Add Math Project 2014 Johor State

8/11/2019 Add Math Project 2014 Johor State

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ADDITIONALMATHEMATICS PROJECT

WORK

Title : Expenditure Bantuan Khas AwalPersekolahan 1 Malaysia in Budget2014

Name :

Identity Card Number :

Exam Registration Number :

Group Members :


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ADDITIONAL MATHEMATICS PROJECT WORK 2014

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CONTENT

Title Page

Content 1

Acknowledgement & Appreciation 2

Objective 3

Introduction 4 - 5

Part A 6 - 16

Part B 16 20

Part C 21 23

Further Exploration 24 25

Conclusion 26

Reflection 27 -28


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CKNOWLEDGEMENT ND

PPRECI TION

I would like to express my gratitude and appreciation to all those who helped me to

complete this Additional Mathematics project for this year. Firstly, I would like to thank the

principal of SMK Convent Batu Pahat, Miss Tan Soo Soo, for giving me this opportunity to

do this project.

I would also like to say thank you to my Additional Mathematics teacher , Miss Hjh.

Roesita bt Hashim, for her guidance in order to complete this project. We had some

difficulties in doing this task, but she taught us patiently and gave us guidance throughtout

the journey until we know what to do.

I would like to thank my parents too because they supported me when I am doing this

project. With their cooperation I finish this project successfully. I also want to say thank you

to my team members, Christine Na, Au Hwi Fei, and Joan Lee for their patience, cooperation,

and for sharing their ideas. These helped me to complete my project as it was planned.

Last but not least, I want to appreciate those who helped me directly and also indirectly in

order for me to complete this project. Thank you so much for the endless help that all of you

gave to me. Thank you .


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INTRODUCTION

BANTUAN KHAS AWAL PERSEKOLAHAN 1 MALAYSIA

On 25 October 2013, the Prime Minister cum Finance Minister, Datuk Seri Najib Tun Razak

has approved an allocation of RM540 million for Bantuan Khas Awal Persekolahan 1

Malaysia while presenting the Budget Year 2014.All students from Year 1 to Form 5 for

2014 school session will receive RM 100 each. The purpose of the aid is to lighten the

financial burden of the students parents. Therefore, students are asked to prepare an

additional mathematics project by using statistics, linear law and mathematics reasoning to

perform the governments plan.

The History of statistics can be said to start around 1749 although, over time, there

have been changes to the interpretation of the word statistics . In early times, the meaning was

restricted to information about states. This was later extended to include all collections of

information of all types, and later still it was extended to include the analysis and

interpretation of such data. In modern terms, "statistics" means both sets of collected

information, as in national accounts and temperature records, and analytical work which

requires statistical inference. Statistical activities are often associated with models expressed using probabilities,

and require probability theory for them to be put on a firm theoretical basis: see History of

probability.

A number of statistical concepts have had an important impact on a wide range of

sciences. These include the design of experiments and approaches to statistical inference such

as Bayesian inference, each of which can be considered to have their own sequence in the

development of the ideas underlying modern statistics.

There has three methods to represent the statistics which are histogram, frequency

polygon and orgive.
http://en.wikipedia.org/wiki/Statisticshttp://en.wikipedia.org/wiki/Statisticshttp://en.wikipedia.org/wiki/Statisticshttp://en.wikipedia.org/wiki/Sovereign_statehttp://en.wikipedia.org/wiki/National_accountshttp://en.wikipedia.org/wiki/Temperature_recordhttp://en.wikipedia.org/wiki/Statistical_inferencehttp://en.wikipedia.org/wiki/Probabilityhttp://en.wikipedia.org/wiki/Probability_theoryhttp://en.wikipedia.org/wiki/Theory_(mathematical_logic)http://en.wikipedia.org/wiki/History_of_probabilityhttp://en.wikipedia.org/wiki/History_of_probabilityhttp://en.wikipedia.org/wiki/Design_of_experimentshttp://en.wikipedia.org/wiki/Bayesian_inferencehttp://en.wikipedia.org/wiki/Bayesian_inferencehttp://en.wikipedia.org/wiki/Design_of_experimentshttp://en.wikipedia.org/wiki/History_of_probabilityhttp://en.wikipedia.org/wiki/History_of_probabilityhttp://en.wikipedia.org/wiki/Theory_(mathematical_logic)http://en.wikipedia.org/wiki/Probability_theoryhttp://en.wikipedia.org/wiki/Probabilityhttp://en.wikipedia.org/wiki/Statistical_inferencehttp://en.wikipedia.org/wiki/Temperature_recordhttp://en.wikipedia.org/wiki/National_accountshttp://en.wikipedia.org/wiki/Sovereign_statehttp://en.wikipedia.org/wiki/Statistics


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Histogram is a graphical display of data using bars of different heights.

