Many students use the words “And/Or” indiscriminately in solving inequalities. However, there is a very important difference. ‘And‘ means you take the intersection of the solutions sets. ‘Or‘ means you take the union of the solutions sets.
For the composite function fg,
To find the range of the composite function, there are 3 approaches
Method 2 (Only for strictly increasing or decreasing function)
Since both function g and f are strictly increasing, we can deduce the range in the following manner:
Determine the range based on the rule and domain of the composite function
Using the same f and g definition above,
http://www.h2maths.webs.com/ is a good website.
H2 math student can use it to help them understand transformation of graph
The website also help students in visualising topics such as
2. Solids of revolution
Meditation can benefit the students in the following ways:
Where to learn meditation?
If students don’t mind attending meditation in a Buddhism enviroment, they can attend this good course near Aljunied MRT.
The course is free
These websites offer many 2nd hand textbooks and assessment books.
I bought 2 books selling at $5 each, which is selling in Popular at $50 each. The books are still in good condition.
You can sell your materials at the same websites too.
1. Notes and Examples
“A-Level Complete H2 Maths Guide “ by Educational Publishing House comprises two volumes-one on Pure Mathematics and the other on Statistics. Both volumes are handy in the sense they provide comprehensive notes on a topical basis, complete with worked examples and TI 84 plus graphing calculator handling instructions. These guides will provide a good H2 math foundation and knowledge on how to use the TI 84 plus calculator.
Recommendation: Strong buy for the easy to understand notes, basic examples and TI 84 plus calculator usage.
Power maths Volume 1 and 2 provide lots of examples which are more challenging than those in “A-Level Complete H2 Maths Guide”. The notes also cover some points not covered in the “A-Level Complete H2 Maths Guide”.
First read the notes and examples from “A-Level Complete H2 Maths Guide” to gain a basic understanding.
Then study the notes and challenging examples given in “Power maths”.
Recommendation: Strong buy for the notes, challenging and numerous examples
2. Challenging Practice Questions
Power Maths Volume 3 and 4 consists of questions from JCs. The questions are challenging and of different variety. Full worked solutions are provided directly below the questions. Students can cover the solutions while attempting to solve the problem.
Recommendation: Get either one or both books for practice.
3. Supplementary reading
Students can get any of the 3 above books written by L.Bostock and S.Chandler. These are classic good books for A level Pure Mathematics. It provides crisp derivations of various formulas, explains concepts very cogently and would certainly go some way in improving the student’s proficiency in handling the subject.
“A concise course in A level Statistics” written by J.Crawshaw and J.Chambers is a book one should pick up when reviewing ‘A’ Level Statistics. Students studying this text will stand to benefit from the thorough knowledge and depth of explanations provided.
Most of these books can be purchased from Popular or Second hand online stores
Finding the intersection between planes is typically 4 marks in A level exam, and can be solved using this method in 1 min 🙂
For example, find the line of intersection of r. ( 1 1 0 )=3 and r.(-1 -1 2 )= 7
Basically, we are finding the solution of these two equations:
x+y = 3
-x-y+2z = 7
Use TI 84 plus calculator.
so we have
So the line of intersection is r = (3 0 5) + a(- 1 1 0), where a is a real number.
1. Achieve a deep understanding of the concepts. Understand the ‘how’ or ‘why’ the concept is such, instead of memorizing the steps.
2. Practise a few routine or basic questions to build foundation, speed and accuracy.
3. Attempt challenging or a variety of problems. Instead of doing all the questions in the practice paper, you can attempt only those that are challenging or different.
4. Compare your solution with the solution provided. Is it correct and as elegant as the provided solution? Can you think of alternative solutions?
5. Produce your own summary notes which can be used for quick revision. It is like producing your own secret manual after all the training and challenges.
6. Teach your peers. The more you teach others, the better you become.
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