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    Sekolah Menengah Agama Persekutuan Kajang, 43000 Kajang, Selangor. Curriculum Development Division Ministry Of Education Malaysia Additional Mathematics ProjectWork 2/2013

    Name I/C Number Class

    : Ummu Aina Nabilah Bt Shaiful Azmi : 960325-10-6304 : 5 Zuhal

    Teachers Name : Madam Siti Azzah Bt Yaacob Date : 10 Jun 2013

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    CONTENTNO. TITTLE PAGE

    1.

    Acknowledgement

    2.

    Objectives

    3.

    Part I

    4.

    Part II

    5.

    Part III

    6.

    Part IV

    7.

    Reflection

    8.

    Reference

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    ACKNOWLEDGEMENTFirst of all, I wish to express gratitude to Allah SWT for His guidance and alsogive me strength and health to do this project work. Finally, the Additional Mathematics Project Work 2 was successfully completed with inspiration, the gift and the instructions were given by Him. Peace and blessings be upon our Prophet Muhammad SAW and the family, next to his companions and tabiin, the gentlemen scholars until the servants of God who follow in their footsteps. Not forgotten to my parents who always make sure that I have been educating and nurturing of smallthough this day in devotion to God Almighty. They also had providing everythingsuch as money , to buy anything that are related to this project, their advice,which is the most needed for this project and facilities such as internet, books, computers and all that. They also supported me and encouraged me to completethis task so that I will not procrastinate in doing it. Then, infinity of appreciation and gratitude goes to my teacher, Madam Azzah bt Yaacob for guiding throughout this project. Even I had some difficulties in doing this task, but she taught me patiently until we knew what to do. She tried and tried to teach me untilI understand what I am supposed to do with the project work. Besides, my friends who were doing this project with me. Even this project is individually but weare cooperated doing this project especially in discussion and sharing ideas toensure our task will finish completely. Last but not least, any party which involved either directly or indirect in completing this project work. May Allah givea great reward for all His servants that are always helpful in upholding His religion. Thank you everyone.

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    OBJECTIVES Every student taking Additional Mathematics is required to carry out a project work in Form 5. The aims of carrying out project work are: a. to apply and adapta variety of problem- solving strategies to solve problems; b. to improve thinking skills; c. to promote effective mathematical communication; d. to develop mathematical knowledge through problem solving in a way that increases students interest and confidence; e. to use the language of mathematics to express mathematical ideas precisely; f. to provide learning environment that stimulates and enhances effective learning; g. to develop positive attitude towards mathematics.

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    PART I

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    a. Describe in brief i. Price Index ii. Weightage iii. Composite index PRICE INDEX

    Measure of change in a set of prices, consisting of a series of numbers arrangedso that a comparison of the values for any two periods or places will show thechange in prices between periods or the difference in prices between places. Price indexes were first developed to measure changes in the cost of living in order to determine the wage increases necessary to maintain a constant standard of living. There are two basic types. Laspeyres-type indexes define a market basketof goods in a base period, then use the prices for those goods to examine changeover space and time. In its simplest form, this is simply the ratio of what those goods cost today to what they cost in the base period. The two most familiarindexes of this type are the consumer price index (CPI) and the producer price index (PPI). The CPI measures changes in retail prices in such component parts asfood, clothing, and shelter. The PPI (formerly called the wholesale price index) measures changes in the prices charged by manufacturers and wholesalers. Paschal-type indexes define a market basket of goods in the current period, then usethe prices of those goods from past periods. The most familiar index of this type is the GDP deflator, used in the U.S. in the national income accounting to differentiate amounts in constant dollars from those in current dollars. WEIGHTAGE

    Weightage means preference of one product in comparison to other product. On theother hand we can say weightage means giving the value of the specific or particular matter or subject higher or lesser than that of or in comparison to simila

    r one. The factors of weightage are The more risk, the more weightage, the longer the period, more the risk, more the uses of Banks facility, less the weightageand last but not least less the Uses of Banks facility, more the benefit weightage and moral dimension or ethical values. 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 performanceover time. Usually, a composite index has a large number of factors which are averaged together to form a product representative of an overall market or sector.For example, the Nasdaq Composite index is a market capitalization-weighted grouping of approximately 5,000 stocks listed on the Nasdaq market. These indexes are useful tools for measuring and tracking price level changes to an entire stock market or sector. Therefore, they provide a useful benchmark against which to

    measure an investor

    s portfolio. The goal of a well diversified portfolio is usually to outperform the main composite indexes.