Example of histogram;

Frequency polygon, line graph is a drawn by joining all the midpoints of the top ofthe bars of a histogram.

Example of frequency polygon;

The graph of the cumulative frequency distribution is better known as cumulative

frequency curve or Ogive.

Example of orgive;


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PART A

a) As a student receiving such aid, I will divide the money into a few parts. I will save 30% of the moneyin the bank that is RM30. I will spend 40% of the money as on education. I will use this RM 40 wisely

by buying reference books, exercise books, stationery and etc. I will use 10% of the aid given forentertainment. Another 20% that is RM 20, will be used to pay my tuition Photostat fees. The piechart below showed the ways I spent the aid.

b) Data on the amount of savings from 40 pupils of 5ST class receiving the Bantuan Khas AwalPersekolahan 1 Malaysia.

Table 1.1:

Total Savings (RM) Number of Pupils

10 0

20 3

30 6

40 11

50 17

60 24

70 32

80 36

90 39

100 40

HOW I SPEND THE AID

SavingsReference Books

Entertaiment

Tuition photostat fees


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Table 1.2:

Total Savings (RM) Number of Pupils

1-10 0

11-20 3

21-30 3

31-40 5

41-50 6

51-60 7

61-70 8

71-80 4

81-90 3

91-100 1

c) Based on the table above,

i) The data is represented by using three different statistical graphs based on the 2 tables

constructed.

Frequency polygon

Bar chart

Orgive


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1. Using FREQUENCY POLYGONbased on Table 1.2.

0

1

2

3

4

5

6

7

8

9

5.5 15.5 25.5 35.5 45.5 55.5 65.5 75.5 85.5 95.5 105.5

N u m

b e r o

f P u p i l s

Total Savings (RM)


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2. Using BAR CHARTbased on Table 1.2

0

1

2

3

4

5

6

7

8

10.5 20.5 30.5 40.5 50.5 60.5 70.5 80.5 90.5 100.5

Series 1, 1

N u m

b e r o

f P u p i l s

Total Savings (RM)


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3. Using OGIVE based on Table 1.1

0

5

10

15

20

25

30

35

40

45

10.5 20.5 30.5 40.5 50.5 60.5 70.5 80.5 90.5 105.5

N u m

b e r o

f P u p i l s

Total savings (RM)


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ii) I find the mean of the total savings by using two methods.

1. Using FORMULA

Total Savings (RM) Midpoint (x) Number of Pupils /Frequency (f)

fx

1-10 5.5 0 0

11-20 15.5 3 46.5

21-30 25.5 3 76.5

31-40 35.5 5 177.5

41-50 45.5 6 27.3

51-60 55.5 7 388.5

61-70 65.5 8 524.0

71-80 75.5 4 302.0

81-90 85.5 3 256.5

91-100 95.5 1 95.5

Total 40 2140

Table 1.2.1 : Total amount of savings from 40 pupils of class 5ST

MEAN, X = fx

f

=2140

140

= 53.5


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2. Using MICROSOFT EXCEL

a. Key in the data collected in the Microsoft Excel.

b. Insert =D12/B12 in the column D14 and press ENTER.


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c. The answer will be shown in the column D14.

d. The final answer is 53.5.


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Standard deviation of total savings is found by using two methods.

1. Using FORMULA OF STANDARD DEVIATION

Total Savings (RM) Number of Pupils /Frequency (f) Midpoint (x) fx fx2

1-10 0 5.5 0 011-20 3 15.5 46.5 720.7521-30 3 25.5 76.5 1950.7531-40 5 35.5 177.5 6301.2541-50 6 45.5 273 12421.551-60 7 55.5 388.5 21561.7561-70 8 65.5 524 3432271-80 4 75.5 302 2280181-90 3 85.5 256.5 21930.75

91-100 1 95.5 95.5 9120.25

Total 40 2140 131130

Table 1.2.2 : Total amount of savings from 40 pupils of class 5ST

2. Using Microsoft Excel

a. Key in table 1.2.2 in the Microsoft Excel.

=

fx

f X2

= 131130

40 53.52

= 20.3966

STANDARD

DEVIATION,


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b. Do a small table to calculate the total frequency, mean and standard deviation.

c. State the total number of frequency and calculate the mean.

d. The standard deviation is calculated by the following step.

SMALL TABLE


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d) If each student is given an additional RM 50 for savings, the new mean and new variance or thetotal savings will be obtained.

New mean = 53.5 + 50

= 103.5

New variance = 20.3961(same as precious variance because when a construct quantity is added, the variance is notaffected.)

