project add math 2013 index number
TRANSCRIPT
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OBJECTIVES
We, the students who took Additional Mathematics are required to
carry out a project while we are in Form 5. This year the Curriculum
Development Division, Ministry of Education has prepared four tasks
for us. We are to choose and complete only ONE task based on our area
of interest. This project can be done in groups or individually, but each
of us are expected to submit an individually written report. Upon
completion of the Additional Mathematics Project Work, we are to gain
valuable experiences and able to :
Apply and adapt a variety of problem solving strategies to solveroutine and non-routine problems;
Experience classroom environment which are challenging,
interesting and meaningful and hence improve their thinking skills;
Experience classroom environment where knowledge and skills are
applied in meaningful ways in solving real-life problems;
Experience classroom environments where expressing ones
mathematical thinking, reasoning and communication are highlyencouraged and expected;
Experience classroom environments that stimulates and enhances
effective learning;
Acquire effective mathematical communication through oral and
writing, and to use the language of mathematics to express
mathematical ideas correctly and precisely;
Enhance acquisition of mathematical knowledge and skills through
problem-solving in ways that increase interest and confidence;
Prepare ourselves for the demand of our future undertakings and in
workplace.
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Realise that mathematics is an important and powerful tool in
solving real-life problems and hence develop positive attitude
towards mathematics;
Train ourselves not only to be independent learners but also tocollaborate, to cooperate, and to share knowledge in an engaging
and healthy environment;
Use technology especially the ICT appropriately and effectively;
Train ourselves to appreciate the intrinsic values of mathematics
and to become more creative and innovative;
Realize the importance and the beauty of mathematics.
FOREWARD
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, Cik Nor Afiza binti
Abdul Rahman 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 ourideas. They were helpful that when we combines and discussed together,
we had this task done.
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HISTORY OF INDEX NUMBER
Price index
A price index (plural: price indices or price indexes) is anormalized average (typically a weightedaverage) of prices for a given
class of goods or services in a given region, during a given interval of
time. It is a statistic designed to help to compare how these prices, taken
as a whole, differ between time periods or geographical locations.
Price indices have several potential uses. For particularly broad indices,
the index can be said to measure the economys price level or a cost of
living. More narrow price indices can help producers with business plansand pricing. Sometimes, they can be useful in helping to guide
investment.
Some notable price indices include:
Consumer price index;
Producer price index;
GDP deflator.
History of early price indices
No clear consensus has emerges on who created the first price index.
The earliest reported research in this area came from Welshman Rice
Vaughan who examined price level change in his 1675 book A
Discourse of Coin and Coinage. Vaughan wanted to separate the
inflationary impact of the influx of precious metals brought by Spainfrom the New World from the effect due to currency debasement.
Vaughan compared labour statutes from his own time to similar statues
dating back to Edward III. These statutes set wages for certain tasks and
provided a good record of the change in wage levels. Vaughan reasoned
that the market for basic labour did not fluctuate much with time and
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that a basic laborers salary would probably buy the same amount of
goods in different time periods, so that a laborer's salary acted as a
basket of goods. Vaughan's analysis indicated that price levels in
England had risen six to eightfold over the preceding century.
While Vaughan can be considered a forerunner of price index research,
his analysis did not actually involve calculating an index. In 1707
Englishman William Fleetwood created perhaps the first true price
index. An Oxford student asked Fleetwood to help show how prices had
changed. The student stood to lose his fellowship since a fifteenth
century stipulation barred students with annual incomes over five
pounds from receiving a fellowship. Fleetwood, who already had an
interest in price change, had collected a large amount of price data going
back hundreds of years. Fleetwood proposed an index consisting of
averaged price relatives and used his methods to show that the value of
five pounds had changed greatly over the course of 260 years. He argued
on behalf of the Oxford students and published his findings
anonymously in a volume entitled Chronicon Preciosum.
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ADDITIONAL MATHEMATICS : PROJECT WORK
2013
Part 1(a)The price of goods sold in shop vary from one shop to another. Shoppers
tend to buy goods which are not only reasonably price but also give
value for their money.
You are required to carry out a survey on four different items based on
the following categories i.e. food,detergent and stationery. The survey
should be done in three differnt shop.
(a)Collect picture,newspaper cuttings or photos on item that you have
chosen. Design a collage to illustrate the chosen item.
Answer:
Stationery
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Detergent
Food
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Part 1(b):
Record the item and their prices systematically as such in Table 1. Since
item may be differently packed, be sure to use consistent measurements
for each item selected so that comparison can be done easily andaccurately.
Answer:
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Part 1(c):
Create at least two suitable graphical representations (the use of ICT is
encouraged) to compare contrast the price of the item chosen.
