Additional Mathematics Power Points

Bahan ini boleh membantu anda memahami konsep dalam Pembelajaran Additional Mathematics.Sila download dan menafaatkan.

Form 5

Curriculum Specifications Additional Mathematics

Integrated Curriculum For Secondary Schools
Form 4
Form 5

Teaching and Learning Calender
Form 4
Form 5

Mind Map For Additional Mathematics

Concept Map in learning Additional Mathematics
Quadratic Functions
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Teaching and Learning Additional Mathematics Module


Chapter 4- Vector
Chapter 6 - Permutations and combinations
Chapter 7 - Probability
Chapter 9 - Motion Along a straight line


Bahan Ini boleh digunakan sebagai bahan ulangkaji untuk anda menghadapi peperiksaan SPM . Bahan disediakan mengikut topik untuk memudahkan anda menambah baik kefahaman anda. Jawapan secara detil disediakan sebagai panduan anda mengetahui keadah penyelesaian setiap soalan.

Kertas Soalan Berformat SPM Additional Mathematics

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Bengkel telah diadakan pada 21 Julai 2007 . Didalam bengkel ini kerja kumpulan telah diberikan. Perbincangan kumpulan dilakukan dengan menyelesaikan soalan SPM 2006. Semuga dengan bengkel ini dapat meningkatkan lagi pencapaian pelajar


The vertical longitude lines are also known as meridians. They converge at the poles and are widest at the equator. Zero degrees longitude is located at Greenwich, England (0°). The degrees continue 180° east and 180° west where they meet and form the International Date Line in the Pacific Ocean.

The equator is located at 0 degrees latitude. It is 24,901.55 miles (40,075.16km) long. The equator divides the planet into the Northern and Southern Hemispheres.
latitude lines run horizontally. Latitude lines are also known as parallels since they are parallel and are an equal distant from each other. To remember latitude, imagine them as the horizontal rungs of a ladder ("ladder-tude"). Degrees latitude are numbered from 0° to 90° north and south. Zero degrees is the equator, the imaginary line which divides our planet into the northern and southern hemispheres. 90° north is the North Pole and 90° south is the South Pole
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Key Words in SPM Additional Mathematics Paper

You should highlight and understand the keywords given in the question because these keywords are the gist of the question. Some commonly found keywords are as follows

KEYWORD Calculate, Find, Determine
What is its implication?
The answer can be obtained after a few steps of determine calculation. Hence, the working must be shown clearly.

KEY WORD Write, state,
The answer can be worked out mentally. Hence, you can write down the answer without the working.

Usually you have to use the answer obtained form the previous section in your calculation.

KEY WORD: Sketch ,
Only a sketch of the graph is required. You can sketch the graph on a plain paper or a writing paper. Accurate plotting on the graph is not required.

KEY WORD : Prove,show,
The answer is usually given. You are required to show clearly the steps how you arrive at the answer. In this type of question, you must be familiar with the mathematical formulas, rules and laws.

KEY WORD : Express
No numerical answer is required. Answer are usually given in terms of variables.

Tips For Answring SPM Paper Additional Mathematics

a) Read the instructions of the examination paper carefully
You must follow the instructions given in the question paper closely.
Answer more questions than is required will not earn any additional
marks. The time you used to answer these additional questions
should instead be used to cheek the answer you have obtained

b) Read all questions carefully
For the section that you are given choices of questions, you must read all the questions so that you are able to make a wise choice. Otherwise, time would be wasted when you decide to answer another question only after you find the question you attempted is difficult

c)Read and follow the instructions given in the question closely.
Before you answer you must read and follow closely the instructions given in the question. Otherwise you will end up losing marks you deserve. Some commonly found instruction are given as follows

Use a graph paper
( found in topics such as Linear Law, Linear programming and statistics)
Draw a graph using the given data From the graph, find the value of x
( found in topics such as Linear Programming and linear law)
Solving by accurate drawing is not accepted
( found in topic such as coordinate Geometry )
Without using a calculator
( found in topics such as Indices and Logarithms and Trigonometry )

Use the time wisely
Time is precious in the examination. You should use the time wisely. You are given a specific duration of time to answer a specific number of questions. You must know the maximum length of time you can allocate to a particular question. Once you have exceed the time allocated and you still cannot answer the question, you should proceed to another question and re-do this questions, marks will not be awarded for correct answer if working are not shown.

80 MARKS ------ 120 MINUTES ( PAPER 1)
100 MARKS ------- 150 MINUTES ( Paper 2)

So , 1 mark = 1.5 minutes
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Why study Mathematics?

