33163167 Project Work Additional Mathematics by NKS

8/9/2019 33163167 Project Work Additional Mathematics by NKS

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..SEKOLAH MENENGAH KEBANGSAAN

PENAMBANG,15350 KOTA BHARU,KELANTAN..

ADDITIONAL MATHEMATICS PROJECT WORK

2010

[ASSIGNMENT 4]

Name : Nur Najwa bt Mohd Yusoff

I/C Number : 930419-11-5538

Class : 5 Amanah

Teacher : Mrs Jaradah bt Saali

Date : 15 July 2010


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CONTENTSAcknowledgement..................................................

Objectives...............................................................

Introduction ...........................................................

Part 1......................................................................

Part 2......................................................................

Part 3......................................................................

Further explorations...............................................

Reflections............................................................

Conclusion..............................................................


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ACKNOWLEDGEMENT


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ACKNOWLEDGEMENT

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

and health to do this project work and finish it on time.

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 to

complete this task so that I will not procrastinate in doing it.

Then I would like to thank to my teacher, Madam Jaradah bt Saali for

guiding me throughout this project. Even I had some difficulties in doing

this task, but she taught me patiently until we knew what to do. She

tried and tried to teach me until I understand what Im supposed to do

with the project work.

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 in completing this project work. Thank you everyone.


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OBJECTIVES


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OBJECTIVES

All science stream students that take Additional Mathematics are

required to carry out a project work while they 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 :

1. Apply and adapt a variety of problem solving strategies to solve

routine and non-routine problems.

2. Experience classroom environments which are challenging, interesting

and meaningful and hence improve their thinking skills.

3. Experience classroom environments where knowledge and skills are

applied in meaningful ways in solving real-life problems.

4. Experience classroom environments where expressing ones

mathematical thinking, reasoning and communication are highly

encouraged

and expected.5. Experience classroom environments that stimulates and enhances

effective learning.

6. Acquire effective mathematical communication through oral and

writing, and to use the language of mathematics to express


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mathematical ideas correctly and precisely.

7. Enhance acquisition of mathematical knowledge and skills through

problem-solving in ways that increase interest and confidence.

8. Prepare ourselves for the demand of our future undertakings and in

workplace.

9.Realise that mathematics is an important and powerful tool in solving

real-life problems and hence develop positive attitude towards

mathematics.

10. Train ourselves not only to be independent learners but also to

collaborate, to cooperate, and to share knowledge in an engaging and

healthy environment.

11. Use technology especially the ICT appropriately and effectively.

12. Train ourselves to appreciate the intrinsic values of mathematics and

to become more creative and innovative.

13. Realize the importance and the beauty of mathematics.


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INTRODUCTION


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INTRODUCTION

A Brief 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

the17th and 18th centuries, particularly in the analysis of games of chance

(gambling). By 1800, astronomy used probability models and statistical

theories, particularly the method of least squares, which was invented

by Legendre and Gauss. Early probability theory and statistics was


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systematized and extended by Laplace; following Laplace, probability

and statistics have been in continual development.

In the 19th century, social scientists used statistical r easoning 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 .


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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 makeinformed 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 stati stics departments.

Statistics is also taught in departments as diverse as psychology,

education, and public health.


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Index Number

Index numbers are today one of the most widely used statistical

indicators. Generally used to indicate the state of the economy, index

numbers are aptly called barometers of economic activity. Index

numbers are used in comparing

production, sales or changes exports or imports over a certain period of

time. The role-played by index numbers in Indian trade and industry is

impossible to ignore. It is a very well known fact that the wage contracts

of workers in our country are tied to the cost of living index numbers.

By definition, an index number is a statistical measure designed to

show changes in a variable or a group or related variables with respect to

time, geographic location or other characteristics such as income,

profession, etc.

Characteristics of anIndex Numbers

1. These are expressed as a percentage: Index number is calculated as a

ratio of the current value to a base value and expressed as a percentage.

It must be clearly understood that the index number for the base year is

always 100. An index number is commonly referred to as an index.

2. Index numbers are specialized averages: An index number is an

average with a difference. An index number is used for purposes of


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comparison in cases where the series being compared could be

expressed in different units i.e. a manufactured products index (a part of

the whole sale price index) is constructed using items like Dairy Products,

Sugar, Edible Oils, Tea and Coffee, etc. These items naturally are

expressed in different units like sugar in kgs, milk in liters, etc.

The index number is obtained as a result of an average of all these items,

which are expressed in different units. On the other hand, average is a

single figure representing a group expressed in the same units.

