ADDITIONAL MATHEMATICS PROJECT WORK 2013 SELANGOR (PROJECT 2)

Transcription

1 ADDITIONAL MATHEMATICS PROJECT WORK 2013 SELANGOR (PROJECT 2) NAME:Wan Nur Emilly Bt Wan Mohd Ariffin CLASS:5 Science3 NO I.C: TEARCHER NAME:PUAN ROIAMAH BASRI

2 CONTENT content page 1. rubric 2 2. content 3 3. introduction 4 4. objective 5 5. Appreciate 6 6. Part Part Part Part 4 18 Reflection 19

3 OBJECTIVE The aims of carrying out project work are : i) To apply and adapt a variety of problem solving strategies to solve problems; ii) To improve thinking skills iii) To promote effective mathematical communication iv) To develop mathematical knowledge through problem solving in a way that increases students interest and confidence v) To use the language of mathematical to express mathemical ideas precisely vi) To provide learning environment that stimulates and enhances effective learning vii) To develop positive attitude towards mathematics

4 APPRECIATE First of all, I wish to express gratitude to Allah s.w.t for his guidance and also giving me the strength to do this project work. Finally, the additional mathematics project work was successfully completed with the inspiration, the gift and the instruction were given by Him. Not forgotten my parents for providing everything, such as money, to buy anything that are related to this project work and their advise, support which are the most needed for this project. Internet, books, computers and all that. They also supported me and encouraged me to complete this task so that I will not procrastinate in doing it. Beside that My father teacher at SMK taman tasik, ampang, Selangor puan rhoimah for sharing ideas to ensure our task will finish completely. Then I would like to thank my teacher, 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 our ideas. They were helpful that when we combined and discussed together, we had this task done.

5 INTRODUCTION (source: 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 price level of consumer items today with that prevalentten 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. Here again, we have to consider all items of production and each item may have undergone a different fractional increase (or even a decrease). How do we obtain a composite measure This composite measure is provided by index numbers which may be defined as advice 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 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 in a single variable with respect to a base. Composite Index Number A composite index number is a number that measures an average relative changes in a group of relative variables with respect to a base.

6 PART 1 (a)describe in brief (i) price index, (ii) weightage (iii) composite index Answer Price index An index number expressing the level of a group of commodity prices relative to the level of the prices of the same commodities during an arbitrarily chosen base period and used to indicate changes in the level of prices from one period to another. Weightage The assignment of a quota(as of members of a legislature)to a particular segment of the population as a special favor or concession in a proportion above that allowable on a strictly numerical basis. Composite index A grouping of equities, indexes or other factors combined in a standardized way, providing a useful statistical measure of overall market or sector performance over time.

7 (b) state four ways of weightage representations.find the examples of the representations using internet or any printed materials. i) Pie chart pie chart 1st Qtr 2nd Qtr 3rd Qtr 4th Qtr ii) Bar Chart Category 1 Category 2 Category 3 Category 4 Series 1 Series 2 Series 3 iii) Percentage

8 PART2 We often hear complaints from the public about inflation. It causes an increase in the household expenditure in a family. The household expenditure for every family is different. a)complete Table 1 for your family s monthly expenditure for thr year Monthly salary Number of family members RM Item Average monthly expenditure for the year 2013 (to the nearest RM) Food Accommodation (Rental/Loan) Transportation (Petrol/loan/bus fare etc) Clothing Education Recreation Utilities (Water/Electricity/Telephone) Medication Miscellaneous TOTAL Percentage of monthly expenses (to the nearest %)

9 b) If we want to compare the cost of living from one year to another, we have to calculate the price index that involves some of the items mentioned above. (i) In order to calculate the price index of all the items above, we have to consider the average monthly expenses of any previous year as the base year. Answer: Item Average monthly expenses for the base year 2008 (RM) Food Accommodation (Rental/Loan) Transportation 450 (Petrol/Loan/Bus fare etc) Clothing 120 Education 1000 Recreation 150 Utilities 180 (Water/Electricity/Telephone) Medication 200 Miscellaneous 1000 TOTAL 4000