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    b. State four ways of weightage representations. Find the examples of the representations using internet or any printed materials. Degree For example :

    Bar chart For example :

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    Ratio For example :

    Pie chart For example :

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    PART II

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    We often hear complaints from the public about inflation. It causes an increasein the household expenditure in a family. The household expenditure for every family is different. a. Complete Table 1 for your familys monthly expenditure for the year 2013

    Item

    Average Monthly Expenditure for the year 2013 (to the nearest RM) 700 650

    Percentage of monthly expenses (to the nearest %) 13 12

    Food Accomodation (Rental / Loan) Transportation (Petrol/ Loan / Bus fare etc) Clothing Education Recreation Utilities (Water / Electricity / Telephone) Medication Miscellaneous TOTAL Table 1

    350 450 1500 200 350 300 1000 5500

    6 8 28 4 6 5 18 100

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    My Family s Monthly Expenditure5% 6% 6% 4% Education 28% Miscellaneous Food Accomodation 8% Clothing RecreationTransportation 12% 18% 13% Medication Utilities

    Comment : My family used up money on education as education is important in ourlife. My family often buys new books every weeks as for us reading is the key tosuccess in life no matter how much the cost of the book. Instead, my family used least money on recreation due to busy of works and studies.

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    b. If we want to compare the cost of living from one year to another, we have tocalculate 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 considerthe average monthly expenses of any previous year as the base year. Select theappropriate year as the base year.

    My Familys Monthly Expenditure Base on Year 2011Mont h/ Item Jan Feb Mac April May Jun July Aug Sept Oct Nov Dis Total Avera geFood 580 610 600 600 610 600 580 580 600 610 580 600 596 Accomoda tion 550 540 530 550 550 540 550 560 550 545 550 560 548 Transporta tion 250 230 240 250 250 250 260 255 260 250 245 250 250 Clothi ng 350 340 350 350 350 350 350 350 350 350350 350 350 Educati on 1350 1340 1300 1300 1310 1320 1300 1300 1280 1300 1285 1280 1305 Recreat ion 80 90 100 90 100 100 100 90 80 100 120 110 97 Utiliti es 280 250 260 250 245 250 260 250 240 245 250 255 253 Medicat ion 180 190 200 200 190 190 200 170 180 200 220 210 194 Miscellane ous 880 910 920 910 895 900 900 945960 900 900 885 908

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    My familys monthly expenditure based on year 2013Mont h/ Item (RM) Jan Feb Mac April May Jun July Aug Oct Nov Dis Total Avera geFoo d 710 690 690 700 695 710 700 710 700 700 700 642 Accomodat ion 650 650 640660 640 650 650 650 655 635 650 594 Transporta tion 365 365 340 350 350 340 355340 350 350 350 321 Clothi ng 440 440 450 455 450 460 440 450 455 450 450 412 Educati on 1550 1510 1500 1450 1500 1490 1510 1500 1480 1500 1500 1374 Recreati on210 200 220 200 180 200 180 190 220 200 200 183 Utiliti es 350 350 345 350 345350 350 345 350 355 350 320 Medicati on 290 300 280 300 310 300 315 300 290 310300 275 Miscellane ous 935 995 1035 1035 1030 1000 1000 1015 1000 1000 1000 920

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    ii.

    Hence, complete Table 2 below :

    Item Food Accomodation (Rental / Loan) Transportation (Petrol / Loan / Bus fareetc) Clothing Education Recreation Utilities (Water / Electricity / Telephone) Medication Miscellaneous TOTAL

    Average monthly expenses for the year 2011 as the base year (RM) 596 548 250 3501305 97 252 194 908 4500 Table 2

    Average monthly expenses for the year 2013 (RM) 642 594 321 412 1374 183 320 275920 5041

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    c. ) 3 ty / Telephone) Medication Miscellaneous TOTAL

    Price indices for the 2013 based on the year 2011 108 108 128 118 105 189 127 142 101 1126

    Weightage 35 35 41 38 34 60 40 45 32 360

    ii) Hence, calculate the composite index for the average monthly expenditure inthe year 2013 based on the selected base year.

