2012

SMKA SULTAN AZLAN SHAH,32600 BOTA, PERAK.

[ADDITIONAL MATHEMATICS

PROJECT WORK]

NAME : NUR DALILA NABIHAN BINTI AHMAD TAJUDDIN

CLASS : 5 IBNU SINA

I/C NUMBER : 951024-02-5178

TEACHER’S NAME : MRS. HAMIDAH BT UDA AHMAD

CONTENT PAGE

NO. CONTENTS PAGES

ACKNOWLEDGEMENT

1. CONTENT

2. RUBRIC FOR ADDITIONAL

MATHEMATICS

3. APPRECIATION

4. OBJECTIVES

5. INTRODUCTION

6. APPLICATION OF STATISTICS

7. ADDITIONAL MATHEMATICS TOV

MARKS

8. MEAN

9. HISTOGRAM

10. OGIVE

11. RANGE

12. STANDARD DEVIATION

13. COMPARING TOV MARKS

14. PEARSON CORRELATION

COEFFICIENT

15. EQUATION RELATING X AND Y

16. FURTHER EXPLORATION

17. FINDING VALUES

18. CONCLUSION

19. REFLECTION

My name is Nur Dalila Nabihan binti Ahmad Tajuddin. 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 sincere gratitude 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 Mathematics

teacher, Mrs. Hamidah bt Uda Ahmad for giving me information about my project work. On

the other hand, I would also like to thank my dear principle, Puan Naemah bt Ramli 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.

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

life. 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.

PREFACE

This project is prepared by the students of class 5 (2012) and it is based on the

Additional Mathematics textbooks, internet search and reference books.

Additional Mathematics is an effective subject in secondary school. Each student who

takes this subject has to carry out a project work on the given tasks. The project work for the

year 2012 is about statistics.

The aim of doing this project is to improve the skills in using Mathematics for

students. Working on this also gives a chance for students to apply their skills on what they

had learnt to solve an assigned project. Therefore, every student stand a chance to improve

their thinking skills, usage of languages and grammar as well as Mathematics skills

throughout the project.

After doing this project, the student will be able to master and understand more on the

applications of Additional Mathematics thet they learnt in their school syllabus. The student

can also learnt some values during the completion of the project such as to learn how to work

together or to be cooperative, improving their communication skills, responsibility and also

not to give up easily on the task given.

OBJECTIVES

Additional Mathematics is one of the compulsory subjects for

SPM science stream candidates. All of the students would have to

carry out a project work based on a topic given and must be submitted

in three weeks time.

The objective of carrying out this project is:

to apply and adapt a variety of problem-solving strategies that

we had learnt to solve the problems.

our thinking skills can be improved.

promotes effective mathematical communication. Our

confidence and interest towards Mathematics will be increase

though solving various types of problems.

to use the language of Mathematics to express Mathematical

ideas precisely.

stimulates and enhances effective earning.

to develop our positive attitude towards Mathematics. This

makes the lesson to be more fun, useful and meaningful.

INTRODUCTION

The history of statistics can be said to start around 1749 although, over time, there have been

changes to the interpretation of what the word statistics means. 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.

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.

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 the 17th 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 the 19th century, social scientists used statistical reasoning

and probability models to advance the new sciences of experimental psychology and

sociology; physical scientists used statistical reasoning and probability models to advance the

new sciences of thermodynamics and statistical mechanics. The development of statistical

reasoning was closely associated with the development of inductive logic and the scientific

method.

Statistics is not a field of mathematics but an autonomous mathematical science, like

computer science 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 close

association 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.

The term statistics is ultimately derived from the New Latin statisticum collegium ("council

of state") and the Italian word statista ("statesman" or "politician"). The German Statistik,

first introduced by Gottfried Achenwall (1749), originally designated the analysis of data

about the state, signifying the "science of state" (then called political arithmetic in English). It

acquired the meaning of the collection and classification of data generally in the early 19th

century. It was introduced into English in 1791 by Sir John Sinclair when he published the

first of 21 volumes titled Statistical Account of Scotland.

Thus, the original principal purpose of Statistic was data to be used by governmental and

(often centralized) administrative bodies. The collection of data about states and localities

continues, largely through national and international statistical services. In

particular, censuses provide regular information about the population.

The first book to have 'statistics' in its title was "Contributions to Vital Statistics" by Francis

GP Neison, actuary to the Medical Invalid and General Life Office.

CUMULATIVE FREQUENCY

0

5

34

CUMULATIVE…0

100

200

0 5

34

91

12

9

15

7

17

2

18

2

18

4

APPLICATIONS OF STATISTICS

IN DAILY LIFE

1.Statistics is the collection of data and its representation or interpretation. Statistics use three

means 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

as the 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.

