add math project 2013.docx

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CONTENT

NAME : AZIZUL HAKIMI B. ZULKAFLEE

IC NUMBER : 960722-33-5071

CLASS : 5 AL – KHAWARIZMI

TEACHER : PUAN FAIZATUL FARAH BINTI ZULKIFLI



CONTENT 2

APPRECIATION 3

OBJECTIVES 4

QUESTION 2 5

PART 1 6-21

PART 2 22-30

PART 3 30-32

FURTHER EXPLORATION 33-36

REFLECTION 372

APPRECIATION



First of all, Grateful to Allah s.w.t for enabling my Additional Mathematics project work Form 5

2013 to be finished successfully.

Thanks to my teacher, Puan Faizatul Farah for helping me in the process of completing this

project work. Indeed, without the help of her, this project work will certainly very difficult for

me to finish in the given time.

Next, I want to say thanks to my parents for providing everything that I need for making this

project work, such as money, laptop and advised that help me to finished this work. They also

supported me to complete this task so that I will not wasting my time with doing unbeneficial

work.

Therefore, a lots of thanks to all my friends who always supporting me. We had made some

discussion and sharing ideas about the project to ensure the work will finish completely.

Thanks go out to all the employees of Aktif Supermarket, Tong Fat Value Mart and Tunas Manja

Supermarket that taking the time to be interviewed by me. Indeed, without the cooperation

from them, I sure that this project will not be completed. Thanks to them.

3

OBJECTIVES



Every student taking Additional Mathematics is required to carry out a project work while they

are in Form 5. This year, the Curriculum Development Division, Ministry of Education has

prepared two tasks. Students are to choose and complete only one task based on their area of interest. Upon completion of the Additional Mathematic Project Work, it is hoped that students

will gain valuable experiences and able to:

Apply and adapt a variety of problem-solving strategies to solve routine and non-routine

problems,

Experience classroom environments which are challenging, interesting and meaningful

and hence improve thinking skills,

Experience classroom environments where expressing ones mathematical thinking,

reasoning and communication are highly encouraged and expected, Acquire effective mathematical communication through oral and writing and to use the

language of mathematics to express mathematical ideas correctly and precisely,

Prepare students; for demands of their future undertakings and in workplace,

Train students 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 and effectively,

Train students to appreciate the intrinsic values of mathematics and to become more

creative and innovative,

Realize the importance and beauty of mathematics.

4

QUESTION 2



BACKGROUNDThe prices of goods sold in shops vary from one shop to another. Shoppers tend to buy goods

which are reasonably priced, giving value for their money. We, as consumers, should learn to

spend wisely and keep our daily expenses to the minimum.

5



PART 1

6



PART 1

(A)

Collecting items

(food, detergent and stationary)

7

FOOD



OREO Cookies

AYAMAS Chicken Nugget

Solivite

8

DETERGENT



BREEZE Detergent

ATTACK Detergent

VANISH Detergent

9

STATIONARY



UHU Glue Stick

PAPERMATE Correction Fluid

STABILO Highlighter

10



PART 1

(B)

Record the items in table(Table A, Table B & Table C)

11

Category Item

Price (RM)

Shop A

Aktif

Supermarket

Shop B

Tong Fat Value

Mart

Shop C

Tunas Manja

Supermarket

Food

OREO

Cookies 3.20 3.50 3.00



(300 g)

AYAMAS

Chicken Nugget

(850 gm)l

8.55 9.15 8.90

Solivite(5x125ml) 4.10 3.55 3.59

Total Price 15.85 16.20 15.49

Table 1(a)

Category Item

Price (RM)

Shop A

Aktif Supermarket

Shop B

Tong Fat ValueMart

Shop C

Tunas ManjaSupermarket

Detergent

BREEZE

Detergent

(1000 ml)

6.50 6.20 6.90

ATTACK

Detergent

(1000 ml)

7.10 7.50 7.90

VANISH

Detergent(800 ml)

21.70 28.50 25.00

Total Price 35.30 42.20 39.80

Table 1(b)

12

Category Item

Price (RM)

