Additional Mathematics 2013 - Fini

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ADDITIONAL MATHEMATICS PROJECT WORK 2013 INDEX NUMBER Name : Mariam Syafini Bt Mohd Saidi Class : 5 Al-Khawarizmi School : Sekolah Menengah Sains Tengku Abdullah, Raub Teacher : Pn. Faizatul Farah Bt Zulkifli

CONTENT Additional Mathematics Project Work 2013

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1. 2. 3. 4.

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ACKNOWLEDGEMENT OBJECTIVES HISTORY OF INDEX NUMBER PART 1

4 5-6

a) b) c) d)

Collecting items Record the items in table Graphical Representations Interpreting , discussing and drawing conclusions e) Identifying and reasoning the large price difference

5.

7-19

PART 2 a) Completing the table b) Calculation of price index c) Calculation of composite index d) Suggesting and reasoning

6. 7. 8.

20-24

PART 3 FURTHER EXPLORATION REFLECTION

ACKNOWLEDGEMENT

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25-28 29-30 31

Alhamdulillah, a big thanks to Allah to give me strength and good health to complete this project. First and foremost, special thanks I give to my beloved parents, Mohd Saidi Bin Ali and Shimaton Binti Hashim for their strong support. They always help me and also supplying equipments and money needed to complete this project. I also would like to thank to my Additional Mathematics teacher, Puan Faizatul Farah Binti Zulkifli as she gives us important guides and commitment during this project work. She helps me by giving some examples of last year student’s project. All problems that I had can be solved by my teacher. Next, a lot of thanks to all my friends for helping me by sharing some ideas and informations regarding this project. We also had made some discussions about this project and try to solve some problems together. Last but not least, I would like to thank to my beloved sister, Mariam Syafiqah Binti Mohd Saidi for giving some helps about this project. She can helps me a lot as she had done the same project but different title last year. She can guide me on how to make this project complete.

OBJECTIVES Additional Mathematics Project Work 2013

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This project carries aims such as :  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 their thinking skills.

 Experience classroom environments 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 highly encouraged 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 problemsolving in ways that increases interest and confidence.

 Prepare students’ for the demands of their future undertakings and in workplace.  Realise that mathematics is an important and powerful tool in solving real-life problems and hence develop positive attitude towards mathematics.

 Train themselves not only to be independent learners but also to collarate, to cooperate, and to share knowledge in an engaging and healthy environment.

 Use technology especially the ICT appropriately and effectively.  Train themselves to appreciate the intrinsic values of mathematics and to become more creative and innovative.

 Realise the importance and the beauty of mathematics.

HISTORY OF Additional Mathematics Project Work 2013

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INDEX NUMBER Index numbers are meant to study the change in the effects of such factors which cannot be measured directly. According to Bowley, Index numbers are used to measure the changes in some quantity which we cannot observe directly. For example, changes in business activity in a country are not capable of direct measurement but it is possible to study relative changes in business activity by studying the variations in the values of some such factors which affect business activity, and which are capable of direct measurement. Index numbers are commonly used statistical device for measuring the combined fluctuations in a group related variables. If we wish to compare the pricelevel of consumer items today with that prevalent ten years ago, we are not interested in comparing the prices of only one item, but in comparing some sort of average price levels. We may wish to compare the present agricultural production or industrial production with that at the time of independence. How do we obtain a composite measure? This composite measure is provided by index numbers which may be defined as adevice for combining the variations that have come in group of related variables over a period of time, with a view to obtain a figure that represents the result of the change in the constitute variables. Index numbers may be classified in terms of the variables that they are intended to measure. In business, different groups of variables in the measurement of which index number techniques are commonly used are (i) price, (ii) quantity, (iii) value and (iv) business activity. Thus, we have index of wholesale prices, index of consumer prices, index of industrial output, index of value of exports and index of business activity, etc. Here we shall be mainly interested in index numbers of prices showing changes with respect to time, although methods described can be applied to other cases. In general, the present level of prices is compared with the level of prices in the past. The present period is called the current period and some period in the past is called the base period.

Index Numbers

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Index numbers are statistical measures designed to show changes in a variable or group of related variables with respect to time, geographic location or other characteristics such as income, profession, etc. A collection of index numbers for different years, locations, etc., is sometimes called an index series.

Simple Index Number : A simple index number is a number that measures a relative change ina single variable with respect to a base.

Composite Index Number : A composite index number is a number that measures an averagerelative changes in a group of relative variables with respect to a base.

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. TheWhole Price Index (WPI). Consumer Price Index (CPI) are some of the popularly used price indices.

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 arecomparing quantities in two different years or over a period of time. It is thequantity 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.