3. Index numbers measures changes that are not directly measurable:

An index number is used for measuring themagnitude of changes in such

phenomenon, which are not capable of direct measurement. Index

numbers essentiallycapture the changes in the group of related variables

over aperiod of time. For example, if the index of industrial production is

215.1 in 1992-93 (base year 1980-81) it means that the industrial

production in that year was up by 2.15 times compared to 1980-81. But it

does not, however, mean that the net increase in the index reflects an

equivalent increase inindustrial production in all sectors of the industry.

Some sectors might have increased their production more than 2.15

times while other sectors may have increased their production only

marginally.


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Uses of index numbers

1. Establishes trends

Index numbers when analyzed reveal a general trend of the

phenomenon under study. For eg. Index numbers of unemployment of

the country not only reflects the trends in the phenomenon but are

useful in determining factors leading to unemployment.

2. Helps in policy making

It is widely known that the dearness allowances paid to the employees is

linked to the cost of living index, generally the consumer price index.

From time to time it is the cost of living index, which forms the basis of

many a wages agreement between the employees union and the

employer. Thus index numbers guide policy making.

3. Determines purchasing power of the rupee

Usually index numbers are used to determine the purchasing power of

the rupee. Suppose the consumers price index for urban non-manual

employees increased from 100 in 1984 to 202 in 1992, the real purchasing

power of the rupee can be found out as follows: 100/202=0.495 It

indicates that if rupee was worth 100 paise in 1984 its purchasing power

is 49.5 paise in 1992.

4. Deflates time series data

Index numbers play a vital role in adjusting the original data to reflect

reality. For example, nominal income(income at current prices) can be


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transformed into real income(reflecting the actual purchasing power) by

using income deflators. Similarly, assume that industrial production is

represented in value terms as a product of volume of production and

price. If the subsequent years industrial production were to be higher by

20% in value, the increase may not be as a result of increase in the volume

of production as one would have it but because of increase in the price.

The inflation which has caused the increase in the series

can be eliminated by the usage of an appropriate price index and thus

making the series real.

Types of index numbers

Three are three types of principal indices. They are:

1. Price Index

The most frequently used form of index numbers is the price index.

A price index compares charges in price of edible oils. If an attempt is

being made to compare the prices of edible oils this year to the prices of

edible oils last year, it involves, firstly, a comparison of two price

situations over time and secondly, the heterogeneity of the edible oils

given the various varieties of oils. By constructing a price index number,

we are summarizing the price movements of each type of oil in this

group of edible oils into a single number called the price index. The

Whole Price Index (WPI). Consumer Price Index (CPI) are some of the

popularly used price indices.


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2. Quantity Index

A quantity index measures the changes in quantity from one

period to another. If in the above example, instead of the price of edible

oils, we are interested in the quantum of production of edible oils in

those years, then we are comparing quantities in two different years or

over a period of time. It is the quantity index that needs to be

constructed here. The popular quantity index used in this country and

elsewhere is the index of industrial production (HP). The index of

industrial production measures the increase or decrease in the level of

industrial production in a given period compared to some base period.

3. Value Index

The value index is a combination index. It combines price and

quantity changes to present a more spatial comparison. The value index

as such measures changes in net monetary worth. Though the value

index enables comparison of value of a commodity in a year to the value

of that commodity in a base year, it has limited use. Usually value index is

used in sales, inventories, foreign trade, etc. Its limited use is owing to

the inability of the value index to distinguish the effects of price and

quantity separately.


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Calculating index number

y Index number Is a measure used to show the change of a certain

quantity for a stated period of time by choosing a specific time as thebase year. In general an index number is the comparison of a quantity at

two different times and is expressed as a percentage.

I = index number

Q1 = quantity at specific t ime

Qo = quantity at base t ime

y The composite index is the weighted mean for all the items in a certainsituation.

=

= Composite index

W = weightage

= index number


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PART I


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The prices of good sold in shops are vary from one shop to another. Shoppers

tend to buy goods which are not only reasonably priced but also give value for

their money. I had carried out a survey on four different items based on the

following categories which is food, detergent and stationery. The survey was

done in three different shops. Informations below shows the results from my

research.