Answer:
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Part 1 (d):
Based on the graphical representations that you have constructed in part
1(c), interpret, discuss and draw consclusion. Comment on your
findings.
Answer:
Based on the graphical representations that I have constructed in Part 1(c), it is
shown that there are large and small differences among the prices of items in each
category between the shops.In the food category, the smallest price difference are
of those of sugar, while the highest is the price of eggs. Besides food, detergent
also shows a large price difference between its items. Among them is the price of
liquid dishwasher and clothes detergent. On the other hand,stationery items doesnt
have any obvious price difference. The graph also show that most of the items that
are high priced comes from the Boulevard Supermarket, while the lowest price
items come from the Discount Store.The graph 1(d) will show the conclusion of
the difference among the shops based upon the shops grand total.
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Part 1(e):
The item that has a large price difference = washing powder
Mean , X = =
=
= 21.17 (2dp)
Standard deviation = = =
=20.678( 3 dp )
Reason of difference in price :
Sales and discount offer by the supermarket.
Supermarket own brand are much cheaper thean the top brands
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Part 2(a):
Every year SMK Indah organises a carnival to raise funds for the school.
This year the school plans to install air conditioners in school libary.
Last year, during the carnival, your class made and sold butter cakes.Because of the popularity of butter cakes, your class has decided to carry
out the same project for this year carnival.
(a)Suggest a shop from Part 1 which you would go to purchase
the ingredients for the butter cakes. State and discuss your reasons
for purchasing from the shop you suggested.
Answer :
Tesco will be the choice. Because they offer the cheapest price and has
more discount.
Part 2(b):
I.Complete Table 2 with the prices of items found in the
shop/supermarket that you have chosen.
Answer :
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II.Composite index =
=
= = 127.32
III. 109.797 =
=
Thus,
Part 2(c):
i.Find out from reliable sources how to determine suitable capacity of
air-conditioner to be installed based on volume/size of a room.
ii.Work in group to estimate the volume of yout school libary. Explain
how you arrive at your answer. Hence, determine the number of air
conditioners with the appropriate capacity required for your libary.
iii.If your class intends to sponsor one air conditioner for the schoollibary, how many butter cakes must your class sell in order to buy the
air conditioner?
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Answer :
How to Calculate :
Reliable sources
from the internet
from the technician (electrical/home)
Volume = Area of the libary Height of the libary
determine the shape of the libary from plan of the libary
determine how to find the area according to yhe shape of the
libary.
determine the height.
determine the average number of student enter the libary at
yhe peak hour
check with the data from (a), estimate the number of air
conditioner needed
Part 3
As a commite member for the carnivel, you are required to prepared an
estimate budget to organise this years carnival. The commite has take
into consideration the increase in expenditure from the privious year due
to inflation. The price of food, trasportation and tents has increased by
15%. The cost of games, prizes and decorations remains the same, where
as the cost of miscellaneous items has increased by 30%.
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a)Complete Table 3 based on the information given above.
Answer:
b) Calculate the composite index for the estimated budget of the
carnival in the year 2010 based on the year 2009. Comment on your
answer.
Answer :
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c) The change in the composite index for the estimated 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 year 2011 based on the year 2009.
Answer :
Given that
Thus,
=
= 124.61 (2 d.p)
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FURTHER EXPLAINATION
Index numbers are being used in many different daily situations, for
example air pollution index, stock market index, gold index and property
index.
Obtain information from the Internet or other reliable sources on the
importance of two different types of index numbers of your choice.
Elaborate the use and the importance of these index numbers in daily life
situations.
Answer :
Air Polution Index
TheAir Pollution Index(API) is used in to measure the quality of air in
Malaysia, based on several sets of air pollution data.
A scale is used to show the health classifications used by the Malaysian
government to determine the API in a specific area:
0-50 Good
51-100Moderate 101-200Unhealthy 201-300Very unhealthy >300HazardousIf the API exceeds 500, a state of emergency is declared in the reporting
area. This usually means that non-essential government services are
suspended, and all ports in the affected area are closed. There may also
be a prohibition of commercial and industrial activities which are under
the private sector in the reporting area excluding the food sector.
http://en.wikipedia.org/wiki/Air_Pollution_Index#Malaysiahttp://en.wikipedia.org/wiki/Air_Pollution_Index#Malaysiahttp://en.wikipedia.org/wiki/Air_Pollution_Index#Malaysiahttp://en.wikipedia.org/wiki/Air_Pollution_Index#Malaysia -
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Body Mass Index
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A graph of body mass index is shown above. The dashed lines represent
subdivisions within a major class. For instance the "Underweight"
classification is further divided into "severe", "moderate", and "mild"
subclasses.
