Addmath folio 2014

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TITLE: The survey of savings the aid among the

students

NAME:RUBEN MANIMARAN

CLASS:5SCIENCE 2

I/C NUMBER:971004016539

TEACHER:PUAN MAHERAN BINTI MUSTAPHA


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NO CONTENTS PAGE REMARK

1 Acknowledgement

2 Introduction , Appreciation

3 History of Statistics

4 Objective

5 Method of Investigation

2 PART A Usage of the money

Collecting dataBar chart

Pie chart

Line graph

Mean and Standard deviation , comment

New mean and new variance

3 PART B Problem (a) method 1

Problem (a) method 2

Problem (b) method 1

Problem (b) method 2

Discussion

4 PART C Plot graph

Linear graph

Problem solving

5 Further Exploration

6 Reflection

7 Conclusion

8 Reference


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In todays society, money is a primary source to

survive in this world to provide our essential

necessities to be human. Therefore, money should

not be spending absentmindedly.

I am absolutely grateful towards the government

for their generosity when they hand out the RM100

aid to every school in Malaysia. This gives students

an advantage to spend the money wisely as being a

student for these days that requires sufficientamount to obtain stationaries and books.

Money is powerful to do good and bad. The choices

are made by ones who receive the money.


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P RT


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PROBLEM (a)

As a student receiving the Bantuan Khas Awal Persekolahan1Malaysia that cost RM100, I used this money to buy some

stationery that I need for school. For example pen, correction

tape, geometrical box and etc.

Practices make perfect. As a Form Five student; I will take SPM

at the end of the year. So, I used some of the money to buy some

reference books and practical books.

Furthermore, I also used the money to pay the payment in school.

By this, I can reduce the burden of my parents.

Expenses Amount(RM)

Stationaries 9

Practical books 25

Class fund 3

Sports club fees 3

Total expenses 40


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PROBLEM (b)

Totalsavings(RM)

Number ofpupils

2 3 4 1 2 3 2 2 1 2


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PROBLEM(C) (i)

PIE CHART

9%

14%

18%

4%

9%

14%

9%

9%

5%

9%

Total Savings of students

10

20

30

40

50

60

70

80

90

100


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BAR Chart

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

10 20 30 40 50 60 70 80 90 100


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LINE GRAPH

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

10 20 30 40 50 60 70 80 90 100


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Problem (c) (ii)

the mean and standard deviation of total savings by using two

methods.

METHOD 1

Total

saving(RM)

1-10 11-20 21-30 31-40 41-50 51-60 61-70 71-80 81-90 91-100

Number of

pupils(f)

2 3 4 1 2 3 2 2 1 2

Midpoint(x) 5.5 15.5 25.5 35.5 45.5 55.5 65.5 75.5 85.5 95.5

F(x) 11.0 46.5 102.0 35.5 91.0 166.5 131.0 151.0 85.5 191

F(x)2 60.5 720.75 2,601 1,260.25 4,140.5 9,240.75 8,580.5 11,400.5 7,310.25 18,240.

Mean,

=

=

=

=45.955


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Variance, 2

=

( 2

=

(45.955)2

=

2,111.862

=2,888.886-2,111.862

=770.024

Standard deviation,

=

=27.749


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Based on the data that I had

collected, I have found out that all

my classmates have saved their

money. The average saving in 5 SN2

is RM45.96. From method 1, I ableto find the answer by taking time

while by using method 2, I able to

find the answer easily without

spending a lot of time.


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Problem (d)

If each student is given an additional RM50 for savings,

calculate the new mean and new variance of the total

savings.

New mean,

=45.955+50

=95.955

New variance, 2

= 770.024


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Problem (a)

Assume that you saved the whole amount of the aid in Bank X which

offers annual profit of 3% and is credited annually. By using at least

two methods, calculate your total savings after 10 years with an

assumption that no additional deposit is done.

