PROJECT ADDITIONAL MATHEMATIC 2010 INDEX NUMBER
NAMA
: MUHAMMAD ASHRAF BIN SHAHARUDIN
KELAS
: 5 SCIENCE 1
1
TEACHER
: PN. ONG YOKE BEE BEE
OBJECTIVES We students taking Additional Additional Mathematics are required to carry out a project project work while we are in Form 5.This year the t he 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 e xpected to submit an individually written report.Upon compl co mpletion etion of the t he Additional Mathematics Project Work,we are to gain valuable experiences and able to:
y
y
y
y
y y
y
Apply and adapt a variety of problem solving strategies to solve routine and nonroutine problems; Experience classroom environments which are challenging, interesting and meaningful and hence improve t heir thinking skills. skills. Experience classroom environments where know ledge and skills are applied in meaningful ways in solving real-life problems Experience classroom environments where expressing ones mathematical thinking,reasoning and communication are highly encouraged and expected Experience classroom environments that stimulates and enhances e ffective learning. Acquire effective mathematical communication through o ral 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
y
Prepare ourselves for the demand of o f our future undertakings and in workplace
y
ealise R ealise
y
y y
y
2
that mathematics is an important and powerful tool in solving real-life problems and hence develop positive p ositive attitude towards mathematics. Train ourselves not only to be independent learners but also to collaborate, to cooperate, and to share knowledge in an engaging and healthy environment Use technology especially the ICT appropriately app ropriately and effectively Train ourselves to appreciate the intrinsic values of mathematics and to become more creative and innovative ealize R ealize
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,Pn. Ong Yoke Bee 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 projectwork.Last but not least, my friends who were doing this project with me and sharing our ideas. They were helpful that when we combined and discussed together, we had this task done.
3
HISTORY OF INDEX NUMBER Price index A price index ( plural : ³price indices´ or ³price indexes´) is a normalized average (typically a weighted average) of prices for a given class ofgoods or services in a given reg ion, during a given interval of time. It is a statisti stat isticc designed to help to compare how these prices, pr ices, taken as a whole, differ between time periods or geographical locations. Price indices have several potential pot ential uses. For particularly broad indices, the index can be s aid to measure the economy's price level or a cost of living. More narrow price indices can help producers with business plans and pricing. So metimes, 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 emerged on who created the first price index. The earliest reported research in this area came from Welshman R ice ice Vaughan who examined price level change in his 1675 book A A
Discourse
of C oin oin and C oinage. oinage. Vaughan wanted to separate the inflationary
impact of the influx of precious metals brought by Spain from the New World from the effect due to currency debasement. Vaughan compared labor statutes from his own time to similar statutes 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 labor did not fluctuate much with time and that a basic laborers salary would probably buy the same amount of goods in different time periods, so that a laborer's salary acted as a basket of goods. Vaughan's analysis indicated that 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
4
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 C hronicon hronicon P reciosum. reciosum.
5
Add Maths : Projek Work 4/2010
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 o nly reasonably price but also give value for their mo ney. You are required to carry out a survey on four different items based on t he 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 : Sationery
6
Detergent
7
Food
8
Part 1(b): ecord R ecord
the item and t heir prices systematically as such in Table 1. S ince item may be differently packed, be sure to use consistent measurements for each item selected so that comparison can be done easily and accurately
Answer :
Category Food
Detergent
9
Item Tesco Self-rising flour 2.80 (500 gram) Sugar 1.40 ( 1 Kilogram ) Butter 3.70 ( 250 gram ) Eggs (Gred A) 3.70 ( 10 unit ) Total Price 11.60 Washing Powder 20.00 ( 3 Kilogram ) Dish Washer 5.00 ( 1000 ml )
Giant
3.80
The Store 3.40
1.40
1.40
3.90
4.60
3.00
3.10
12.10 22.00
12.50 21.50
4.20
4.10
Stationery
Liquid Bleach ( 1000 ml ) Tile Cleaner ( 1000 ml ) Total Price Pencil(Shaker) Highlighter Permanent Marker Card Indexing Total Price Grand Total
7.00
6.50
5.90
11.20
10.80
10.50
43.20 9.10 3.70 3.70
43.50 9.40 3.60 3.10
42.00 8.40 3.30 4.00
14.90 31.40 86.20
15.20 31.30 86.90
16.20 31.90 86.40
Part 1(c): Create at least two suitable graphical representations (the use o f ICT is encouraged) to compare contrast the price of the item chosen.
Answer :
10
50 45 40 35 30 Tesco
25
Giant 20
The Store
15 10 5 0 Food
Detergent
Stationery
45 40 35 30 25
Tesco
20
Giant The Store
15 10 5 0 Food
11
Detergent
Stationery
Grand Total
Tesco Giant The Store
Part 1 (d): 12
Based on the graphical representations that you have constructed in part 1(c), interpret, discuss and draw consclusion. Comment o n 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 doesn¶t 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.
50 45 40 35 30 Tesco
25
Giant 20
The Store
15 10 5 0 Food
Part 1(e): 13
Detergent
Stationery
The item that has a large price difference = washing powder
= = = 21.17 (2dp) Standard deviation = = = Mean , X =
=20.678( 3 dp ) eason R eason
of difference in price :
y
Sales and discount offer by the supermarket.
y
Supermarket own brand brand are much cheaper thean the top brands brands
Part 2(a): 14
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 c lass made and sold butter cakes. Because of the popularity of butter cakes, your class has decided to carry out the same project for this yera carnival. car nival. (a)Suggest (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.offer choice.o ffer the cheapest pricer and has more discount. d iscount.