Based onWorld Health Organizationdatahere.The body mass index (BMI), orQuetelet index, is a statistical measure
of body weight based on a person's weight and height. Though it does
not actually measure thepercentage of body fat, it is used to estimate a
healthybody weightbased on a person's height. Due to its ease of
measurement and calculation, it is the most widely used diagnostic tool
to identify weight problems within a population, usually whether
individuals areunderweight,overweightorobese. It was invented
between 1830 and 1850 by theBelgianpolymathAdolphe
Queteletduring the course of developing "social physics". Body mass
index is defined as the individual's body weight divided by the square of
his or her height. The formulae universally used in medicine produce
aunit of measureof kg/m2. BMI can also be determined using a BMI
chart. which displays BMI as a function of weight (horizontal axis) and
height (vertical axis) using contour lines for different values of BMI or
colours for different BMI categories.
http://en.wikipedia.org/wiki/World_Health_Organizationhttp://en.wikipedia.org/wiki/World_Health_Organizationhttp://en.wikipedia.org/wiki/World_Health_Organizationhttp://www.who.int/bmi/index.jsp?introPage=intro_3.htmlhttp://www.who.int/bmi/index.jsp?introPage=intro_3.htmlhttp://www.who.int/bmi/index.jsp?introPage=intro_3.htmlhttp://en.wikipedia.org/wiki/Body_fat_percentagehttp://en.wikipedia.org/wiki/Body_fat_percentagehttp://en.wikipedia.org/wiki/Body_fat_percentagehttp://en.wikipedia.org/wiki/Body_weighthttp://en.wikipedia.org/wiki/Body_weighthttp://en.wikipedia.org/wiki/Body_weighthttp://en.wikipedia.org/wiki/Underweighthttp://en.wikipedia.org/wiki/Underweighthttp://en.wikipedia.org/wiki/Underweighthttp://en.wikipedia.org/wiki/Overweighthttp://en.wikipedia.org/wiki/Overweighthttp://en.wikipedia.org/wiki/Overweighthttp://en.wikipedia.org/wiki/Obesehttp://en.wikipedia.org/wiki/Obesehttp://en.wikipedia.org/wiki/Obesehttp://en.wikipedia.org/wiki/Belgiumhttp://en.wikipedia.org/wiki/Belgiumhttp://en.wikipedia.org/wiki/Adolphe_Quetelethttp://en.wikipedia.org/wiki/Adolphe_Quetelethttp://en.wikipedia.org/wiki/Adolphe_Quetelethttp://en.wikipedia.org/wiki/Adolphe_Quetelethttp://en.wikipedia.org/wiki/Units_of_measurementhttp://en.wikipedia.org/wiki/Units_of_measurementhttp://en.wikipedia.org/wiki/Units_of_measurementhttp://en.wikipedia.org/wiki/Units_of_measurementhttp://en.wikipedia.org/wiki/Adolphe_Quetelethttp://en.wikipedia.org/wiki/Adolphe_Quetelethttp://en.wikipedia.org/wiki/Belgiumhttp://en.wikipedia.org/wiki/Belgiumhttp://en.wikipedia.org/wiki/Obesehttp://en.wikipedia.org/wiki/Overweighthttp://en.wikipedia.org/wiki/Underweighthttp://en.wikipedia.org/wiki/Body_weighthttp://en.wikipedia.org/wiki/Body_fat_percentagehttp://www.who.int/bmi/index.jsp?introPage=intro_3.htmlhttp://en.wikipedia.org/wiki/World_Health_Organization -
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Usage
While the formula previously called the Quetelet Index for BMI dates
to the 19th century, the new term "body mass index" for the ratio and
its popularity date to a paper published in the July edition of 1972 in
theJournal of Chronic Diseases byAncel Keys, which found the BMI
to be the best proxy for body fat percentage among ratios of weight and
height; the interest in measuring body fat being due to obesity becoming
a discernible issue in prosperous Western societies. BMI was explicitlycited by Keys as being appropriate forpopulation studies, and
inappropriate for individual diagnosis. Nevertheless, due to its
simplicity, it came to be widely used for individual diagnosis, despite its
inappropriateness.
