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    Sekolah Menengah Agama Persekutuan Kajang,

    43000 Kajang, Selangor.

    Curriculum Development Division Ministry Of

    Education Malaysia

    Additional Mathematics Project Work 2/2013

    Name : Ummu Aina Nabilah Bt Shaiful Azmi

    I/C Number : 960325-10-6304

    Class : 5 Zuhal

    Teachers Name : Madam Siti Azzah Bt Yaacob

    Date : 10 Jun 2013

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    CONTENT

    NO. 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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    ACKNOWLEDGEMENT

    First of all, I wish to express gratitude to Allah SWT for His guidance and

    also give 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 small though this day in devotion to God Almighty.They also had providing everything such 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 complete this 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 until I 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 we are cooperated doing this project especially in discussion

    and sharing ideas to ensure our task will finish completely.

    Last but not least, any party which involved either directly or indirect incompleting this project work. May Allah give a 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 tocarry out a project work in Form 5.

    The aims of carrying out project work are:a.to apply and adapt a 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 expressmathematical ideas precisely;

    f. to provide learning environment that stimulates andenhances effective learning;

    g.to develop positive attitude towards mathematics.

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    PART I

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    a. Describe in briefi. Price Index

    ii. Weightageiii. Composite index

    PRICE INDEXMeasure of change in a set of prices, consisting of a series of numbers arranged so that a comparison of

    the values for any two periods or places will show the change 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 basket of goods in a base period,

    then use the prices for those goods to examine change over 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

    familiar indexes 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 as food, 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 use

    the 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.

    WEIGHTAGEWeightage means preference of one product in comparison to other product. On the other hand we can

    say weightage means giving the value of the specific or particular matter or subject higher or lesser thanthat of or in comparison to similar 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 weightage and last but not

    least less the Uses of Banks facility, more the benefit weightage and moral dimension or ethical values.

    COMPOSITE INDEXA 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. 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 usinginternet 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 increase in 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)

    Percentage of

    monthly

    expenses

    (to the nearest

    %)

    Food 700 13

    Accomodation

    (Rental / Loan)650 12

    Transportation

    (Petrol/ Loan / Bus fare etc)350 6

    Clothing 450 8

    Education 1500 28

    Recreation 200 4

    Utilities(Water / Electricity / Telephone)

    350 6

    Medication 300 5

    Miscellaneous 1000 18

    TOTAL 5500 100

    Table 1

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    Comment :

    My family used up money on education as education is important in our life. My family often buys new

    books every weeks as for us reading is the key to success 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.

    28%

    18%

    13%

    12%

    8%

    6%

    6%

    5%4%

    My Family's Monthly Expenditure

    Education

    Miscellaneous

    Food

    Accomodation

    Clothing

    Recreation

    Transportation

    Medication

    Utilities

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    b. If we want to compare the cost of living from one year to another, we have to calculate the priceindex 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 averagemonthly expenses of any previous year as the base year. Select the appropriate year as the

    base year.

    My Familys Monthly Expenditure Base on Year 2011

    Mont

    h/

    Item

    FoodAccomoda

    tion

    Transporta

    tion

    Clothi

    ng

    Educati

    on

    Recreat

    ion

    Utiliti

    es

    Medicat

    ion

    Miscellane

    ous

    Jan 580 550 250 350 1350 80 280 180 880

    Feb 610 540 230 340 1340 90 250 190 910

    Mac 600 530 240 350 1300 100 260 200 920

    April 600 550 250 350 1300 90 250 200 910

    May 610 550 250 350 1310 100 245 190 895

    Jun 600 540 250 350 1320 100 250 190 900

    July 580 550 260 350 1300 100 260 200 900

    Aug 580 560 255 350 1300 90 250 170 945

    Sept 600 550 260 350 1280 80 240 180 960

    Oct 610 545 250 350 1300 100 245 200 900

    Nov 580 550 245 350 1285 120 250 220 900

    Dis 600 560 250 350 1280 110 255 210 885

    Total

    Avera

    ge

    596 548 250 350 1305 97 253 194 908

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    My familys monthly expenditure based on year 2013

    Mont

    h/

    Item

    (RM)