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P A R T O N Additional Mathematics Project Work 2013

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E a)

Collecting items Foods 1.

KINDER BUENO

2. MOUNTAIN DEW

3. TASTO POTATO CHIPS

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Detergent 1.

DAIA DETERGENT POWDER

2. COMFORT ULTRA

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3. DYNAMO DETERGENT

Stationary 1.

G-SOFT MECHANICAL PENCIL

2. UHU GLUE STICK

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3. STABILO EXAM GRADE ERASER

b)

CATEGORY

Record the items in table

PRICE(RM )

ITEMS

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FOOD

ECONSAVE

COLD STORAGE

GIANT

1. KINDER BUENO (43g)

3.20

4.10

3.50

2. MOUNTAI N DEW (600ml) 3. TASTO POTATO CHIPS (13g)

2.89

3.30

3.29

3.50

3.70

3.62

TOTAL PRICE

9.59

11.10

10.41

TABLE A ( FOOD )

CATEGORY

PRICE(RM)

ITEMS

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DETERGENT

ECONSAVE

COLD STORAGE

GIANT

1. DAIA

13.99

14.20

13.70

2. COMFORT ULTRA

7.99

8.20

7.60

3. DYNAMO

12.99

13.20

12.70

TOTAL PRICE

34.97

35.60

34.00

TABLE B ( DETERGENT )

Additional Mathematics Project Work 2013 CATEGORY ITEMS

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PRICE(RM)

ECONSAVE

COLD STORAGE

GIANT

2.10

2.50

2.20

2. UHU GLUE STICK

1.50

2.00

1.60

3. STABILO EXAM GRADE ERASER

1.00

1.20

0.80

TOTAL PRICE

4.60

5.70

5.60

1. G-SOFT MECHANICA L PENCIL

STATIONARY

TABLE C ( STATIONARY )

c)

Graphical Representations

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FOOD CATEGORY 12

10

8

GIANT

6

COLD STORAGE ECONSAVE 4

2

0 KINDER BUENO

MOUNTAIN DEW

TASTO POTATO CHIPS

DETERGENT CATEGORY Additional Mathematics Project Work 2013

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45 40 35 30 25

GIANT COLD STORAGE

20

ECONSAVE

15 10 5 0 DAIA

COMFORT ULTRA

DYNAMO

STATIONARY CATEGORY

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8

7

6

5

4

GIANT COLD STORAGE ECONSAVE

3

2

1

0 G-SOFT MECHANICAL PENCIL

UHU GLUE STICK

STABILO EXAM GRADE ERASER

OVERALL TOTAL Additional Mathematics Project Work 2013

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TOTAL PRICE ITEMS ACCORDING SHOPS

GIANT COLD STORAGE ECONSAVE

d) Interpreting, discussing and drawing Additional Mathematics Project Work 2013

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conclusions Based on the graphical representations that I have constructed in Part 1(c), there are large and small price difference between the three items in each category. The items are sold in three different shops which are categorised as Shop A, Shop B and Shop C. The shops are Econsave Supermarket, Giant Supermarket, Cold Storage Supermarket. According to the food category, the largest price difference seen is the Tasto Potato Chips while the smallest price difference seen is the Mountain Dew. Moreover, based on the detergent category, the largest price difference seen is Daia Detergent Powder while the two others can be categorised as the small price difference. Then, in the stationary category, the largest price difference seen is G-Soft Mechanical Pencil while the smallest price difference seen is Stabilo Exam Grade Eraser. Lastly, I will compare the total price for each category. For the food category the highest total price is the items sold in the Cold Storage Supermarket while the lowest total price is the items sold in the Econsave Supermarket. For the detergent category, the highest total price is also the items sold in the Cold Storage Supermarket while the lowest total price is the items sold in the Giant Supermarket. Based on the last category which is stationary, the highest total price and the smallest total price is the items sold in the same shops as the in the food category.

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e) Identifying and reasoning the large price difference Based on the graphical representations that I have constructed in Part 1(c), there are large and small price difference between the three items in each category. The items are sold in three different shops which are categorised as Shop A, Shop B and Shop C. The shops are Econsave Supermarket, Giant Supermarket, Cold Storage Supermarket. According to the food category, the largest price difference seen is the Tasto Potato Chips while the smallest price difference seen is the Mountain Dew. Moreover, based on the detergent category, the largest price difference seen is Daia Detergent Powder while the two others can be categorised as the small price difference. Then, in the stationary category, the largest price difference seen is G-Soft Mechanical Pencil while the smallest price difference seen is Stabilo Exam Grade Eraser. As for conclusions, there are many reasons based on the largest and smallest price difference. One of it is the the quality and the size of the items. Usually the better quality may come with expensive price also the items that is in bigger size. The other reasons that I can conclude is that the place where the shops are located. For example, the Cold Storage Supermarket is usually located in a luxurious shopping complex such as in the Mid Valley Megamall. Then, the price of most of items may come with quite expensive price.

