing from theshop you suggested.

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


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Question

(b) Complete Table 2 with the prices of the itemsfound in the shop/supermarket that you have

chosen.Answer:

Question

(i) Calculate the price index for each of the ingredients inTable 2 for the year 2010 based on the year 2009

Answer:

Ingredient QuantityPer cake

Price in the year2009(RM)

Price in theyear

2010(RM)Self-raisingflour

250g 0.90 0.90

Sugar 200g 0.35 0.33Butter 250g 3.30 3.89Eggs(Grade A) 5 eggs

(300g)1.25 1.62

Ingredient QuantityPer cake

Price in theyear

2009(RM)

Price in theyear

2010(RM)

Price indexfor the year2010 basedon the year

2009 ()

Self-raisingflour 250g 0.90 0.90 100Sugar 200g 0.35 0.33 94.29Butter 250g 3.30 3.89 117.88Eggs(GradeA)

5 eggs(300g)

1.25 1.62 129.6


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1.Self-raising flour

=

2.Sugar

=

3.Butter

=

4.Eggs(Grade A)

=


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Question

(ii) Calculate the composite index for making a butter cakein the year 2010 based on the year 2009. Discuss how you

obtained your answers.

Answer:

To calculate the composite index,weightage is needed (W),

Ingredients Weightage (W)Self-raising flour

Sugar

Butter

Eggs(Grade A)

Composite index

=112.2


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Question

(iii) In the year 2009,the butter cake was sold at RM15.00each.Suggest a suitable selling price for the butter cake

in the year 2010.Give reasons for your answer.

Answer:

On 2009,RM 15.00

On 2010, price=

= =18.38

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

RM18.38.The increase in price is also suitable because of the

rise in the price of the ingredients.


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Question

(c)(i) Find out from reliable sources how to determine suitablecapacity of air conditioner to be installed based on the

volume/size of a room.Answer:

For common usage,air conditioner is rated according to horsepower (1HP), which is approximately 700W to 1000W ofelectrical power. It is suitable for a room size 1000ftwhich isaround 27mof volume.

Question

(ii) Work in groups to estimate the volume of your schoollibrary. Explain how you arrive at your answer. Hence,determine the number of air conditioners with the appropriatecapacity required for your library.

Answer:

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

Height=3.2m

Width=6.25m

Length=23.5m

Volume of the room=3.206.2523.50=470.00m

1 unit of air conditioner is for 27m

For 470.00m=

=17.4

That means our school library needs 17 unit of air conditioner.


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Question

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

school library, how many butter cakes must your class sell inorder to buy the air conditioner?

Answer:

1 unit of 1HP air conditioner=RM700

Cost for a cake =0.9+0.33+3.89+1.62 =6.74

Selling price =RM18.38

Profit =18.38-6.74

=RM11.64

Number of cakes to buy 1 unit of air conditioner =

= 60.13 = 60 cakes


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Part 3

As a committee member for the carnival, you are required toprepare an estimated budget to organize this years carnival.

The committee 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 costof games, prizes and decorations remains the same, whereasthe cost of 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 1380.00Games 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


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Question

a) Calculate the composite index for the estimated budget ofthe carnival in the year 2010 based on the year 2009.

Comment on your answer.Solution .

Expenditure Amount in2009(RM)

Amount in2010(RM)

PriceIndex, II=

Weightage,W

Food 1200.00 1380.00 115 12

Games 500.00 500.00 100 5Transportation 300.00 345.00 115 3Decorations 200.00 200.00 100 2Prizes 600.00 600.00 100 6Tents 800.00 920.00 115 8Miscellaneous 400.00 520.00 130 4

Composite Index

=

=

= =111.625

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

because some price in the year 2009 increased in the year2010.


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Question .a) 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 year2011 based on the year 2009.

Solution .

Composite index for the year 2009 to the year 2010

=111.625

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

=

=111.625111.625

124.60


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Further Exploration

Index numbers are being used in many different daily situations,for example air pollution index, stock market index, gold indexand property index.

Obtain information from the internet or other reliable sources onthe importance of two different types of index number of yourchoice. Elaborate the use and the importance of these indexnumbers in daily life.

Air Pollution Index

Air pollution is the introduction ofchemicals, particulatematter, orbiological materials that cause harm or discomfort tohumans or other living organisms, or damages the natural

environment into the atmosphere.The atmosphere is a complex dynamic natural gaseous systemthat is essential to support life onplanet Earth. Stratosphericozone depletion due to air pollutionhas long been recognized as a threat to human health as wellas to the Earth's ecosystems.