METHOD 1

a=100

r=

=1.03

Tn=arn-1

T10=ar9

= (100) (1.03)9

=130.48

Method 2

Years Total savings (RM)

1st

100

2nd

1001.03=103

3rd

1031.03=106.09

4th

106.091.03=109.27

5th

109.271.03=112.55

6th

112.551.03=115.93

7th

115.931.03=119.41

8th 119.411.03=122.999

th 122.991.03=126.68

10th

126.681.03=130.48


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PROBLEM (b)

Bank Y offers a profit of 0.25% per month and is credited

monthly. By using at least two methods, calculate your totalsavings after 10 years with an assumption that no additional

deposit is done.

Method 1

T1=100

a=100

r=

=1.0025

T120=arn-1

=100(1.0025)119

=RM134.60


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Method 2

Months Total savings (RM)

1st 100.00

2nd 100.0 100.253rd 100.25 4th 100.50 5th 100.75 6th 101.00 7th 101.26 8th 101.50 9th 101.76 10th 102.02 11th 102.27 12th 102.53 13th 102.79 14th 103.04 15th 103.30 16th 103.56 17th 103.82 18th 104.08 19th 104.34 20th 104.60 21st 104.86 22nd 105.12 23rd 105.39 24th 105.65 25th 105.91 26th 106.18 27th 106.45 28th 106.71 29th 106.98 30th 107.25 31st 107.51 32nd 107.79 33rd 108.05 34th 108.32 35th 108.59 108.8636th 108.86 109.1337th 109.13 109.41


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38th 109.41 109.6839th 109.68 109.9540th 109.95 110.2341st 110.23 110.5042nd 110.50 110.78

43rd 110.78 111.0644th 111.06 111.3345th 111.33 111.6146th 111.61 111.8947th 111.89 112.1748th 112.17 112.4549th 112.45 112.7450th 112.74 113.0251st 113.02 113.3052nd 113.30 113.5953rd 113.59 113.87

54th 113.87 114.1655th 114.16 114.4456th 114.44 114.7357th 114.73 115.0158th 115.01 115.3059th 115.30 115.5960th 115.59 115.8861st 115.88 116.1762nd 116.17 116.4663rd 116.46 116.7564th 116.75 117.04

65th 117.04 117.3366th 117.33 117.6367th 117.63 117.9268th 117.92 118.2269th 118.22 118.5170th 118.51 118.8171st 118.81 119.1072nd 119.10 119.4073rd 119.40 119.7074th 119.70 120.0075th 120.00 120.30

76th 120.30 120.6077th 120.60 120.9078th 120.90 121.2079th 121.20 121.5180th 121.51 121.8181st 121.81 122.1282nd 122.21 122.4283rd 122.42 122.73


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84th 122.73 123.0385th 123.03 123.3486th 123.34 123.6587th 123.65 88th 123.96 124.27

89th 124.27 124.5890th 124.58 124.8991st 124.89 125.2092nd 125.20 125.5193rd 125.51 125.8394th 125.83 126.1495th 126.14 126.4696th 126.46 126.7897th 126.78 127.0998th 127.09 127.4199th 127.41 127.73

100th 127.73 128.06101st 128.06 128.37102nd 128.37 128.69103rd 128.69 129.00104th 129.00 129.33105th 129.33 129.65106th 129.65 129.98107th 129.98 130.30108th 130.30 130.63109th 130.63 130.96110th 130.96 131.28

111th 131.28 131.61112th 131.61 131.94113th 131.94 132.27114th 132.27 132.60115th 132.60 132.93116th 132.93 133.26117th 133.26 133.60118th 133.60 133.93119th 133.93 134.26120th 134.26 134.60


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Problem (c)

Discuss your findings.

After 10 years, total saving in Bank X will be

RM130.48 while in Bank Y will be RM134.60. All in

all, Bank Y offers more profit which result in

RM4.12 more than Bank X of the total saving after

10 years. Hence, I will choose Bank Y to save the

whole among of the aid.


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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 Muthussaving.

x 25 35 51 65 77 90 100

y 50 51 52 54 61 67 73

The savings of both students are related by the equation py=

+kx ,

where k and p are constants.

