Add Maths II

7/31/2019 Add Maths II

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INTRODUCTION

We students taking Additional Mathematics are required to carry out a project work whilewe are in Form 5.This year the Curriculum Development Division, Ministry of Education has

prepared four tasks for us. We are to choose and complete only ONE task based on our area ofinterest. This project can be done in groups or individually, and I gladly choose to do this

individually. Upon completion of the Additional Mathematics Project Work, we are to gain

valuable experiences and able to:

riety of problem solving strategies to solve routine and non-routine

problems

hence improve their thinking skills.

ge and skills are applied in meaningfulways in solving real-life problems

and communication are highly encouraged and expected

that stimulates and enhances effective learning.

language of mathematics to express mathematical ideas correctly and precisely

knowledge and skills through problem-solving in ways

that increase interest and confidence

-life problems and

hence develop positive attitude towards mathematics.

to share knowledge in an engaging and healthy environment

appropriately and effectively

and innovative

We are expected to submit the project work within three weeks from the first day the task is

being administered to us. Failure to submit the written report will result in us not receiving

certificate.


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APPRECIATION

My name is Norashikin bt Mohd Nor. I am thankful that this Additional Mathematics Project can

be done just in time. For this, I would like to seize the opportunity to express my sinceregratitude for those who had been helping me during my work.

First and foremost, I would like to say a big thank you to my Additional Mathematicsteacher, Mr Abdul Hadi bin Azmi as he gives us important guidance and commitment during

this project work. He has been a very supportive figure throughout the whole project.. On the

other hand, I would also like to thank my dear principle, Tuan Haji Ghazali bin Mat Salleh for

giving me the permission to carry out this project.

Also, I would like to thank my parents. They had brought me the things that I needed

during the project work was going on. Not only that, they also provided me with the nice

suggestion on my project work so that I had not meet the dead and throughout this project. forhelping me and always supporting me to help complete this project work..

Lastly, I would like to say thank you to my friends and the modern access in our daily

life. They have done a great job at collecting form 4 end of year result for additional mathematics

and sharing information with other people including me. Without them this project would neverhave had its conclusion All of my relevant information come from my friends and the internet. I

managed to use all these access in our daily life, such as: computer to finish my Additional

Mathematics project.

Not forgetting too all the other people who were involved directly or indirectly towardsmaking this project a reality.


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PART A

By the 18th century, the term "statistics" designated the systematic collection of demographic

and economic data by states. In the early 19th century, the meaning of "statistics" broadened,

then including the discipline concerned with the collection, summary, and analysis of data.

Today statistics is widely employed in government, business, and all the sciences. Electronic

computers have expedited statistical computation, and have allowed statisticians to develop

"computer-intensive" methods.

The term "mathematical statistics" designates the mathematical theories of probability and

statistical inference, which are used in statistical practice. The relation between statistics and

probability theory developed rather late, however.

In the 19th century, statistics increasingly used probability theory, whose initial results were

found in the17th and 18th centuries, particularly in the analysis of games of chance(gambling).By 1800, astronomy used probability models and statistical theories, particularly the method of

least squares, which was invented by Legendre and Gauss

Early probability theory and statistics was systematized and extended by Laplace; following

Laplace, probability and statistics have been in continual development. In the19th century, social

scientists used statistical reasoning and probability models to advance the new sciences of

experimental psychology and sociology; physical scientists used statistical reasoning andprobability models to advance the new sciences of thermodynamics and statistical mechanics.

The development of statistical reasoning was closely associated with the development ofinductive logic and the scientific method

Statistics is not a field of mathematics but an autonomous mathematical science, like computerscience or operations research. Unlike mathematics, statistics had its origins in public

administration and maintains a special concern with demography and economics.

Being concerned with the scientific method and inductive logic, statistical theory has closeassociation with the philosophy of science; with its emphasis on learning from data and making

best predictions, statistics has great overlap with the decision science and microeconomics. With

its concerns with data, statistics has overlap with information science and computer science.


