Upload
nur-najwa
View
223
Download
1
Embed Size (px)
Citation preview
8/9/2019 33163167 Project Work Additional Mathematics by NKS
1/50
..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
8/9/2019 33163167 Project Work Additional Mathematics by NKS
2/50
CONTENTSAcknowledgement..................................................
Objectives...............................................................
Introduction ...........................................................
Part 1......................................................................
Part 2......................................................................
Part 3......................................................................
Further explorations...............................................
Reflections............................................................
Conclusion..............................................................
8/9/2019 33163167 Project Work Additional Mathematics by NKS
3/50
ACKNOWLEDGEMENT
8/9/2019 33163167 Project Work Additional Mathematics by NKS
4/50
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.
8/9/2019 33163167 Project Work Additional Mathematics by NKS
5/50
OBJECTIVES
8/9/2019 33163167 Project Work Additional Mathematics by NKS
6/50
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
8/9/2019 33163167 Project Work Additional Mathematics by NKS
7/50
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.
8/9/2019 33163167 Project Work Additional Mathematics by NKS
8/50
INTRODUCTION
8/9/2019 33163167 Project Work Additional Mathematics by NKS
9/50
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
8/9/2019 33163167 Project Work Additional Mathematics by NKS
10/50
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 .
8/9/2019 33163167 Project Work Additional Mathematics by NKS
11/50
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.
8/9/2019 33163167 Project Work Additional Mathematics by NKS
12/50
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
8/9/2019 33163167 Project Work Additional Mathematics by NKS
13/50
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.
8/9/2019 33163167 Project Work Additional Mathematics by NKS
14/50
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
8/9/2019 33163167 Project Work Additional Mathematics by NKS
15/50
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.
8/9/2019 33163167 Project Work Additional Mathematics by NKS
16/50
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.
8/9/2019 33163167 Project Work Additional Mathematics by NKS
17/50
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
8/9/2019 33163167 Project Work Additional Mathematics by NKS
18/50
PART I
8/9/2019 33163167 Project Work Additional Mathematics by NKS
19/50
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
8/9/2019 33163167 Project Work Additional Mathematics by NKS
20/50
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
8/9/2019 33163167 Project Work Additional Mathematics by NKS
21/50
Question (c)
8/9/2019 33163167 Project Work Additional Mathematics by NKS
22/50
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,
8/9/2019 33163167 Project Work Additional Mathematics by NKS
23/50
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
8/9/2019 33163167 Project Work Additional Mathematics by NKS
24/50
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
8/9/2019 33163167 Project Work Additional Mathematics by NKS
25/50
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.
8/9/2019 33163167 Project Work Additional Mathematics by NKS
26/50
PART II
8/9/2019 33163167 Project Work Additional Mathematics by NKS
27/50
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
8/9/2019 33163167 Project Work Additional Mathematics by NKS
28/50
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 :
8/9/2019 33163167 Project Work Additional Mathematics by NKS
29/50
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.
8/9/2019 33163167 Project Work Additional Mathematics by NKS
30/50
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.
8/9/2019 33163167 Project Work Additional Mathematics by NKS
31/50
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 =
8/9/2019 33163167 Project Work Additional Mathematics by NKS
32/50
PART III
8/9/2019 33163167 Project Work Additional Mathematics by NKS
33/50
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
8/9/2019 33163167 Project Work Additional Mathematics by NKS
34/50
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
8/9/2019 33163167 Project Work Additional Mathematics by NKS
35/50
8/9/2019 33163167 Project Work Additional Mathematics by NKS
36/50
FURTHER
EXPLORATIONS
8/9/2019 33163167 Project Work Additional Mathematics by NKS
37/50
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.
8/9/2019 33163167 Project Work Additional Mathematics by NKS
38/50
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.
8/9/2019 33163167 Project Work Additional Mathematics by NKS
39/50
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
on patients and members of sensitive
groups (children, aged or weak people),
and also cause the general publicunpleasant feelings.
251-
350Very unhealthy
A level which may have a serious impact
on patients and members of sensitive
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.
8/9/2019 33163167 Project Work Additional Mathematics by NKS
40/50
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.
8/9/2019 33163167 Project Work Additional Mathematics by NKS
41/50
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.
8/9/2019 33163167 Project Work Additional Mathematics by NKS
42/50
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.
8/9/2019 33163167 Project Work Additional Mathematics by NKS
43/50
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.
8/9/2019 33163167 Project Work Additional Mathematics by NKS
44/50
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.
8/9/2019 33163167 Project Work Additional Mathematics by NKS
45/50
REFLECTIONS
8/9/2019 33163167 Project Work Additional Mathematics by NKS
46/50
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...
8/9/2019 33163167 Project Work Additional Mathematics by NKS
47/50
I really love you...
You are my real friend...
You my partner...
You are my soulmate...
I LOVE U ADDITIONAL MATHEMATICS..
8/9/2019 33163167 Project Work Additional Mathematics by NKS
48/50
CONCLUSIONS
8/9/2019 33163167 Project Work Additional Mathematics by NKS
49/50
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.
8/9/2019 33163167 Project Work Additional Mathematics by NKS
50/50