The main reason for studying mathematics to an advanced level is that it is interesting and enjoyable. People like its challenge, its clarity, and the fact that you know when you are right. The solution of a problem has an excitement and a satisfaction.
You should also be aware of the wide importance of Mathematics, and the way in which it is advancing at a spectacular rate. Mathematics is about pattern and structure; it is about logical analysis, deduction, calculation within these patterns and structures. When patterns are found, often in widely different areas of science and technology, the mathematics of these patterns can be used to explain and control natural happenings and situations. Mathematics has a pervasive influence on our everyday lives, and contributes to the wealth of the country.
Suggestions for Preparing for and Taking Math Tests
  1. Keep a list of things to remember - problems stressed by the instructor, definitions, terms, diagrams and graphs, formulas.
    Keep up with the work - some courses can be passed by cramming, but math isn’t one of them. Skills in math, as in sports, must be practiced.
  2. Study copies of old exams, chapter tests from the book, or make up your own. Then practice them with the same limits as the real exam.
    Get a good night’s sleep before the test so that you are rested and alert; a quick review before the test should be a summary only.
    Arrive at the test early so that you can be relaxed when the exam begins.
  3. Quickly look over the test and budget your time - don’t spend too much time on any single problem or section of the test.
    Do some work on each problem - try to work at least part of each problem because partial credit is better than none.
  4. Check your answers and look for careless mistakes during the last few minutes of your test time (budget this important time).

Let's Learn Permutation

BY THE PERMUTATIONS of the letters abc we mean all of their possible arrangements:
abc, acb, bac, bca, cab,cba
There are 6 permutations of three different things. As the number of things (letters) increases, their permutations grow astronomically. For example, if twelve different things are permuted, then the number of their permutations is 479,001,600.
Now, this enormous number was not found by counting them. It is derived theoretically from the Fundamental Principle of Counting:
If something can be chosen, or can happen, or be done, in m different ways, and, after that has happened, something else can be chosen in n different ways, then the number of ways of choosing both of them is m· n.
For example, imagine putting the letters a, b, c, d into a hat, and then drawing two of them in succession. We can draw the first in 4 different ways: either a or b or c or d. After that has happened, there are 3 ways to choose the second. That is, to each of those 4 ways there correspond 3. Therefore, there are 4· 3 or 12 possible ways to choose two letters from four. ab , ba, ca, da, ac, bc, cb, db, ad, bd, cd , dc
ab means that a was chosen first and b second; ba means that b was chosen first and a second; and so on.
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Math Study Skills
  1. Read what the instructor will be lecturing on before you go to class.Read slowly. Reading mathematics is not like reading a novel or even history. Speed reading techniques are not appropriate. Every word and symbol is important to the meaning. Do not skip the symbolic part of the text. This is often the most important part. If you do not understand a symbol, look in the glossary or in the earlier part of the text. Symbols are often explained when they are first introduced. If you still can not find out what a symbol means, ASK!Read with a pencil in hand. Every time the author does a problem, do it on your own—either before or after you read his or her explanation. This makes sure you know what steps have been shown and, more importantly, which ones were omitted. If there is something you do not understand, try to formulate a question about it. Often if you can ask a specific question, you can answer it yourself. If you can’t answer it, you know what part of the instructor’s lecture requires your complete attention. Your question is ready if the lecture does not clear up your misunderstanding.
  2. Understand the concepts.Don’t be satisfied with vague ideas about how to work problems. Do the examples yourself, understand the concept illustrated, then try making up your own examples. Keep in mind that the questions on the exam may be very different from the example in the book.
  3. Practice.Be sure you understand the concepts before you practice. Then practice will help you remember and give you confidence in your mastery. Force yourself to remember the methods as you work problems; don’t look back in the book.
  4. Keep up with assignments (whether they are graded or not).The pace is much faster in college and keeping up to date with assignments helps you to better understand what is going on in class.Mathematics is not a spectator sport. The only way you can learn mathematics is by doing it. Following are some suggestions for getting the most out of the time you spend on homework.
    Understand the purpose of homework. Homework in mathematics classes is assigned to help you understand certain concepts and to help you build certain skills. Homework is not assigned to you because it is important to get the right answers. Your instructor already knows the answers.
    Try to understand the process, not the specific problem. Classify problems in the assignment by problem type. Although this is often done for you by the directions, it is not always. Do each assigned problem and then check it in the back of the book. Try to figure out why you missed the ones you did instead of just working toward the answer. A similar problem may be on a test or quiz.
    Mark homework problems you still do not understand and get help with them before the next class. The next lecture may build on a concept or skill you did not understand in the homework. When you do get help, make notes on what you learned, so that you can study them for the test.
    Before closing the book, look back over the assignment and try to explain to yourself what the assignment was about, what each kind of problem was asking, how you got the answers and what the answers tell you. This process will help you understand the material and will help you discover what you don’t understand.
    Keep your homework in a convenient and neat notebook so that you will be able to find questions or difficulties you have quickly and easily. This will also provide an invaluable study guide for tests.
  5. Ask questions.Do not hesitate to ask questions. Ask your instructor for help after you have tried to pull class notes and textbook explanations together for review and still don’t understand. Write down specific problems so you have them ready; don’t be vague and say you just don’t understand.
  6. Don’t hesitate.Get help right away. Tutoring and help sessions are available. The longer you wait before getting help, the harder it will be to get caught up. Most of the time when you feel lost, it is just one concept that you are missing, so get help quickly. One missed concept in a math class will make the rest of your math career a hardship. Don’t feel embarrassed to ask questions and get help; even the best mathematicians have felt completely lost at some point.