additional mathematics 2013 - fini

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ADDITIONAL MATHEMATICS

PROJECT WORK 2013

INDEX NUMBERName : 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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NO. TITLE PAGE

1. ACKNOWLEDGEMENT

2. OBJECTIVES3. HISTORY OF INDEX

NUMBER4. PART 1

a) Collecting itemsb) Record the items in

tablec) Graphical

Representationsd) Interpreting ,

discussing and drawing conclusions

e) Identifying and reasoning the large price difference

5. PART 2a) Completing the tableb) Calculation of price

indexc) Calculation of

composite indexd) Suggesting and

reasoning

6. PART 37. FURTHER

EXPLORATION8. CONCLUSION


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ACKNOWLEDGEMENT

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.


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OBJECTIVES

This project carries aims such as :

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 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 problem-solving 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.


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HISTORY OF

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


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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.

I ndex Numbers

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 IndexThe 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.


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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.

P

A

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T Additional Mathematics Project Work 2013

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O

N

E

a) Collecting items

Foods

1. KINDER BUENO

2. MOUNTAIN DEW


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3. TASTO POTATO CHIPS

Detergent

1. DAIA DETERGENT POWDER


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2. COMFORT ULTRA

3. DYNAMO DETERGENT

Stationary

1. G-SOFT MECHANICAL PENCIL

2. UHU GLUE STICK


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3. STABILO EXAM GRADE ERASER

b) Record the items in table

CATEGORY

ITEMS PRICE(RM)

ECONSAVE

COLD STORAG

E

GIANT


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FOOD

1. KINDER BUENO (43g)

3.20 4.10 3.50

2. MOUNTAIN DEW (600ml)

2.89 3.30 3.29

3. TASTO POTATO CHIPS (13g)

3.50 3.70 3.62

TOTAL PRICE

9.59 11.10 10.41

TABLE A ( FOOD )

CATEGORY ITEMS PRICE(RM)

ECONSAVE

COLD STORAG

E

GIANT

1. DAIA

13.99 14.20 13.7


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DETERGENT

02.

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 )

CATEGORY ITEMS PRICE(RM)


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ECONSAVE

COLD STORAG

E

GIANT

STATIONARY

1. G-SOFT

MECHANICAL PENCIL

2.10 2.50 2.20

2. UHU GLUE STICK 1.50 2.00 1.603. STABILO

EXAM GRADE ERASER

1.00 1.20 0.80

TOTAL PRICE

4.60 5.70 5.60

TABLE C ( STATIONARY )


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c) Graphical Representations

FOOD CATEGORY

KINDER BUENO MOUNTAIN DEW TASTO POTATO CHIPS

0

2

4

6

8

10

12

GIANTCOLD STORAGEECONSAVE


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DETERGENT CATEGORY

DAIA COMFORT ULTRA DYNAMO0

5

10

15

20

25

30

35

40

45



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STATIONARY CATEGORY

G-SOFT MECHAN-ICAL PENCIL

UHU GLUE STICK STABILO EXAM GRADE ERASER

0

1

2

3

4

5

6

7

8



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OVERALL TOTAL

TOTAL PRICE ITEMS ACCORDING SHOPS



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d) Interpreting, discussing and drawing 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 differenceseen 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 differenceseen 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


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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.

P

A

R

T Additional Mathematics Project Work 2013

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T

W

Oa) Completing the table

Items(for 10 packets of Nasi Lemak)

Quantity Price in the year

2012(RM)

Price in the year

2013(RM)

I

For the flavoured rice :

Rice 1 kg 2.70 3.20Santan 150 g 1.40 2.20Onion 10 g 0.15 0.30Ginger 10 g 0.15 0.40Salt 2 g 0.05 0.15

II

For the Sambal :

Red Onion 10 g 0.05 0.15Garlic 5 g 0.04 0.10Dried Chillies 100 g 1.00 1.20Ikan Bilis 200 g 2.00 2.50


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Cooking Oil 100 g 0.25 0.50

III

Miscellaneous :

Fried groundnuts 200 g 0.50 0.80Fried crispy Ikan Bilis 150 g 1.50 2.20Cucumber 200 g 0.20 0.605 Eggs 300 g 1.50 2.00Banana leaves (1 bundle)

300 g 1.00 1.80

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 = Q1Q0 X 100 ,

where Q1 - Price in the year 2013 Q0 - Price in the year 2012

Items(for 10 packets of Nasi

Price in the year

Price in the year

Price Index


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Lemak) 2012(RM) 2013(RM)For the flavoured rice :Rice 2.70 3.20

Santan 1.40 2.20

Onion 0.15 0.30

Ginger 0.15 0.40

Salt 0.05 0.15

For the Sambal :Red Onion 0.05 0.15

Garlic 0.04 0.10

Dried Chillies 1.00 1.20

Ikan Bilis 2.00 2.50

Cooking Oil 0.25 0.50

Miscellaneous :Fried groundnuts 0.50 0.80

Fried crispy Ikan Bilis 1.50 2.20

Cucumber 0.20 0.60

5 Eggs 1.50 2.00

Banana leaves (1 bundle)

1.00 1.80

Total Price 12.34


additional mathematics 2013 - fini

Documents

project complete

project carries

year students project

reallife problems

mathematical ideas

additional mathematics

language of mathematics

nonroutine problems