Shop A

Aktif

Supermarket

Shop B

Tong Fat Value

Mart

Shop C

Tunas Manja

Supermarket

UHU



Stationary Glue

Stick

3.99 4.80 3.65

PAPERMATE

Correction

Fluid

4.20 3.90 4.50

STABILO

Highlighter 4.30 4.20 4.60

Total Price 12.49 12.90 12.75

Table 1(c)

13



PART 1(C)

Graphical representations

14

FOOD CATEGORY



15

0

5

10

15

20

25

30

OREO COOKIES AYAMAS Chicken

Nugget

Solivite

Tunas Manja

Tong Fat2

Aktif



Graph 1(b)

16

DETERGENT CATEGORY

0

1

2

3

4

5

6

7

8

9

10

OREO Cookies AYAMAS Chicken

Nugget

Fernleaf Solivite

Aktif Supermarket

Tong Fat Value Mart

Tunas Manja Supermarket



17

0

10

20

30

40

50

60

70

80

BREEZE

Deterent

ATTACk

Detergent

VANISH

Detergent


Tong Fat Value Mart

Aktif Supermarket



Graph 1(a)

18

0

5

10

15

20

25

30

BREEZE Detergent ATTACK Detergent VANISH Detergent

Aktif Supermarket

Tong Fat Value Mart




STATIONARY CATEGORY

19

0

2

4

6

8

10

12

14

UHU Glue Stick PAPERMATE

Correction

Fluid

STABILO

Highlighter


Tong Fat Value Mart

Aktif Supermarket



Graph 1(c)

20

0

1

2

3

4

5

6

UHU Glue Stick PAPERMATE

Correction Fluid

STABILO Highlighter

Aktif Supermarket

Tong Fat Value Mart

Tunas Manja

Supermarket



e)

Based on the graphical representations that I have constructed in Part 1(c), we can see that

there are large and small price different among three shops that are Aktif Supermarket,

Tong Fat Value Mart and Tunas Manja Supermarket in each category.

In the food category, we can see that the largest price difference is the AYAMAS

Chicken Nugget while the smallest price different is OREO Cookies. In the detergent

category, we can see that a large price different for VANISH Detergent and the small

price different for the other two detergent. In the stationary category, a large price

different can be seen for UHU Glue Stick while the other two items just show a small

price different.

Next when we compared the total price for each category, we can see that for food

category the highest total price is Tong Fat Value Mart while the lowest total price is

Tunas Manja Supermarket. In the detergent category, the highest total price is Tong Fat

Value Mart while the lowest total price is Aktif Supermarket. In the last category which

is stationary, the highest total price is Tunas Manja Supermarket while the lowest total

price is once again Aktif Supermarket.

As a conclusion, we as a consumer can see that different shops offer different prices

for the same product. So, we must think carefully before buying anything. We are

encouraged to compare the prices between any shop before buying anything. The

decision is in our hand. So remember to make a right decision.

e)

I have identify an item that has a large price difference among the shops. Detergent has

a large price difference among the shops. In my opinion the situations occur due to a

few relevant reasons. First of all, it is about the location of the shop. The shop located in

the big city such as Tong Fat Value Mart sold their goods in higher prices while the other

two shops that are located in the sub-city offer a lower price.

Secondly, it is about the quality of product. The more quality product will have ahigher price. The more you pay , the more quality the detergent you will get.

21



PART 2

22



PART 2

(A)

Completing the table

23

Every year my school will organizes a carnival to raise fund for school improvement projects.

This year my school plans to install CCTV in order to enhance its security. Last year, during the



carnival, my class made and sold nasilemak. Due to the popularity of this local food, my class

has decided to carry out the same project for this year’s carnival.

a) I have observed the prices of the given items in making nasilemak for the year 2013. I

have recorded it in Table 2.