Question (a)

Picture

Stationery

Food


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Detergent

Question (b)

Data

Category ItemPrice (RM)

Mydin Mall Embat Shop Si Comel

Food

1.Self raising flour(500g) 2.00 2.50 2.10

2. Sugar(1000g) 1.80 1.90 1.85

3. Butter (250g) 3.50 3.60 3.604. Eggs (Grade A) 8.20 8.50 8.40

Total price 15.50 16.50 15.95

Detergent

1. Dishwash 1.80 2.00 1.95

2. Softener 3.90 4.20 4.00

3. Floor cleaner 10.90 11.00 11.30

4. Powder D/gent 9.50 9.50 9.60Total price 26.10 26.70 26.85

Stationery

1. Eraser 0.80 0.80 0.70

2. Marker 3.00 3.60 3.90

3. Pencil colour 5.50 5.40 5.304. Scissor 2.30 2.30 2.40

Total price 11.60 12.10 12.30

Grand total 53.20 55.30 55.10


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Question (c)


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Question (D)

Based on all the graph in question 1(C) , we can conclude that Mydin Mall

offers the lowest price for their customers. Then followed by Si Comel and

Embat Shop. This is because the supplier of the Mydin Mall gives the special

price for it as it buy by bulk. Si comel offer the normal price for their customer

as it does not get special price from the supplier. While, Embat Shop have to

sold the items at the higher price because the shop buy the items by bulk from

Mydin Mall.

Other factors that influenced the prices of goods in the shops is such as

the location of the shop, the population of the customers, the status of the

shop, the size of the shop, and the rent for the shop.

Mydin Mall can offer the lowest price because it is situated at stratergic

place so indirectly this factor can attract customer buy at the mall. When there

are many customers, the demand of the items will be high and the mall can buy

by bulk directly with the supplier to get the special price. The status of the shop

also influenced the price of the goods sold. As example the shop with status

mall will offer the lowest price than the shop with status mini market. The size

of the shop also will influenced the price. When the size of the shop is bigger its

mean it can sell many different items in the shop. Indirectly the shop will

known as one stop center and it will attract many customers as the people

nowadays are very busy. Mydin Mall is a bigmall and it provides many items

that we need in our life. Eventhough Mydin Mall have to pay rent for the place,


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but it not gives too much effects to the price of goods sold as it has many

buyers.

Si Comel and Embat Shop cannot offer the prices as Mydin Mall because

they are situated outside the urban area like Mydin Mall. So the population of

the customer will not be as many as customer in Mydin Mall. These shops get

the supply for their goods from Mydin Mall. Even they buy by bulk with Mydin

Mall but their prices still will be higher than Mydin Mall. The size of these shop

also small and cannot provide too much goods for their customers. They just

sold basic needed for their customers. As they not have too much customers,

so the rent that they have to pay will influenced the price of the goods sold.

As a conclusion, there are many factors that affect the price of the goods

solds in a shop. So, we must be a smart customer to ensure we can get the

lowest price. The

graph below will show the conclusion of the difference among the shops

based upon the shops grand total.

50

51

52

53

54

55

56

57

58

Grand Total

Mydin Mall

Si Comel

Embat Shop


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Question (e)

The item that has large price different among the shops is marker. Mydin

Mall sold it at RM 3.00, Si Comel sold it at RM3.90 while Embat Shop sold it atRM 3.60.

Calculate the mean

Calculate the standard deviation

Or

0.3742

The difference of the price of the marker in these three shops is maybe

due to the price given by the supplier to the shops. Mydin Mall can sold it at

lowest prices because the demand of the buyers for the the item is high so it

can buy by bulk with the supplier. So the shop can get the special price. The


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demand of the item in Embat Shop and Si Comel are low. This is because the

customers are more interested to buy the stationery items in mall or stationery

shops as there are more options to choose. So Embat Shop and Si Comel

cannot buy by bulk the stationery items with their supplier.


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PART II


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Every year my school organises a carnival to raise funds for the school. This

year my school plans to install air conditioners in the school library. Last year,

during the carnival, my class made and sold butter cakes. Because of the

popularity of butter cakes, my class has decided to carry out the same project

for this years carnival.

Question (a)

From the data in Part 1, I would go to Mydin Mall to purchase the ingredients

for the butter cakes. This is because Mydin Mall offers the lowest price among

the shops for the items I want to buy. So my class will able to sold the butter

cakes at the low price and get some profits form the sale. Futhermore, Mydin

Mall is located not far from my school. So it is easier to my friends and I to go

there.

Question (b)

Ingredient Quantity per cakePrice in the year

2009 (RM)Price in the year

2010 (RM)

Self-raisingflour

250 g 0.90 1.00

Sugar 200 g 0.35 0.36

Butter 250 g 3.30 3.50

Eggs (Grade A) 5 eggs (300 g) 1.25 1.37

(i)Calculate Price Index


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Self raising-four

Sugar

=102.86

Butter

=106.06

Eggs (Grade A)

=109.60

(ii)Composite index

=

=107.74

To calculate composite index firstly use the formula of composite index.