PART B

A. Assume that l saved the whole amount of the aid in Bank X which offers annual profitof 3% and is credited annually. I calculate my total savings after 10 years with anassumption that no additional deposit is done by using two methods.

METHOD I1. Using FORMULA of SUM OF GEOMETRIC PROGRESSIONS a. STEP 1 : Form a number sequences

100, 100 x , 100 x .....

100, 103, 106.09 b. STEP 2 : Find the first term, a, and the common ratio, r.

Frist Term, a : 100

Common Ratio, r : = 1.03

c. STEP 3 : Substitute the information into the formulaSn = a {r

n - 1}r 1

S10 = 100 {1.0310 - 1}

1.03 1=1146.3879

d. Total savings after 10 years with a profit of 3% per year in Bank X isRM1146.39

METHOD II

2. Using MICROSOFT EXCELa. Insert 100 in column B2 in the Microsoft Excel.


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b. Insert =B2*1.03 in column B3 and press ENTER.

c. Copy column B3 and paste into column B4.

d. Repeat copying the column above and pasting into the column below untilcolumn B11.

e. Insert =SUM(B2:B11) in column B13 and press ENTER.

f. The final answer is RM1146.39.


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B. Assume that l saved the whole amount of the aid in Bank Y which offers monthly profit of 0.25% and is credited monthly. I calculate my total savings after 10 yearswith an assumption that no additional deposit is done by using two methods.

METHOD I1. Using FORMULA of SUM OF GEOMETRIC PROGRESSIONS a. STEP 1 : Form a number sequences

100, 100100.25/100, 100100.25/100100.25/100 100, 100.25, 100.50

b. STEP 2 : Find the first term, a, and the common ratio, r.Frist Term, a : 100Common Ratio, r : 100.25 100 = 1.0025

c. Let years into month. 10years 12 = 120 months

d. STEP 3 : Substitute the information into the formulaSn = a {r n - 1}

r 1S120 = 100 {1.0025

120 - 1}1.0025 1

=13974.1419e. Total savings after 10 years with a profit of 0.25% per month in Bank Y is

RM13974.14.

METHOD II

2. Using MICROSOFT EXCELa. Insert 100 in column B2 in the Microsoft Excel.

b. Insert =B2*1.0025 in column B3 and press ENTER. c.


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c. Copy column B3 and paste into column B4.

d. Repeat copying the column above and pasting into the column below untilcolumn B121


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e. Insert =SUM(B2:B121) in column B123 and press ENTER.

f. The final answer is RM13974.00.

Discuss of my findings above :

After my calculation, I find out the amount of the total savings after 10 years with assumptionthat no additional deposit is done in the both banks are totally different. By using formulaand Microsoft Excel, the amount of total savings after 10 years in Bank X is about RM1146.39 while the amount of total savings after 10 years in Bank Y is about RM13974.14.Obviously, the total savings after 10 years in Bank Y is more than Bank X. The difference

between the total savings of both banks is about RM12827.75.

If I save the whole amount of the aid, RM100, in Bank Y, I can earn RM13874.14 as interestafter 10 years. But I can only earn RM1046.3879 as interest after 10 years if I save theRM100 in Bank X.Therefore, I prefer to save the RM100 in the Bank Y because I can earnmore interest in Bank Y compare to Bank X.


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PART C

The following are the savings in RM, of two students, Ali and Muthu for the first seven months,

where x is Alis savings and y is Muthus savings.

a) A graph of y against x is drawn by using the data in the table above.

b) A straight line graph is drawn from the equation p y = + k x .

i. STEP 1 : Write the equation in form of Y = mX + c.

x 25 35 51 65 77 90 100

y 50 51 52 54 61 67 73

0

10

20

30

40

50

60

70

80

25 35 51 65 77 90 100

y

x


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( py = + k x )

xy = +

Y = mX + c

Y = xy X = x 2

m = c =

COMMENT:

After comparing, I find that the graph in (a) and (b) have several differences. The graph in (a) is a graph of

y against x, that is y acts as y-axis and x acts as x-axis. While, the graph in (b) is a graph of xy against x 2,

x2 625 1225 2601 4225 5929 8100 10000

xy 1250 1785 2652 3510 4697 6030 7300

0

1000

2000

3000

4000

5000

6000

7000

8000

0 2000 4000 6000 8000 10000 12000

(8100 , 6000)

(0 , 1012.5)

x2

xy


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that is xy acts as y-axis and x 2 acts as x-axis. Besides, I also find that the graph in (a) is not in linear graph

because a straight line cannot be obtained by joining all the point on the graph. While, the graph in (b) is

in linear graph because a straight line of the best fit is obtained by joining up all the point on the graph. In

addition, I can calculate the value of k and p in the equation through the graph in (b) but not the graph in(a).

c) i. From the graph in (b), I find the value of k and p.