Items

(for 10 packets of NasiLemak )

Quantity Price in the year

2012(RM)

Price in the year

2013(RM)

I

For the flavoured rice :

Rice 1 kg 2.70 3.40

Santan 150 g 1.40 2.00

Onion 10 g 0.15 0.30

Ginger 10 g 0.15 0.25

Salt 2 g 0.05 0.10

II

For the Sambal :

Red Onion 10 g 0.05 0.15

Garlic 5 g 0.04 0.10

Dried Chillies 100 g 1.00 1.60

IkanBilis 200 g 2.00 2.80

Cooking Oil 100 g 0.25 0.60

III

Miscellaneous :

Fried groundnuts 200 g 0.50 0.70

Fried crispy IkanBilis 150 g 1.50 2.40Cucumber 200 g 0.20 0.50

5 Eggs 300 g 1.50 2.40

Banana leaves (1 bundle) 300 g 1.00 1.60

Table 2

24



PART 2

(B)Calculate the price index

25

a) I have calculated the price index for each of the items in Table 2 for the year 2013 based

on the year 2012.



By using formula, I =

X 100 ,

where Q1 - Price in the year 2013

Q0 -Price in the year 2012

Items


Price in the year

2012(RM)

Price in the year

2013(RM)

Price Index


Rice 2.70 3.40 125.926

Santan 1.40 2.00 142.857

Onion 0.15 0.30 200.000

Ginger 0.15 0.25 166.667

Salt 0.05 0.10 200.000For the Sambal :

Red Onion 0.05 0.15 300.000

Garlic 0.04 0.10 250.000

Dried Chillies 1.00 1.60 160.000

IkanBilis 2.00 2.80 140.000

Cooking Oil 0.25 0.60 240.000

Miscellaneous :

Fried groundnuts 0.50 0.70 140.000

Fried crispy IkanBilis 1.50 2.40 160.000Cucumber 0.20 0.50 250.000

5 Eggs 1.50 2.40 160.000

Banana leaves (1 bundle) 1.00 1.60 160.000

Total Price 12.34 17.30 2795.450

Table 3

26



PART 2

(C)

Calculate the composite index

27

a) I have calculated the composite index for the cost of a packet of nasilemak in the year

2013 based on the year 2012.



By using formula,Ī =∑

∑,

where∑ - sum of price index times weightage

∑ - sum of weightage

We can calculate the composite index for the cost of a packet of nasilemak in the year

2013 based on the year 2012. We use quantity of an item as the weightage.

Items


Price Index , I Weightage , w


Rice 125.926 1000 g 125926.00

Santan 142.857 150 g 21428.55

Onion 200.000 10 g 2000.00

Ginger 166.667 10 g 1666.67

Salt 200.000 2 g 400.00

For the Sambal :

Red Onion 300.000 10 g 3000.00

Garlic 250.000 5 g 1250.00

Dried Chillies 160.000 100 g 16000.00

IkanBilis 140.000 200 g 28000.00

Cooking Oil 240.000 100 g 24000.00

Miscellaneous :

Fried groundnuts 140.000 200 g 28000.00

Fried crispy IkanBilis 160.000 150 g 24000.00

Cucumber 250.000 200 g 50000.00

5 Eggs 160.000 300 g 48000.00

Banana leaves (1 bundle) 160.000 300 g 48000.00

Total 2795.450 2737 g 421671.22

28



PART 2

(D)

Calculate the suitable selling price

29

Referring back to the formula above,

Ī =∑

∑,

Ī =

,



Ī = 154.06

The answer above is the composite index for the cost of 10 packets of nasilemak , to find

the composite index for the cost of a packet of nasilemak , the answer above must be

divided by 10.

So,

Ī =

Ī =15.41

b) In the year 2012, the nasilemak was sold at RM2.00 each. For this year, i suggest we

should sell nasilemak at RM2.50 each. It is because the cost of a packets of nasilemak in

the year 2013 is higher than the cost in the year 2012. The price of each item in the year

2013 is also higher compared to 2012. In addition, I think that RM2.50 is an affordable

price for the student nowadays. So, it will not burn a hole in their pockets.

30



PART 3

31

In order to upgrade the security, my school has decided to install closed-circuit TV (CCTV).

a) I suggest that my school should install sixteen cameras in order to upgrade the security

of my school. Eight cameras should be placed in the hostel’s compound while the rest

can be placed in the academic block’s compound. It is because the cameras can prevent

crimes from happening, especially in the hostel. Cases of theft, burglary, truancy,

bullying and so on can be prevented from occurring. Teachers also can monitor students

more effectively. I also have made a plan of the placement of the cameras.