Get the value for the formula. Lets quantity per cake be as weightage, W.

Obtain the price index from the calculation in question (i). Then, calculate by

using the calculator.

(iii) On 2009, RM 15.00

On 2010, suitable price is :


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Thus, the suitable price for the butter cake for the year 2010 is RM 16.20.

The increase in price is also suitable because of the rise in the price of the

ingredients.


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Question (c)

(i)To determine suitable capacity of air conditioner to be installed based on

volume/ size of a room

For common usage, air conditioner is rated according to horse power

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

suitable for a room size 1000ft which is around 27m of volume. If we buy

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

(ii)Estimate the volume of school libraryBy using a measuring tape, the dimension for the library is:

Height=3.6m

Width=9.0m

Length=20.12m

Volume of the room=3.6 x 9.0 x 20.12

=651.90

One unit of air conditioner with 3HP is for 81

For

8.048

This means our school library needs 8 unit of air conditioner.

(iii) My class intends to sponsor one air conditioner for the school library.

The calculation below is to find how many butter cakes we must sell in

order to buy the air conditioner.


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1 unit of 3 HP air conditioner = RM 1800Cost for a cake = RM 6.23Selling price = RM 16.20Profit =RM 16.20- RM6.23

= RM 9.97

Number of cakes to buy 1 unit of air conditioner =


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PART III


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As a committee member for the carnival, I am required to prepare an

estimated budget to organise this years carnival. I has taken into consideration

the increases in expenditur from the previous year due to inflation The price of

food, transportation and tents has increased by 15%. The cost of games, prizes

and decorations remains the same, whereas the cost of miscellaneous items

has increase by 30%.

(a)Table 3 has been completed based on the above information.

Expenditure Amount in 2009 (RM) Amount in 2010 (RM)

Food 1200.00 1380.00

Games 500.00 500.00

Transportation 300.00 345.00

Decorations 200.00 200.00

Prizes 600.00 600.00

Tents 800.00 920.00Miscellaneous 400.00 520.00

Table 3

(b)Calculation to find the composite index

ExpenditureAmount in2009 (RM)

Amount in2010 (RM)

Price Index, Weightage,W

Food 1200.00 1380.00 115 12Games 500.00 500.00 100 5

Transportation 300.00 345.00 115 3

Decorations 200.00 200.00 100 2

Prizes 600.00 600.00 100 6

Tents 800.00 920.00 115 8


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Miscellaneous 400.00 520.00 130 4

Composite Index

=

=

The total price for the year 2010 increase by 111.625%. This is because some price

in the year 2009 increased in the year 2010.

(c)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 thechange from the year

2010 to the year 2011. Below are the calculation to determine the

composite index of the budget for the year 2011 based on the year 2009.

Composite index for the year 2009 to the year 2010

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

=111.625


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FURTHER

EXPLORATIONS


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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.


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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 temperatureinversion, 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.


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CAI Description Health Implications

0-50 Good

A level that will not impact patients

suffering from diseases related to air

pollution.

51-

100Moderate

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-

250Unhealthy

A level that may have harmful impacts


groups (children, aged or weak people),

and also cause the general publicunpleasant feelings.

251-

350Very unhealthy

A level which may have a serious impact


groups in case of acute exposure.

351-500 Hazardous

A level which may need to take

emergency measures for patients andmembers of sensitive groups and have

harmful impacts on the general public.


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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 ppmv but 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 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 dot-com spike on the NASDAQ, a

result of the large number of tech. companies on that index.

A stock market index is a method of measuring a section of the

stock market. Many indices are cited by news or financial services firmsand 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.


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A national index represents the performance of the stock market

of a given nationand 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

Wilshire 5000 Index, the original total market index, 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 orLimited Partnerships), 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. Some examples include the Wilshire US REIT

which tracks more than 80 American Real Estate Investment Trusts and

the Morgan Stanley Biotech Index which 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.


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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 with holding 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.


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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 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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REFLECTIONS


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After spending countless hours, days and night to finish

this project and also sacrificing my time for chatting and

movies 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 play Time..

Sacrificing my Chatting...

Sacrificing my Facebook...

Sacrificing my internet...

Sacrifing my Anime...

Sacrificing my Movies...

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..


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CONCLUSIONS


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CONCLUSI

ON

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 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. If people do

not believe that additional mathematics is simple, it is only because they do not

realize how complicated life is.


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33163167 Project Work Additional Mathematics by NKS

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Transcript of 33163167 Project Work Additional Mathematics by NKS