ADDITIONAL MATHEMATICS MARKS FOR PUPIL

(TOV MARKS)

NO. NAME MARKS % TIME TAKEN FOR

PRACTICES

1. Anis Hasniza

2. Faruq Muntasir

3. Firdaus Imran

4. Fithriah

5. Intan Musfirah

6. Mior Ahmad Asyraff

7. Mohd Haniff

8. Muhammad Taufiq

9. Muhammad Rashid

10. Muhammad Syafiq

11. Nazatul Atilah

12. Nor Nadzirah

13. Nor Shafiqah

14. Nur Dalila Nabihan

15. Nur Farhana

16. Nur Syifa Husna

17. Nur Hazirah

18. Nur Syahirah

19. Nurul Izzati

20. Nurul Jannah

21. Nurul Mashitah

22. Nurul Shafiqah

23. Siti Zulaihah

24. Sharifah Nor Hajar

25. Syaiful Arif

FREQUENCY TABLE

MARKS NO. OF

STUDENTS

(f)

MIDPOINT

(x)

fx CUMULATIVE

FREQUENCY

(cf)

1-10

11-20

21-30

31-40

41-50

51-60

The sum of all terms divided by the number of terms

Based on formula

∑

∑ =

1. A histogram is

constructed based on

the frequency

distributions

2. The values of data are

plotted on horizontal axis

(x-axis) while the

frequencies

are plotted on the vertical

axis (y-axis)

FREQUENCY DISTRIBUTIONS

FOR HISTOGRAM

MARKS CLASS

BOUNDARIES

NO. OF

STUDENTS

1-10

11-20

21-30

31-40

41-50

51-60

MODE

The term that appears must frequently

in asset of data

An ogive is known as cumulative frequency

Values of upper boundaries are plotted on the

horizontal axis (x-axis) while values of

cumulative frequencies are plotted on the

vertical axis (y-axis)

In the frequency table, prepare column for

‘upper boundary’ and ‘cumulative

frequencies’

Plot the grapg of cumulative frequency against

the upper boundary of each class

In the frequency table, remember to insert on

additional class with frequency ‘0’ and

cumulative frequency ‘0’ before the first class.

Draw a smooth curve that passes through each

point that is plotted.

FREQUENCY FOR OGIVE

MARKS NO. OF

STUDENTS

UPPER

BOUNDARY

CUMULATIVE

FREQUENCY

1-10

11-20

21-30

31-40

41-50

51-60

FINDING MEDIAN USING

OGIVE

MEDIAN

The value that divides an ordered set

of data into equal halves

FINDING RANGE USING

FREQUENCY POLYGON

RANGE = Midpoint Of Highest Class –

Midpoint Of Lowest Class

()

(square root of variance)

MARKS NO. OF

STUDENTS

MIDPOINT

(x)

X2

fx2

1-10

11-20

21-30

31-40

41-50

51-60

∑ = ∑ 2=

MODE =

MEDIAN =

MEAN =

ACHIEVEMENT

My TOV mark is really not satisfied. I have to

work hard and struggle to gain best result for

SPM 2012.

NO NAME TIME

TAKEN FOR

PRACTICES

MARK

GAINED

xy X2

Y2

1. Anis Hasniza

2. Faruq Muntasir

3. Firdaus Imran

4. Fithriah

5. Intan Musfirah

6. Mior Ahmad

7. Mohd Haniff

8. Muhd Taufiq

9. Muhd Rashid

10. Muhd Syafiq

11. Nazatul Atilah

12. Nor Nadzirah

13. Nor Shafiqah

14. Nur Dalila

15. Nur Farhana

INTERPRETING DATA

Conjecture is a proposition that cannot be proved

but it is real and never proved.

Mathematics

Patterns, formulation the conjecture that the new

and proved facts with vigorous deduction from

axions and definition are selected with care.

The Orem

To be conjecture, a statement most usually

recommended in general where the name of

proposer will be combined on conjecture.

My conjecture for this Rubric Project :

Students that spend more time to make an

exercise for Additional Mathematics for a

week will score high in examinations.

x

y

yxa=b

a and b constants

log10 y + a log10 x =log10 b

log10 x log10 y

FINDING VALUES

log10 y = -a log10 x + log10 b

Finding mass – (a) (gradient)

Finding b as y-intercept

log10 y = a log10 x + log10 b

After doing research, answering question,

drawing graph, making conjecture, conclusion

and some problem solving, I realize that

Additional Mathematics is very important in

daily life.

About this project, overall, is quite joyful

and interesting because I need to plan it

carefully and systematic because it is about

my future. In fact, the further exploration is a

good session because it can open my mind

about linear law.

In a nutshell, I can apply the concept and

skills that I had in solving problems in

Additional Mathematics, I think this project is

very beneficial for all students.

From this project, I learnt the importance of perseverance as time had

been invested to ensure the completion and excellence of this project.

Similarly, I learnt the virtue of working together as I have helped and

received help from my fellow peers in the production of this project

as sharing knowledge is vital in achieving a single goal. Also, I learnt

to be thankful and appreciative. This is because, I able to apply my

mathematical knowledge in daily life and appreciate the beauty of

mathematics. All and all, I have spent countless hours doing this

project. I realized that this subject is a compulsory to me. Without it, I

can’t fulfill my big dreams and wishes.

It always makes me wonder why

This subject is so difficult for me…

I always tried to love every part of it..

It always an absolute obstacle for me..

Throughout the day and night…

I sacrified precious time to heve fun

And even the weekend that I always looking

Forward 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….