GUARD

CAMERA



32

FURTHER EXPLORATION

Index number is being used in many different daily situations, for example, air pollution index,

stock market index, gold index and property index.

Price index

CANTEENMAIN

HALL

BLOCKA

BLOCKB

BLOCK

C

BLOCK

D

COMPUTER

LAB

BLOCK

F

BLOCK

E

BLOCK

D

BLOCK

C

BLOCK

B

BLOCK

A



A price index ( plural : ³price indices´ or ³price indexes´) is a normalized average(typically a

weighted average) 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 economy's price level or a cost of living. More narrow price indices can help

producers with business plans and pricing. Sometimes, they can be useful in helping to guide

investment . Some notable price indices include:

Consumer price index

Producer price index

GDP deflator

33

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 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 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 perhapsthe 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

260years. He argued on behalf of the Oxford students and published his findings anonymously

in a volume entitled ChroniconPreciosum.

34

I have obtained some information from the internet or other reliable sources on the

importance of two difference types of index number of my choice.

The first index number is Air Pollution Index

The Air Pollution Index (API) is a simple and generalized way to describe the air quality

in China, Hong Kong and Malaysia. It is calculated from several sets of air pollution data.

In mainland China the API was replaced by an updated Air Quality Index in early 2012.

China

China's State Environment Protection Agency (SEPA) is responsible for measuring the level of air

pollutions in China. As of 28 August 2008, SEPA monitors daily pollution level in 86 of its major

cities. The API level is based on the level of 5 atmospheric pollutants, namely sulfur

http://en.wikipedia.org/wiki/China

http://en.wikipedia.org/wiki/Hong_Kong

http://en.wikipedia.org/wiki/Malaysia

http://en.wikipedia.org/wiki/Mainland_China

http://en.wikipedia.org/wiki/Air_Quality_Index

http://en.wikipedia.org/wiki/SEPA

http://en.wikipedia.org/wiki/Sulfur_dioxide


http://en.wikipedia.org/wiki/SEPA

http://en.wikipedia.org/wiki/Air_Quality_Index

http://en.wikipedia.org/wiki/Mainland_China

http://en.wikipedia.org/wiki/Malaysia

http://en.wikipedia.org/wiki/Hong_Kong

http://en.wikipedia.org/wiki/China



dioxide (SO2), nitrogen dioxide (NO2), suspended particulates (PM10), carbon monoxide (CO),

and ozone (O3) measured at the monitoring stations throughout each city.

API Mechanics

An individual score is assigned to the level of each pollutant and the final API is the highest of those 5 scores. The pollutants can be measured quite differently. SO2, NO2 and

PM10 concentration are measured as average per day. CO and O3 are more harmful and are

measured as average per hour. The final API value is calculated per day.

The scale for each pollutant is non-linear, as is the final API score. Thus an API of 100 does not

mean twice the pollution of API at 50, nor does it mean twice as harmful. While an API of 50

from day 1 to 182 and API of 100 from day 183 to 365 do provide an annual average of 75, it

does not mean the pollution is acceptable even if the benchmark of 100 is deemed safe. This is

because the benchmark is a 24 hour target. The annual average must match against the annual

target. It is entirely possible to have safe air every day of the year but still fail the annual

pollution benchmark.

35

The second index number is Stock market index

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

market. It is computed from the prices of selected stocks (sometimes a weighted average). It is

a tool used by investors and financial managers to describe the market, and to compare the

return on specific investments. An index is a mathematical construct, so it may not be invested in directly. But many mutual

funds and exchange-traded funds attempt to "track" an index (see index fund), and those funds

that do may not be judged against those that do not.