From the equation of the graph in (b), I find that k is the gradient of the graph and p is a part ofthe y-intercept of the graph .

The final answer: k = 6.081 10 -4 and p =

ii. From the graph in (b), I find that if Ali s savings is RM55 , the Muthus savings will be RM 49.77 .

Alis savings is x = RM55

x2 = RM3025 , xy = RM2737.50

Muthus savings is y = RM2737.50 RM55

= RM49.77

xy = +

Y = mX + c

Where, Y = xy X = x 2

m = c =

= m

=y2 - y1

x2 - x1

=6000 1012.5

8100 - 0= 0.6157

=

1012.5

=

c

p

=

1

1012.5

=2

2025= 0.6157p

= 6.081 10 -4

k


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FURTHER EXPLOR TION

MySave Account (with effect from 8th January 2009)

RANGE (RM) NOMINAL RATES (p.a.) EFFECTIVE RATES (p.a.)

Up to 3,000 0.00% 0.00%

Above 3,000 0.60% 0.60%

MaxSave Account (with effect from 18th August 2008)

RANGE (RM) NOMINAL RATES (p.a.) EFFECTIVE RATES (p.a.)

Up to 1,000 0.00% 0.00%

Up to 10,000 0.60% 0.60%

Up to 20,000 0.80% 0.80%

Up to 50,000 1.20% 1.20%

Up to 100,000 1.70% 1.71%

Above 100,000 2.00% 2.01%

EasiSave Account Rates (% p.a.)

RM50,000 and below 0.25

RM50,001 to RM100,000 0.50

RM100,001 to RM500,000 0.60

Above RM500,000 0.70

Interest is calculated daily and credited half yearly on 30 June and 31 December


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COMMENTS:

I would like to choose the savings plan offered by RHB Bank. It is because RHB Bank offer

a higher interest rate (1.20% p.a.) compared to OCBC Bank which only offer (0.25% p.a.).

The welfare provided by RHB Bank is also more comparing to OCBC bank. It is because the

multi-tiered interest rates in the savings plan of RHB Bank are calculated daily and credited

half-yearly in June and December. I can also access ATM and cashless shopping via e-post

facility. It is also up-to-date, reliable, and competitive. It is also convenient in updating my

passbook automatically via the Passbook Update Machine. Therefore, I think the savings plan

offered by RHB bank is more economical and suitable for me.


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CONCLUSION

In conclusion, we should use the aid given wisely. We should not spend them on

unimportant things. For example, use them to buy video games, watch movies and ect. With

that, we will not waste the aid given to us. The remaining can be put into the bank to earn the

profit given. We should be more clever to choose the correct bank with the most profitable

interest. We have to plan before new make any decision. By doing this, we will not be

cheated by the bankers.

It is important for us to save money. The most important reason we need to save is formedical expenses. This is sometimes covered by medical cards and employers but we always

need some spare cash for the things they don't cover or to pay the premiums. Savings also

help pay for the quality of the medical services we need.

Saving money helps us pay for our dream home without paying too much interest to

the bank. We could save from a young age and be surprised to see how much we have at the

end. We need to save to be able to afford a college education for ourselves and our futuregenerations. It helps us to get a better job.


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REFLECTION

Throughout the project while I was conducting it, I learned many stuff. This includes

on usage of knowledge and ways to conduct the project. While I was conducting the project, I

collected information from the internet and regarding the savings. Besides, I manipulated my

knowledge in other fields such as accounting and economics in this research. However, the

most important this I have learnt from this project is to plan before we do something. In this

project, I was regarded as the student of receiving Bantuan Khas Awal Persekolahan

1Malaysia. I was required to explain how am I going to use this money so that it achieve the

government objectives.

Thus, planning is required and information was given. While planning, I made few

tables on total profit incurred, average interest rate per month and also annual profit. This has

taught me that a lot of work should be done such as consideration and provision for

repayment before making a savings. We must be able to save our money in bank which offer

higher profit and advantages and should not make decision in a haste because great haste make

great waste.

Besides, I learned how to cooperate with friends. My friends and I discussed about the

project and we shared ideas among ourselves. This discussion has made me more confident

when doing something. I also learned to be disciplined in terms of punctuality, doing project

and not least to avoid plagiarism.

In a nutshell, I have learned something about the future and how serious can it be

if we make a wrong decision. Moreover, work that we done must be original and not totally

derived from other people. These two images have expressed my opinions from this project.


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Everything comes with a plan. Without a plan, we will fail. Just like the saying goes, wedont plan to fail but we fail to plan .

A perfectly good business plan is a must to be done to have a long-lasting andprofitable business.

-END OF PROJECT-

Add Math Project 2014 Johor State

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