Understanding Composite Functions

For the composite function fg,

Understanding composite functionsTo find the range of the composite function, there are 3 approaches

Method 1ex

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:

composite

Method 3

Determine the range based on the rule and domain of the composite function

Using the same f and g definition above,

Tex2Img_1399597518

Tex2Img_1399597421

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Why students should Meditate?

Meditation can benefit the students in the following ways:

  1. Better focus and concentration. Mediation can lead to better concentration. Students can absorb what the teacher is teaching in class, without being distracted. And when doing their own study or assignment, they can reach the ” flow state”, where they can accomplish much more. 3 hours of doing Math just pass by quickly. They can study everywhere, in the MRT or even noisy places, without being distracted.
  2. Less Anxiety. Meditation can help to reduce anxiety. Students can perform better in tests and exams when they have less anxiety.
  3. More creativity. Meditation has been found to improve creativity. Challenging questions in exam require creativity to solve. Students aiming for distinctions need to be prepared to meet questions containing new ideas. They need to be creative in coming up with their own solution to solve the problem.
  4. More patience: Students sometimes get frustrated when they cannot solve a Math problem. Meditation helps in cultivating patience. Challenging math problem require patience and persistence to solve.

Where to learn meditation?

If students don’t mind attending meditation in a Buddhism enviroment, they can attend this good course near Aljunied MRT.

http://www.fpmtabc.org/education_beginners.php

The course is free

2nd hand textbook and assessment book

These websites offer many 2nd hand textbooks and assessment books.

https://carousell.com/

http://bookfishing.com.sg

http://www.secondhandbooks.com.sg/about.php

http://bookinbookout.com/index.html

http://www.usedbook.sg/ad-category/textbooks

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.

Recommended H2 math materials

1. Notes and Examples

pure maths

stats

“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.

1

2

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-Math-H1-H2-Volume-3-250x360

Power-Math-H1-H2-Volume-4-250x360

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

Mathematics_The_Core_Course_for_Alevel-500x500

                   OR

1

                   OR

2

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.

Recommendation: Optional

advanced_level_statistics

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.

Recommendation: Optional

Most of these books can be purchased from Popular or Second hand online stores

How to quickly find the intersection between planes

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.

sol

so we have

x= 3-y

y= y

z=5

So the line of intersection is r = (3 0 5) + a(- 1 1 0),  where a is a real number.

How to do well in maths

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.