Types of indexes [edit]


http://en.wikipedia.org/wiki/Nitrogen_dioxide

http://en.wikipedia.org/wiki/Particulate

http://en.wikipedia.org/wiki/Carbon_monoxide

http://en.wikipedia.org/wiki/Ozone

http://en.wikipedia.org/wiki/Stock_market


http://en.wikipedia.org/wiki/Stock

http://en.wikipedia.org/wiki/Weighted_average

http://en.wikipedia.org/wiki/Investor

http://en.wikipedia.org/wiki/Portfolio_(finance)

http://en.wikipedia.org/wiki/Mutual_fund


http://en.wikipedia.org/wiki/Exchange-traded_fund

http://en.wikipedia.org/wiki/Index_fund

http://en.wikipedia.org/w/index.php?title=Stock_market_index&action=edit&section=1

http://en.wikipedia.org/w/index.php?title=Stock_market_index&action=edit&section=1

http://en.wikipedia.org/wiki/Index_fund

http://en.wikipedia.org/wiki/Exchange-traded_fund



http://en.wikipedia.org/wiki/Portfolio_(finance)

http://en.wikipedia.org/wiki/Investor

http://en.wikipedia.org/wiki/Weighted_average

http://en.wikipedia.org/wiki/Stock



http://en.wikipedia.org/wiki/Ozone

http://en.wikipedia.org/wiki/Carbon_monoxide

http://en.wikipedia.org/wiki/Particulate

http://en.wikipedia.org/wiki/Nitrogen_dioxide




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.

A 'national' index represents the performance of the stock market of a given nation—and byproxy, 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, the

BrazilianIbovespa, the Russian RTSI, the Indian SENSEX 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 or limited

partnerships), NASDAQ and American Stock Exchange. Russell Investment Group added to the

family of indices by launching the Russel 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.

36

REFLECTION

After doing research, I had learned many values and I learned that the usage of index number is

important in our daily life . This project work had taught me to be more confident when doing

something especially the homework given by the teacher. I also learned to be a disciplined type

of student which is always sharp on time while doing some work and researching the

information from the internet. Without my teacher, parents, and my friends, I will never have

http://en.wikipedia.org/wiki/MSCI_World

http://en.wikipedia.org/wiki/S%26P_Global_100

http://en.wikipedia.org/wiki/S%26P_500

http://en.wikipedia.org/wiki/Nikkei_225

http://en.wikipedia.org/wiki/Ibovespa

http://en.wikipedia.org/wiki/SENSEX

http://en.wikipedia.org/wiki/FTSE_100

http://en.wikipedia.org/wiki/Wilshire_5000

http://en.wikipedia.org/wiki/United_States


http://en.wikipedia.org/wiki/New_York_Stock_Exchange

http://en.wikipedia.org/wiki/American_Depositary_Receipt

http://en.wikipedia.org/wiki/Limited_partnership


http://en.wikipedia.org/wiki/NASDAQ

http://en.wikipedia.org/wiki/American_Stock_Exchange

http://en.wikipedia.org/wiki/Russell_Investment_Group

http://en.wikipedia.org/w/index.php?title=Wilshire_US_REIT&action=edit&redlink=1


http://en.wikipedia.org/wiki/Real_estate_investment_trust


http://en.wikipedia.org/w/index.php?title=Morgan_Stanley_Biotech_Index&action=edit&redlink=1


http://en.wikipedia.org/wiki/Biotechnology

http://en.wikipedia.org/wiki/Linux_Weekly_News


http://en.wikipedia.org/wiki/Linux

http://en.wikipedia.org/wiki/Linux



http://en.wikipedia.org/wiki/Biotechnology


http://en.wikipedia.org/w/index.php?title=Morgan_Stanley_Biotech_Index&action=edit&redlink=1




http://en.wikipedia.org/w/index.php?title=Wilshire_US_REIT&action=edit&redlink=1

http://en.wikipedia.org/wiki/Russell_Investment_Group

http://en.wikipedia.org/wiki/American_Stock_Exchange

http://en.wikipedia.org/wiki/NASDAQ



http://en.wikipedia.org/wiki/American_Depositary_Receipt

http://en.wikipedia.org/wiki/New_York_Stock_Exchange



http://en.wikipedia.org/wiki/Wilshire_5000

http://en.wikipedia.org/wiki/FTSE_100

http://en.wikipedia.org/wiki/SENSEX

http://en.wikipedia.org/wiki/Ibovespa

http://en.wikipedia.org/wiki/Nikkei_225

http://en.wikipedia.org/wiki/S%26P_500

http://en.wikipedia.org/wiki/S%26P_Global_100

http://en.wikipedia.org/wiki/MSCI_World



an effort to finished this project. So, thanks to them for helping me to finished this project

successfully.

37

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add math project 2013.docx