Problem (a)

Plot a graph of y against x, by using suitable scale.

0

10

20

30

40

50

60

70

80

0 20 40 60 80 100 120

Graph of y against x


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Problem (b)

Use the above data, draw a suitable straight line graph from the equation py=

+kx.

py=

+kx

=

=

(

)+

y=

(

) +

x

xy=

x2

xy=

x2

y=mx+c

x2 625 1225 2601 4225 5929 8100 10000

xy 1250 1785 2652 3510 4697 6030 7300


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Compare and comment your graphs in (a) and (b).

Problem (c)

From your graphs in (b), find

(i) the value of k and p

=

=c

=1000

P=0.001

=

=m

0

1000

2000

3000

4000

5000

6000

7000

8000

0 2000 4000 6000 8000 10000 12000


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=

=

K=0.00062

(ii) Muthus savings when Alis savings is RM55.

Alis savings = x= RM55

x2=RM3025

From graph, x=3025

Y=2900

Thus, Muthus savings = y

xy=2900

y=

=RM52.73

There are many saving plans offered in the market nowadays. Choose one saving plan

from two different financial institutions.


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Public Bank

Public Bank Wise Account for kids 2.82%

Fixed deposit

3.15% per years

3.05% 6 months

3.00% 3 months

Maybank

Yippie Savings Accounts

Effective rate: 1.45-3.01%

Minimum deposit: RM1

Benefits:


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Free coin box

Cash rewards for YippieClud members who excels in their PMR,SPM,STPM and

Tertiary level exams

Free Personal Accident Insurance coverage of up to RM70000

A chance to win fantastic prize in various contents

From the survey I have done, I can conclude that saving

money has its own importance and how we should spend and

save the money wisely. The importance of saving money include

for the emergency, retirement, education and so on. How can

someone use money wisely? Firstly, buy only the items most

From the two different financial institutions, as a

student, I will choose Maybank as my personal account

because it has many benefits for me such as cash

rewards and accident insurance.


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needed. Secondly, come up with a budget. And lastly, save

up the money.

I have successfully completed this additional mathematics project work.

One of the conclusion I can make is that the importance of Additional

Mathematics in our daily life.

Furthermore, I also learnt that corporate among each other is also

importance in our life. Without the helping from my friends, I cannot finish

the project in such short time. So, I would like to thank my friends that help

me throughout the process I do the project work.

Perseverance yields success. I have learnt that perseverance is important

to us when doing something. One that persevere in doing some task, never


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give up no matter how difficult the task given, finally he would reach

success.

Last but not least, this project has taught me a valuable lesson on the

importance of saving money and how money should be spent wisely forraining days.

A BRIEF OF HISTORY

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 require 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


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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.

APPRECIATION

First of all, I would like to thanks my additional mathematics teacher,

Puan Maheran as she gives an important guidance and commitment

during this project work. She has been a very supportive figure

throughout the whole project .Next; I would like to thank my school for

giving me the chance to create this project work. School also provides

us space to discuss and carry out this project work. Not forgetting, my

beloved parents who provided everything I needed in this project worksuch as money, Internet, books, and so on. They contribute their time

and spirit on sharing their experience. Their support may raise the spirit

in me to do this project work smoothly .Then, I would like to thank the

bank management who was willing to share their experience on


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business activity and experiences on saving money. Last but not lease,

I would like to thank my friends as well for helping me to collect data

that I needed. Not forgetting too all the people who were involved

directly and indirectly towards making this project a reality. Thank you.

The objective of this project work is:

1.Apply mathematics to everyday situation and appreciate the

important and the beauty of mathematics in everyday in everyday

lives.2.Improve problem solving, thinking skill, reasoning and

mathematics communication.


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3.Develop positive attitude and personalities and intrinsic

mathematical values such as accuracy, confidence and

systematic reasoning.

4.Stimulate learning environment that enhances effective learning,

inquiry based and team work.

5.Develop mathematical knowledge in a way, which increases

students interest and confidence.

Addmath folio 2014

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