10 (ii) Hence, complete Table 2 below Item Average monthly expenses for the year 2008 as the base year (RM) Food Accommodation (Rental/Loan) Transportation (Petrol/Loan/Bus fare etc) Clothing Education Recreation Utilities (Water/Electricity/Telephone) Medication Miscellaneous TOTAL TABLE 2 (c) (i) Complete Table 3 on the above information. Average monthly expenses for the year 2013 (RM) Item Price Indices for the Weightage year 2013 based on the year 2008 Food Accomodation(Rental/Loan) Transportation(Petro/Loan/Bus fare etc) Clothing Education Recreation Utilites(Water/Electricity/Telephone) Medication Miscellanous TOTAL Table 3

11 Formula to calculate price index : ii) Hence, calculate the composite index for the average monthly expenditure in the year 2013 based on the selected base year. Answer : Formula to calculate composite index : Formula ; I = price index/index number W = weightage = (d) Make a conclusion about your family's expenditure based on your findings. Answer : The conclusion is the conjecture is correct. Conjecture is average money expenses for year 2012 is to be lower than year 2013.

12 PART 3 Your family is planning to buy a new television set. (a) You have conducted a survey on the price of the television for two different brands from three different shops. You would like to make a comparison between two modes of payment, namely, cash payment and payment by installment. Table 4 (a) shows the prices of televisions by cash payment in three different shops whereas Table 4(b) shows the prices of televisions by installment. Complete Table 4 (a) and 4(b) using the data you obtained Answer: Brand Size of TV (Inches) Price (RM) Shop A Shop B Shop C Mean Price(RM) Standard deviation (RM) samsung penasonic TABLE 4(a)

13 Brand Price (RM) Mean price (RM) Standard deviation (RM) Hup liong Ramli electronics and hardware TS SH Table4(b) b) I want to buy a size 32 inch TS television. This is because there are only five member sin my family and only requires medium-sized television for our living room. I choose this brand because I am confident of its quality as our family has long been using this brand for other electrical appliances in our home. Although the brand TS is m oreexpensive than the brand SH, our family still can afford to buy it. I plan to buy from Ramli Electronics & Hardware store because they offer 2 years of warranty. In addition, they also offer the lowest price of televisions compared to the other two shops.

14 c) If I am one of the panel for the award, I would prefer Ramli Electronics & Hardwareshop because the mean price of all types of television for both brands is the lowest compared to the other two shops. Standard deviation for the telivisons at the shop isalso the lowest. It shows that the prices of television offered by the Ramli Electronics& Hardware shop is reasonable and affordable.

15 Part 4 a)the average monthly expenditure that you have modified in a table Item Average monthly expenditure (RM) Modified expenditure (RM) food Accomondation (rental/loan) Transportation (petrol/loan/bus fare etc) Clothing Education Recreation Utilities (water/electricity/telephone) Medication miscellaneous television TOTAL

16 Item Average monthly expenditure (RM) Food 400 Accommodation (rental/loan) 300 Transportation (petrol/loan/bus fare etc) 200 Clothing 100 Education 100 Recreation 50 Utilities (water/electricity/telephone) 100 Medication 100 Savings 250 Parents 600 Miscellaneous 300 TOTAL 2500

17 CONCLUSION Rich countries are able to achieve high level of literacy instead only a few poor countries achieved stable literacy level. REFLECTION While I conducting this project, a lot of information that I had found. I have learnt how index number appear in our daily life. Apart from that, this project encourages the student to work together and share their knowledge. It is also encourage student to gather information from the internet, improve thinking skills and promote effective mathematical communication. Not only that, I had learned some moral values that I practice. This project had taught me to responsible on the works that are given to me to be completed. This project also had made me felt more confidence to do works and not to give easily when we could not find the solution for the question. I also learned to be more discipline on time, which I was given about three weeks to complete this project and pass up to my teacher just in time. I also enjoy doing this project I spend my time with friends to complete this project and it had tighten our friendship. Last but not least, I proposed this project should be continue because it brings a lot of moral value to the student and also test the students understanding in Additional Mathematics. END OF PROJECT