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

Index (API) orPollutant Standard Index (PSI) is a numberused by government agencies to characterize the quality of theair at a given location. As the AQI increases, an increasinglylarge percentage of the population is likely to experienceincreasingly severe adverse health effects. To compute the AQIrequires an air pollutant concentration from a monitor or model.The function used to convert from air pollutant concentration to


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AQI varies by pollutant, and is different in different countries. Airquality index values are divided into ranges, and each range isassigned a descriptor and a color code. Standardized publichealth advisories are associated with each AQI range. An

agency might also encourage members of the public to takepublic transportation or work from home when AQI levels arehigh.

Limitations of the AQI

Most air contaminants do not have an associated AQI. Manycountries monitor 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 airemissions by fresh air. Stagnant air, often caused byan anticyclone or temperature inversion, or other lackof winds lets air pollution remain in a local area.

Indices by locationSouth Korea

The Ministry of Environment of South Korea uses theComprehensice Air-quality Index (CAI) to describe the ambientair quality based on health risk of air pollution. The index aimsto help the public easily understand air quality level and protectthe health of people from air pollution. - The CAI has values of 0through 500, which are divided into six categories. The higher

the CAI value, the greater the level of air pollution. - Of valuesof the five air pollutants, the highest is the CAI value.


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CAI Description Health Implications

0-50 GoodA level that will not impact patientssuffering from diseases related to airpollution.

51-100

Moderate A level which may have a meager impacton patients in case of chronic exposure.

101-150

Unhealthy forsensitivegroups

A level that may have harmful impacts onpatients and members of sensitivegroups.

151-250 Unhealthy

A level that may have harmful impacts onpatients and members of sensitivegroups (children, aged or weak people),

and also cause the general publicunpleasant feelings.

251-350

Very unhealthyA level which may have a serious impacton patients and members of sensitivegroups in case of acute exposure.

351-500

Hazardous

A level which may need to take

emergency measures for patients andmembers of sensitive groups and haveharmful impacts on the general public.


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Malaysia

The 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) arereported in PM10 particulate matter is reported in g/m.Unlike the American AQI, the index number can exceed 500.Above 500, a state of emergency is declared in the reportingarea. Usually, this means that non-essential governmentservices are suspended, and all ports in the affected areaclosed. There may also be a prohibition on private sectorcommercial and industrial activities in the reporting areaexcluding the food sector.


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A stock market index is a method of measuring a section ofthe stock market. Many indices are cited by news or financialservices 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) companieswithout regard for where they are domiciled or traded. Twoexamples 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 investorsentiment on the state of its economy. The most regularlyquoted market indices are national indices composed of thestocks of large companies listed on a nation's largest stockexchanges, such as the American S&P 500, theapanese Nikkei 225, and the British FTSE 100.

The concept may be extended well beyond an exchange. TheDow ones 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 NewYork Stock Exchange (but not ADRs) and most traded onthe NASDAQ and American Stock Exchange. RussellInvestment Group added to the family of indices by launching

the Russell Global Index.More specialised indices exist tracking the performance ofspecific sectors of the market. The Morgan Stanley BiotechIndex, for example, consists of 36 American firms inthe biotechnology industry. Other indices may track companiesof a certain size, a certain type of management, or even morespecialized criteria one index published by Linux Weekly


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News tracks stocks of companies that sell products andservices based on the Linux operating environment.

Index versions

Some indices, such as the S&P 500, have multipleversions.[1] These versions can differ based on how the indexcomponents are weighted and on how dividends are accountedfor. 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 nettotal return, which accounts for dividend reinvestment after thededuction of a withholding tax. As another example,

the Wilshire 4500 and Wilshire 5000 indices have five versionseach: full capitalization total return, full capitalization price, float-adjusted total return, float-adjusted price, and equal weight. Thedifference between the full capitalization, float-adjusted, andequal weight versions is in how index components areweighted.

Uses and importance of air pollution index and stock marketindex

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

government to measure the air quality index and to detect anypollutants in our countrys air.This is to ensure the air is cleanand safe for us to inhale.Besides that,an early warning can begiven to us if the air pollution is to high for us to get out of ourhomes. This warning is given based upon readings andinterpretations of the air pollution index.


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

countrys economical state sometimes depend on it.


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Conclusion

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

or the water. Especially in conducting an air-pollution survey. Inconclusion, index number is a daily life essecities. Without it,

surveys cant be conducted, the stock market cant be interpret

and many more. So ,we should be thankful of the people whocontribute in the idea of index number.


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Reflection

After spending countless hours, days and night to finish this

project and also sacrificing my time video games and magazine 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...

Sacrificing my Anime...

Sacrificing my magazine...

I realized something really important in you...


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I really love you...

You are my real friend...

You my partner...

You are my soulmate...

I LOVE U ADDITIONAL MATHEMATICS...

33845495 additional mathematics project work 4

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