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STATISTICS TODAY

During the 20th century, the creation of precise instruments for agricultural research, public

health concerns (epidemiology, biostatistics, etc.), industrial quality control, and economic and

social purposes(unemployment rate, econometry, etc.) necessitated substantial advances instatistical practices.

Today the used of statistic has broadened far beyond its origin. Individuals and organisations usestatistics to understand data and make informed decisions throughout the natural and social

sciences, medicines, business, and other area.

Statistics are generally regarded not as the subfield of mathematics but rather as a distinct, allied,field. Many universities maintain separate mathematics and statistic departments. Statistic is also

taught in department as diverse as psychology , education and public health


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APPLICATIONS OF STATISTICS IN DAILY LIFE

1.Statistics is the collection of data and its representation or interpretation. Statistics use threemeans of comparison through the data mean, median & mode.

2. What is mean? Mean is used as one of the comparing properties of statistics. It is defined asthe average of all the clarifications.

It helps teachers to see the average marks of the students.

It is used in factories, for the authorities to recognize whether the benefits of the workers is

continued or not.

It is also used to contrast the salaries of the workers.

To calculate the average speed of anything.

It is also used by the government to find the income or expenses of any person.

Using this the family could balance their expenses with their average income.

4. What is median & what are its daily applications? Median is defined as the middle value of

any observation.Its applications in daily life are as follow:

It is used to measure the distribution of the earnings.

Used to find the players height e.g. football players.

To find the middle age from the class students.

Used to find the poverty line.

5. What is mode & what is its importance in our daily life? Mode contains the highest frequency

in any data.

Its applications areas follows:-It is used to influx of the public transport.

The no. of games succeeded by any team of players.

The frequency of the need of infants.

Used to find the number of the mode is also seen in calculation of the wages, in the patients

going to the hospitals, the mode of travel etc


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PART B

FREQUENCY TABLE

Marks Frequency, fMidpoint, x f(x)

Cumulative

frequency

0-9 9 4.5 40.5 9

10 19 8 14.5 116 17

20-29 11 24.5 269.5 28

30-39 13 34.5 448.5 41

40-49 15 44.5 667.5 56

50-59 11 54.5 599.5 67

60-69 7 64.5 451.5 7470-79 6 74.5 447 80

80-89 5 84.5 422.5 85

90-99 2 94.5 189 87

HISTOGRAM

0

2

4

6

8

10

12

14

16

4.5 14.5 24.5 34.5 44.5 54.5 64.5 74.5 84.5 94.5

No. of student's add maths TOV marks


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FREQUENCY POLYGON

OGIVE

0

2

4

6

8

10

12

14

16

4.5 14.5 24.5 34.5 44.5 54.5 64.5 74.5 84.5 94.5


0

10

20

30

40

50

60

70

80

90

0 10 20 30 40 50 60 70 80 90 100



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MEASURES OF CENTRAL TENDENCIES

i. Modal class= 40-49

ii. Mean=fxf

= 3651.587

= 41.97

iii. Median=L+

= ()

= 41.17

The mean is a more suitable measure of central tendency because it reflects the central value

around which the data seems to cluster. The mode is not suitable because the data does not seem

to cluster about mode


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MEASURES OF DISPERSION

Range = midpoint of highest class - midpoint of lowest class

90 + 99 0 + 92 2

= 85

When comparing the range of two sets of data, the set with a greater range is said have a greatervariation or dispersion. Thus, the range of this overall data have a greater dispersion.

Standard Deviation = ( )

= ( ()= = 15.18

The standard deviation answer is getting from the square root of a variance which is also ameasure of dispersion that has same unit as each value of data.


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Marks Frequency, f Midpoint, x f(x) f(x)2

0-9 9 4.5 40.5 182.25

10 19 8 14.5 116 1682

20-29 11 24.5 269.5 6602.75

30-39 13 34.5 448.5 15473.25

40-49 15 44.5 667.5 29703.75

50-59 11 54.5 599.5 3672.75

60-69 7 64.5 451.5 29121.75

70-79 6 74.5 447 33301.5

80-89 5 84.5 422.5 35701.25

90-99 2 94.5 189 17860.5

87 495 3651.5 173301.75

(b) My TOV mark is higher than all three measure of central tendencies. So, my result is increase

based on the comparison.