BMI provided a simple numeric measure of a person's "fatness" or
"thinness", allowing health professionals to discuss over- and under-
weight problems more objectively with their patients. However, BMI
has become controversial because many people, including physicians,have come to rely on its apparent numerical authority for medical
diagnosis, but that was never the BMI's purpose; it is meant to be used
as a simple means of classifying sedentary (physically inactive)
individuals with an average body composition. For these individuals, the
current value settings are as follows: a BMI of 18.5 to 25 may indicate
http://en.wikipedia.org/wiki/Ancel_Keyshttp://en.wikipedia.org/wiki/Ancel_Keyshttp://en.wikipedia.org/wiki/Ancel_Keyshttp://en.wikipedia.org/wiki/Ancel_Keys -
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optimal weight; a BMI lower than 18.5 suggests the person
isunderweightwhile a number above 25 may indicate the person
isoverweight; a BMI below 17.5 may indicate the person hasanorexia
nervosaor a related disorder; a number above 30 suggests the person
isobese(over 40, morbidly obese).
For a given height, BMI is proportional to weight. However, for a given
weight, BMI is inversely proportional to thesquare of the height. So, if
all body dimensions double, and weight scales naturally with the cube of
the height, then BMI doubles instead of remaining the same. This results
in taller people having a reported BMI that is uncharacteristically high
compared to their actual body fat levels. In comparison, thePonderal
indexis based on this natural scaling of weight with the third power of
the height. However, many taller people are not just "scaled up" shortpeople, but tend to have narrower frames in proportion to their height. It
has been suggested that instead of squaring the body height (as the BMI
does) or cubing the body height (as thePonderal indexdoes), it would
be more appropriate to use an exponent of between 2.3 and 2.7.
http://en.wikipedia.org/wiki/Underweighthttp://en.wikipedia.org/wiki/Underweighthttp://en.wikipedia.org/wiki/Overweighthttp://en.wikipedia.org/wiki/Overweighthttp://en.wikipedia.org/wiki/Overweighthttp://en.wikipedia.org/wiki/Anorexia_nervosahttp://en.wikipedia.org/wiki/Anorexia_nervosahttp://en.wikipedia.org/wiki/Anorexia_nervosahttp://en.wikipedia.org/wiki/Anorexia_nervosahttp://en.wikipedia.org/wiki/Obesityhttp://en.wikipedia.org/wiki/Obesityhttp://en.wikipedia.org/wiki/Obesityhttp://en.wikipedia.org/wiki/Ponderal_indexhttp://en.wikipedia.org/wiki/Ponderal_indexhttp://en.wikipedia.org/wiki/Ponderal_indexhttp://en.wikipedia.org/wiki/Ponderal_indexhttp://en.wikipedia.org/wiki/Ponderal_indexhttp://en.wikipedia.org/wiki/Ponderal_indexhttp://en.wikipedia.org/wiki/Ponderal_indexhttp://en.wikipedia.org/wiki/Ponderal_indexhttp://en.wikipedia.org/wiki/Ponderal_indexhttp://en.wikipedia.org/wiki/Obesityhttp://en.wikipedia.org/wiki/Anorexia_nervosahttp://en.wikipedia.org/wiki/Anorexia_nervosahttp://en.wikipedia.org/wiki/Overweighthttp://en.wikipedia.org/wiki/Underweight -
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CONCLUSION
For a given height, BMI is proportional to weight. However, for
a given weight, BMI is inversely proportional to thesquare of
the height. So, if all body dimensions double, and weight scalesnaturally with the cube of the height, then BMI doubles instead
of remaining the same. This results in taller people having a
reported BMI that is uncharacteristically high compared to their
actual body fat levels. In comparison, thePonderal indexis based
on this natural scaling of weight with the third power of the
height. However, many taller people are not just "scaled up"
short people, but tend to have narrower frames in proportion totheir height. It has been suggested that instead of squaring the
body height (as the BMI does) or cubing the body height (as
thePonderal indexdoes), it would be more appropriate to use an
exponent of between 2.3 and 2.7.
http://en.wikipedia.org/wiki/Ponderal_indexhttp://en.wikipedia.org/wiki/Ponderal_indexhttp://en.wikipedia.org/wiki/Ponderal_indexhttp://en.wikipedia.org/wiki/Ponderal_indexhttp://en.wikipedia.org/wiki/Ponderal_indexhttp://en.wikipedia.org/wiki/Ponderal_indexhttp://en.wikipedia.org/wiki/Ponderal_index -
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REFLECTION
After spending countless hours, days and night to finish this project and alsosacrificing my time, video games and magazine in this month , there are several
things that I can say...
Additional maths
You are like a very bright star..
Smiling at me..
Every time teacher teaches me bout you
Additional maths
Who says you so difficult?
Who says you kill them off?
Who says you hurt parents feeling?
You, one of the greatest creature of God..
You, open my eyes..
Telling me little by little bout The Knower of All
Know, I feel so grateful
That He has given me the chance to get to know you
Additional Maths,
I love you