project work add math

7/28/2019 Project Work ADD MATH

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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


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


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


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


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

project work add math

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