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PART C

x 1 2 3 4 5 6 7 8 9 10

y 15 24 33 42 54 65 73 80 86 95

Based on the graph above, it is positive linear correlation which 0 < r < 1.

0

10

20

30

40

50

60

70

80

90

100

1 2 3 4 5 6 7 8 9 10

MARKS

NUMBER OF EACH STUDENT SPENT IN DOING EXERCISE OF ADDITIONAL

MATHEMATICS (h)


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1 1 15 15 1 225

2 2 24 48 4 576

3 3 33 99 9 1089

4 4 42 168 16 1764

5 5 54 270 25 29166 6 65 390 36 4225

7 7 73 511 49 5329

8 8 80 640 64 6400

9 9 86 774 81 7396

10 10 95 950 100 9025

TOTAL 55 567 3865 385 38945

Pearson correlation coefficient r =

()()()( ()( ()

=()()()

()()

= 0.9969

The range of the correlation coefficient is from -1 to 1. Since our result is 0.9969, we canconclude that the strength of the linear relationship between x and y is strong.

Based on data above, I am agreed if more time is taking to make revision in additional

mathematics, more mark will get.


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1 1 15 15 1

2 2 24 48 4

3 3 33 99 9

4 4 42 168 16

5 5 54 270 256 6 65 390 36

7 7 73 511 49

8 8 80 640 64

9 9 86 774 81

10 10 95 950 100

TOTAL 55 567 3865 385

X = = 5.5

Y = = 56.7

b =

()

= = 9.05

y56.7 = 9.05 (x - 5.5)

y = 9.05x49.75 + 56.7

= 9.05x + 6.95


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y = 9.08X + 6.95R = 0.9938

0

20

40

60

80

100

120

0 2 4 6 8 10 12


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Prediction of score for student who spent 7 hours per week is 68%.

Regression analysis is widely used for prediction, where its use has substantial overlap with the

field of machine learning. Regression analysis is also used to understand which among the

independent variables are related to the dependent variable, and to explore the forms of these

relationships. So, Im agreed that least square regression line is suitable in help me for prediction

y = 9.08X + 6.95R = 0.9938

0

20

40

60

80

100

120

0 2 4 6 8 10 12


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FUTHER EXPLORATION

x 1.2 2.4 2.8 3.5 3.9 4.3

y 9.13 3.23 2.56 1.83 1.56 1.35

log10 x 0.0792 0.3802 0.4472 0.5441 0.5911 0.6335

log10 y 0.9605 0.5092 0.4082 0.2625 0.1931 0.1303

1-

0.0000

0.2000

0.4000

0.6000

0.8000

1.0000

1.2000

0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000

Y

x

Relationship Between X And YSeries1f(X)=-1.522341*x+1.09


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2(i)GRAPHICALLY

0.0000

0.2000

0.4000

0.6000

0.8000

1.0000

1.2000

0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000

y

x

Relationship Between X And Y

Series1

f(X)=-1.522341*x+1.09

Y-intercept = 1.09


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2(ii) - STATISTICALLY

6335.00792.0

1303.09605.0

a

5.1a


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It always makes me wonder whyThis subject is so difficult for me

I always tried to love every part of it..It always an absolute obstacle for me..

Throughout all day and all nightI sacrified precious time to have fun

And even the weekend that I always lookingForward to go out with my family

I had spent to do my project..

But, when I have completed it..

I found that Additional Mathematics is interesting..So, from now on, I will do my best on every second that

I will learn Additional Mathematics


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CONCLUSION

After doing research, answering questions, drawing graphs and some problem solving, I saw thatthe usage of statistics is important in daily life. It is not just widely used in markets but also in

interpreting the condition of the surrounding like the air or the water. Especially in conducting an

air-pollution survey. In conclusion, statistics is a daily life necessity. Without it, surveys cannotbe conducted, the stock market cannot be interpret and many more. Therefore, we should be

thankful of the people who contribute in the idea of statistics.

Documents

Add Maths II