2012 SMKA SULTAN AZLAN SHAH,32600 BOTA, PERAK.
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
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CONTENT RUBRIC FOR ADDITIONAL MATHEMATICS APPRECIATION OBJECTIVES INTRODUCTION APPLICATION OF STATISTICS ADDITIONAL MATHEMATICS TOV MARKS MEAN HISTOGRAM OGIVE RANGE STANDARD DEVIATION COMPARING TOV MARKS PEARSON CORRELATION COEFFICIENT EQUATION RELATING X AND Y FURTHER EXPLORATION FINDING VALUES CONCLUSION REFLECTION
ACKNOWLEDGEMENT
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 l ogic, 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
200 100 0 0
5 4 1 3 9 9 7 2 2 4 2 5 1 1 7 8 8 1 1 1
CUMULATIVE…
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)
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NAME
Anis Hasniza Faruq Muntasir Firdaus Imran Fithriah Intan Musfirah Mior Ahmad Asyraff Mohd Haniff Muhammad Taufiq Muhammad Rashid Muhammad Syafiq Nazatul Atilah Nor Nadzirah Nor Shafiqah Nur Dalila Nabihan Nur Farhana Nur Syifa Husna Nur Hazirah Nur Syahirah Nurul Izzati Nurul Jannah Nurul Mashitah Nurul Shafiqah Siti Zulaihah Sharifah Nor Hajar Syaiful Arif
MARKS %
TIME TAKEN FOR PRACTICES
FREQUENCY TABLE MARKS
1-10 11-20 21-30 31-40 41-50 51-60
NO. OF MIDPOINT STUDENTS ( x) ( f )
fx
CUMULATIVE FREQUENCY ( cf )
The sum of all terms divided by the number of terms
Based on formula
∑ ∑
=
2. The values of data are plotted on horizontal axis ( x-axis) while the frequencies are plotted on the vertical axis ( y-axis)
1. A histogram is constructed based on the frequency distributions
FREQUENCY DISTRIBUTIONS FOR HISTOGRAM
MARKS 1-10 11-20 21-30 31-40 41-50 51-60
CLASS BOUNDARIES
NO. OF STUDENTS
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
1-10 11-20 21-30 31-40 41-50 51-60
NO. OF UPPER CUMULATIVE STUDENTS BOUNDARY FREQUENCY
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
2
NO. OF MIDPOINT X STUDENTS ( x)
1-10
11-20 21-30 31-40 41-50 51-60
∑ =
2
∑ =
fx
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
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.
Anis Hasniza Faruq Muntasir Firdaus Imran Fithriah Intan Musfirah Mior Ahmad Mohd Haniff Muhd Taufiq Muhd Rashid Muhd Syafiq Nazatul Atilah Nor Nadzirah Nor Shafiqah Nur Dalila Nur Farhana
TIME MARK TAKEN FOR GAINED PRACTICES
xy
2
X
2
Y
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 a y x =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.