Part 2(b) : 15
I. Complete Table 2 with w ith the prices of items found in the shop/supermarket that you have chosen.
Answer : Ingredient
Quantity per cake
Price in 2009 (R m) m)
Price in 2010 (R M) M)
Price index 2010 based 2009 P
Self-raising flour
250g
0.90
1.40
Sugar
200g
0.35
0.28
Butter
250g
3.30
3.70
Eggs (Grade A)
5eggs(300g)
1.25
1.85
= =
II. Composite index =
= 127.32
= Thus,
III. 109.797
=
Part 2(c) : 16
=
i. Find out from reliable sources how to determine suitable capacity of air-conditioner to be installed based on volume/si vo lume/size ze of a room. roo m. ii. Work in group to estimate the vo lume 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 school libary, how many butter cakes must your class sell in order to buy the air conditioner?
Answer : How to Calculate Calculate : y
y
eliable R eliable
Part 3 17
from the internet from the technician (electrical/home suppliance)
Volume = Area of the libary × Height He ight of the libary determine the shape of the libary from plan of the libary determine how to find the area according acco rding to yhe shape o f 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 est imate the number of air conditioner needed
y
sources
As a commite member for the carnivel, you are required to prepared an estimate budget to organise this year¶s carnival. The commite has take into consideration 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%. a) Complete Table 3 based on the information given above.
Answer: Expenditure
Food Games Transportation Decorations Prizes Tents Miscellaneous
Amount in 2009 (R M) M) 1200.00 500.00 300.00 200.00 600.00 800.00 400.00
Amount in 2010 (R M) M)
Price Index
Weight
1.15 × 1200 = 1380 1 × 500 = 500 1.15 × 300 = 345 1 × 200 = 200 1 × 600 = 600 1.15 × 800 = 920 1.3 × 400 = 520
115 100 115 100 100 115 130
12 5 9 2 6 8 4
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 :
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 :
Thus, Given
that
18
=
= 124.61 (2 d.p)
19
FUR THE THER EXPLONATION Index numbers are being used in many different daily situations, for example air po llution llution 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
The Air 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 t he health classifications used by the Malaysian government to determine determine the API in a specific area:
0-50
Good
51-100 Moderate
101-200 Unhealthy
201-300 Very unhealthy
>300
Hazardous
If 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 activities which are under the private sector in the reporting area excluding the food sector.
20
Body mass index
A graph of body bod y 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 on ased on W orld orld H ealth ealth Organization
data here.
The body mass index (BMI), or Quetelet index, is a statistical measure of body weight based on a person's weight and height. Though it does not actually measure the percentage of body fat, it is used to estimate a healthy body weight based 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 are underweight, overweightor obese. It was invented between 1830 and 1850 by the Belgianpolymath Adolphe Quetelet during the course of developing "social "soc ial physics".Body mass index is defined as the individual's individual's body weight divided by the square of his or her height. The formulae universally used in medicine produce 2
a unit of measure of kg/m . BMI can also be determined using a BMI chart. which displays BMI as a function of weight (horizontal (ho rizontal axis) and height (vertical axis) using contour lines for different values of BMI or colours for different BMI categories.
21
SI units
Imperial units
Usage While the formula previously called the Quetelet Index for BMI dates to the 19th century, the t he new term "body mass index" for the ratio and its po pularity pularity date to a paper published in the July edition of 1972 in the J ournal of ournal of C h t he BMI to Chronic ronic Diseases by Ancel Keys, which found the be the best proxy for body fat percentage among ratios rat ios of weight and height; the interest in measuring body fat being due to obesity becoming a discernible issue in prospero us Western societies. BMI was explicitly cited by Keys as being appropriate for population population studies, studies, and inappropriate for individual diagnosis. Nevertheless, due to its simplicity, simplicity, it came to be widely used for individual diagnosis, diagnos is, despite its inappropriateness. BMI provided a simple numeric measure o f a person's "fatness" or "thinness", allowing health professionals 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 nu merical authority for medical diagnosis, but that was never t he BMI's purpose; it is meant to be used as a simple means of classifying sedentary (physically inactive) individuals with an average bod y composition. For these individuals, the current value settings are as follows: a BMI of 18.5 to 25 may indicate optimal weight; a BMI lower than 18.5 suggests the person is underweightwhile a number above a bove 25 may indicate tthe he person is overweight; a BMI below 17.5 may indicate the person has anorexia nervosa or a related disorder; a number above 30 suggests the person is obese (over 40, morbidly obese).
22
For a given height, BMI is proportional to weight. However, for a g iven weight, BMI is inversely proportional to the square of the height. So, if all body dimensions double, and weight scales naturally with the cube of o f the height, then BMI doubles instead of o f remaining the same. This results in taller people having a reported repo rted BMI that is uncharacteristically high compared to their actual body fat levels. In comparison, thePonderal index is based on this natural scaling of weight with the third power of o f the height. However, many taller people are not just "scaled up" short people, but tend to have narrower frames in proportion to their height. It has been suggested that instead of squaring the body bo dy height (as the BMI does) do es) or cubing the body height (as the Ponderal index does), it would be more appropriate to use an exponent of between 2.3 and 2.7.
23
CONCLUSION
After doing research, answering questions, drawing graphs and some problem solving, I saw that the usage of index number 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 essecities. Without it, surveys can¶t be conducted, the stock market can¶t be interpret and many more. So ,we , we should be thankful of the peo ple who contribute in the idea of o f statistics.
24
EFLECTION R EFLECTION
After spending countless hours, days and night to finish this project and also sacrificing 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
25