    = 101.94 d. Make a conclusion about your familys expenditure based on your findings. From the findings, I can see the increasing of my familys expenditure especially on recreation. When all of us are bigger, more pressure on us as more thinghave to be done. So, spending time with family for recreation will be the best solution for us to handle the pressure.

    = 36698 360

    = 108(35) + 108(35) + 128(41) + 118(38) + 105(34) + 189(60) + 127(40) + 142(45)+ 101(32) 35 + 35 + 41 + 38 + 34 + 60 + 40 + 45 + 32

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    PART III

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    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 differentshops. 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.

    Cash paymentSize of Television (inches) 24 32 40 24 32 40 Price (RM) Shop A 1650 2050 2999 1900 2300 3050 Shop B 1900 2300 3150 2300 2500 3300 Table 4(a) Shop C 1500 1980 2890 1650 2050 3000 Mean Price (RM) 1683 2110 3013 1950 2283 3117 Standard Deviation (RM) 168.4 137.4 106.6 267.7 188.2 123.1

    Brand

    A

    B

    Payment by installmentBrand Size of Television (inches) 24 32 40 24 32 40 Price (RM) Shop A 1950 23503299 2200 2600 3350 Shop B 2185 2585 3435 2585 2785 3585 Table 4(b) Shop C 19502430 3340 2100 2500 3450 Mean Price (RM) 2028 2455 3358 2295 2628 3462 Standard

    Deviation (RM) 116.7 97.55 56.96 209.1 125.3 83.45

    A

    B

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    b. Determine the brand and size of the television that you have decided to buy.Give your reasons based on the findings from part (a) above. I have decided to buy television from brand A with the size of 40 inch. The reasons of my choice arebecause the prices for brand A are more cheaper than brand B paid by cash nor installment. We can see it from my findings as the measure of dispersion for brand A is lower than brand B. The lower the measure of dispersion from the mean andstandard deviation from zero, the lower the prices of the televisions. So, I strongly choose television from brand A with the size 40 inch.

    c. The Ministry of Domestic Trade and Consumer Affairs wishes to present the Fair Prices Shop Award for one of the above shops. If you are one of the panels forthis award, determine the shops that deserve the award. Do you consider the value of mean and the value of standard deviation in making your decision? Give your justification. In my opinion, the Fair Prices Shop Award should be given to Shop B. As one of the panels, I consider the value of mean and the value of standard deviation in making my decision as I think it is important for us to know theunit of dispersion for each shop. Here are the brief reason why I used the method. The mean of set of prices the sum of the prices divided by the number of prices. Along with the median and the mode, the mean is just one measure of the central tendency of a set of scores, but the mean is by far the most common and themost useful. Although the mean tells us where the center of a set of scores is,it does not tell us how variable those scores are. So in addition to a measureof central tendency, we need a measure of variability. Standard deviation measures how spread out the values in a data set are around the mean. More precisely,

    it is a measure of the average distance between the values of the data in the set and the mean. If the data values are all similar, then the standard deviationwill be low (closer to zero). If the data values are highly variable, then the standard variation is high (further from zero). So, from my calculation and findings it is clearly shown that Shop B have a lower measure of dispersion means theprices is maintain at one stage. So, in my opinion I will choose Shop B to receive the Fair Prices Shop Award.

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    PART IV

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    a. Your family has a fixed monthly income. In order to buy the television, yourfamily needs to make some adjustment on the various types of expenditure. [You can choose to pay by cash or by installment] Show the average monthly expenditurethat you have modified in a table. b. Assuming you has just started working with a monthly salary of RM 2500. You intend to save 10% of your salary every month. Plan your monthly expenditure as in Table 1 above and add other items such assavings and contributions to your parents.

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    REFLECTIONWhile doing this project, I have spent countless hours doing this project. I realized that this subject is compulsory to me. Without it, I cant fulfill my big dreams and wishes.

    I used to Hate Additional Mathematics It always make me wonder why this subject is so difficult It always an absolute obstacle for me Throughout day and night I sacrificed my precious time to have fun From Monday, Tuesday, Wednesday, Thursday, Friday And even the weekend that I always looking forward to From now on, I will domy best on every second That I will learn Additional Mathematics full of effort!!! And with the help of Madam Azzah

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