    Foo

    d

    Accomodat

    ion

    Transporta

    tion

    Clothi

    ng

    Educati

    on

    Recreati

    on

    Utiliti

    es

    Medicati

    on

    Miscellane

    ous

    Jan 710 650 365 440 1550 210 350 290 935

    Feb 690 650 365 440 1510 200 350 300 995

    Mac 690 640 340 450 1500 220 345 280 1035

    April 700 660 350 455 1450 200 350 300 1035

    May 695 640 350 450 1500 180 345 310 1030

    Jun 710 650 340 460 1490 200 350 300 1000

    July 700 650 355 440 1510 180 350 315 1000

    Aug 710 650 340 450 1500 190 345 300 1015

    Oct 700 655 350 455 1480 220 350 290 1000

    Nov 700 635 350 450 1500 200 355 310 1000

    Dis 700 650 350 450 1500 200 350 300 1000

    Total

    Avera

    ge

    642 594 321 412 1374 183 320 275 920

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    ii. Hence, complete Table 2 below :

    ItemAverage monthly

    expenses for the year

    2011 as the base year(RM)

    Average monthly

    expenses for the year

    2013(RM)

    Food 596 642

    Accomodation

    (Rental / Loan)548 594

    Transportation

    (Petrol / Loan / Bus fare etc)250 321

    Clothing 350 412

    Education 1305 1374

    Recreation 97 183

    Utilities

    (Water / Electricity / Telephone)252 320

    Medication 194 275

    Miscellaneous 908 920

    TOTAL 4500 5041

    Table 2

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    c. ) 3 .Item

    Price indices for the 2013 based

    on the year 2011Weightage

    Food 108 35

    Accomodation

    (Rental / Loan)108 35

    Transportation

    (Petrol / Loan / Bus fare etc)128 41

    Clothing 118 38

    Education 105 34

    Recreation 189 60

    Utilities

    (Water / Electricity / Telephone) 127 40

    Medication 142 45

    Miscellaneous 101 32

    TOTAL 1126 360

    ii) Hence, calculate the composite index for the average monthly expenditure in the year 2013 based on

    the selected base year.

    = 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

    = 36698

    360

    = 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 thing have to be done. So, spending time

    with family for recreation will be the best solution for us to handle the pressure.

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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 threedifferent 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.

    Cash payment

    Brand

    Size of

    Television

    (inches)

    Price (RM)

    Mean

    Price(RM)

    Standard

    Deviation

    (RM)Shop A Shop B Shop C

    A

    24 1650 1900 1500 1683 168.4

    32 2050 2300 1980 2110 137.4

    40 2999 3150 2890 3013 106.6

    B

    24 1900 2300 1650 1950 267.7

    32 2300 2500 2050 2283 188.2

    40 3050 3300 3000 3117 123.1

    Table 4(a)

    Payment by installment

    Brand

    Size of

    Television

    (inches)

    Price (RM)

    Mean

    Price

    (RM)

    Standard

    Deviation

    (RM)Shop A Shop B Shop C

    A

    24 1950 2185 1950 2028 116.7

    32 2350 2585 2430 2455 97.55

    40 3299 3435 3340 3358 56.96

    B24 2200 2585 2100 2295 209.1

    32 2600 2785 2500 2628 125.3

    40 3350 3585 3450 3462 83.45

    Table 4(b)

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    b. Determine the brand and size of the television that you have decided to buy. Give your reasons basedon 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 are

    because 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 and standard 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 Awardfor one of the above shops. If you are one of the panels for this 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 the unit 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 the most 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 measure of 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 deviation will 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 the prices 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, your family needs to makesome adjustment on the various types of expenditure.

    [You can choose to pay by cash or by installment]

    Show the average monthly expenditure that 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% ofyour salary every month.

    Plan your monthly expenditure as in Table 1 above and add other items such as savings and

    contributions to your parents.

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    REFLECTION

    While doing this project, I have spent countless hours doing this

    project. I realized that this subject is compulsory to me. Without it, Icant 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 do my best on every second

    That I will learn Additional Mathematics full of effort!!!

    And with the help of Madam Azzah