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P A R T T W Additional Mathematics Project Work 2013

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O a)

Completing the table

Items (for 10 packets of Nasi Lemak)

Quantity

Price in the year 2012(RM)

Price in the year 2013(RM)

For the flavoured rice : I

Rice Santan Onion Ginger Salt For the Sambal :

1 kg 150 g 10 g 10 g 2g

2.70 1.40 0.15 0.15 0.05

3.20 2.20 0.30 0.40 0.15

II

Red Onion Garlic Dried Chillies Ikan Bilis Cooking Oil Miscellaneous :

10 g 5g 100 g 200 g 100 g

0.05 0.04 1.00 2.00 0.25

0.15 0.10 1.20 2.50 0.50

III

Fried groundnuts Fried crispy Ikan Bilis Cucumber 5 Eggs Banana leaves (1 bundle)

200 g 150 g 200 g 300 g 300 g

0.50 1.50 0.20 1.50 1.00

0.80 2.20 0.60 2.00 1.80

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b)

Calculation of price index

The table below shows the price index for each of the items 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 (for 10 packets of Nasi Lemak)

Price in the year 2012(RM)

Price in the year 2013(RM)

Price Index

2.70 1.40 0.15 0.15 0.05

3.20

118.519 157.143 200.000 266.667 300.000

For the flavoured rice : Rice Santan Onion Ginger Salt For the Sambal : Red Onion Garlic Dried Chillies Ikan Bilis Cooking Oil Additional Mathematics Project Work 2013

0.05 0.04 1.00 2.00 0.25

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2.20 0.30 0.40 0.15 0.15 0.10 1.20 2.50 0.50

300.000 250.000 120.000 125.000 200.000

Miscellaneous : Fried groundnuts Fried crispy Ikan Bilis Cucumber 5 Eggs Banana leaves (1 bundle) Total Price

0.50 1.50 0.20 1.50 1.00 12.34

0.80 2.20 0.60 2.00 1.80

18.10

160.000 146.667 300.000 133.333 180.000 2957.329

c) Calculation of composite index By using formula, Ī = where ∑ ∑

∑ ∑

,

- sum of price index × weightage - sum of weightage

The table below shows the composite index for the cost of a packet of nasi lemak in the year 2013 based on the year 2012.

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Items (for 10 packets of Nasi Lemak) For the flavoured rice : Rice Santan Onion Ginger Salt For the Sambal : Red Onion Garlic Dried Chillies Ikan Bilis Cooking Oil Miscellaneous : Fried groundnuts Fried crispy Ikan Bilis Cucumber 5 Eggs Banana leaves (1 bundle) Total

Price Index , I

Weightage , w

118.519 157.143 200.000 266.667 300.000

1000 g 150 g 10 g 10 g 2g

118519.00 23571.45 2000.00 2666.67 600.00

300.000 250.000 120.000 125.000 200.000

10 g 5g 100 g 200 g 100 g

3000.00 1250.00 12000.00 25000.00 20000.00

160.000 146.667 300.000 133.333 180.000 2957.329

200 g 150 g 200 g 300 g 300 g 2737 g

32000.00 22000.05 60000.00 39999.9 54000.00 8094209.47

Based on the formula given from the previous page,

Ī= Ī=

∑ ∑

,

,

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Ī = 2957.33 The answer above is the composite index for the cost of 10 packets of nasi lemak. To find the composite index, the composite index for the cost of a packet of nasi lemak, the answer above must be divided by 10. So,

Ī= Ī = 295.73

d)

Suggesting and reasoning

In the year 2012, the nasi lemak was sold at RM2.00 each. For this year which is 2013, I think we should sell the nasi lemak at RM2.50 each. The reasons are because the cost of a packet of nasi lemak in the year 2013 is higher than the cost in the year 2012. The price for 2013 of the nasi lemak is affordable for students.

P A Additional Mathematics Project Work 2013

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

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a) Suggesting, reasoning and illustrating My suggestion is that my school should install sixteen CCTVs in order to upgrade the security of my school. Eight CCTVs should be placed at the hostel area while the eight others should be placed at the school area. It is because the cameras can prevent discipline problems from happening especially at the hostel area. The teachers can use the CCTVs provided to control students when the teachers are not around the hostel area or even around the school area. I also had illustrate a plan to show where the CCTVs should be placed.

SCHOOL AREA - Closed-Circuit TV ( CCTV )

SCHOOL FIELD

GUARD

CANTEEN

TECHNO BLOCK

BLOCK C (BUDI)

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BLOCK B (AMAL)

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BLOCK A (ILMU)

MAIN HALL

HOSTEL AREA ( ASPURA ) - Closed-Circuit TV ( CCTV )

BLOCK D (MARIKH)

BLOCK C (MUSYTARI)

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BLOCK B (ZUHAL)

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BLOCK A (KEJORA)

HOSTEL AREA ( ASPURI ) - Closed-Circuit TV ( CCTV )

BLOCK F (MARIKH ZUHAL)

BLOCK E (MUSYTARI KEJORA)

b)

I had viewed a website which is http://www.lelong.com.my. In the website, there are some lists that shows some of the prices of CCTVs for school in Malaysia. The cost of installation of the CCTV is about RM312.50 each. So, the total cost of installation for the sixteen CCTV is about RM5000.

c)

My class have to sell about 200 packets of nasi lemak if my class intends to sponsor 10% of the cost for the installations. This is because 10% of RM5000 is RM500. If we managed to sell at least 300 packets of nasi lemak with price of each packet is RM2.50, we will get about RM750. We will give the school RM500 while the balance of the money can be save as our class’s saving.

d)

I am very sure that my class will achieve the 10% target. This is because the number of students in our school is not so many so we can easily achieve our target. Moreover, I think my class should not carry out a different project instead but if they want to, they can carry out a project such as selling drinks, biscuits, cupcakes and others.

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FURTHER EXPLORATION Index numbers are being used in many different daily situations, for example, air pollution index, stock market index, gold index and property index. I had obtain some informations from the internet a nd also other reliable sources on the importance of two different types of index numbers of my choice. I had chosen stock market index and air pollution index to be elaborate on the use and the importance of the index numbers in daily life situations.

THE IMPORTANCE OF STOCK MARKET INDEX Although the stock market is much more dynamic than the indexes suggest, along with the fact that there are different ways to calculate the indexes, causing calculation bias, the stock market indexes are useful in a number of ways to stock investors. First, the market indexes provide an historical perspective of stock market performance, giving investors more insight into their investment decisions. Investors who do not know which individual stocks to invest in can use indexing as a method of choosing their stock investments. By wanting to match the performance of the market, investors can invest in index mutual funds or index exchange-traded funds (ETFs) that track the performance of the indexes with which they are aligned. This form of investing gives investors the opportunity to do as well as the markets and not significantly underperform the markets. The second benefit of stock market indexes is that they provide a yardstick with which investors can compare the performance of their individual stock portfolios. Individual investors with professionally managed portfolios can use the indexes to determine how well their managers are doing in managing their money. The third major use of stock market indexes is as a forecasting tool. Studying the historical performance of the stock market indexes, you can forecast trends in the market. The Internet bubble is a prime example, which in hindsight provides 20/20 vision. The price-to-earnings (P/E) ratio of the stock markets was in the high 20s to low 30s in 1999–2000, indicating that the markets could not sustain the rapid increase in stock prices. The P/E ratio for the market historically has ranged between the high single digits and the low 30s, with an average around 15. The P/E ratio for the S&P 500 was 17 on August 4, 2006, an indication that the stock market was not particularly overvalued. Consequently, the market indexes provide investors with a useful tool for forecasting trends in the market.

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THE IMPORTANCE OF AIR POLLUTION INDEX

Air quality is defined as a measure of the condition of air relative to the requirements of one or more biotic species or to any human need or purpose. 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. The AQI can go up (meaning worse air quality) due to a lack of dilution of air pollutants. Stagnant air, often caused by an anticyclone, temperature inversion, or low wind speeds lets air pollution remain in a local area, leading to high concentrations of pollutants and hazy conditions. An agency might encourage members of the public to take public transportation or work from home when AQI levels are high. Most air contaminants do not have an associated AQI. Many countries monitor ground-level ozone, particulates, sulfur dioxide, carbon monoxide and nitrogen dioxide and calculate air quality indices for these pollutants.

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REFLECTION While conducting this project, I had learnt so many knowledge. I had found that Additional Mathematics is not a boring subject but it is a fun subject same as Mathematics Modern. It just that this subject is a little bit difficult. This subject could helps us too much in our daily life. Other than that, I had learnt that it is more important to give cooperation and helps also ideas among our friends. Without all of that, I am sure that this project will not be done completely. Sharing informations are also needed and important. Last but not least, the moral values that I had learnt are we should never give up and give more efforts to complete our work. This is because we will achieve success if we have more efforts towards our lessons and also our work.

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