Archives for April 2009

Why Ten Years Series Books Are Missing From Bookshelves?

Copyright issues hit 10-year series

Source: Asiaone

My Point of View:

Since the O level Elementary and Additional Mathematics syllabus have recently changed, the ten years series might not be so relevant, instead it could cause more confusion when students are not fully aware of the out of syllabus questions.

What are your thoughts on this matter? Does it affect you?

Announcement: GCE 'O' Level Secondary 3 Additional Math Programme Starts 19th April 2009

For current GCE 'O' Level Secondary 3 Additional Math students:

If you are facing challenges in understanding and making sense of Additional Math, you must seek help NOW! And not wait till end of year, thinking that you still have time. The truth is consistency is the key to good grades!

Our Company, Winners Education Group is launching the Additional Mathematics Ultimate Leap Programme for Secondary 3 this Sunday 19th April 2009.

We would like to invite you to

understand the abstracts in an easier manner
"see" Additional Mathematics using everyday life analogies
expose themselves to real application questions
build up their confidence for more challenging topics
instill more interest in Additional Mathematics

Based on our many years of experience, the challenges of Additional Mathematics surface very early in their Secondary 3 and very often left unattended. Misconceptions get accumulated and create very unhappy students who are unmotivated due to the repeated failures.

So start early and build strong foundation, one concept at a time.

To join the programme, please contact us at

Click here for more programme details.

O level A-Math: 2 Different Approaches To Solve Identity Question In Factor - Remainder Theorem

In O level Additional Mathematics, there is a small section on Identity inside the topic of Factor & Remainder Theorem. Today I am going to share with you the 2 different approaches to solve this kind of questions.

Substitution Method (My preferred method)

I am going to use the question below to show you the step by step solutions of both methods.

Given that [pmath]3x^2+x-2=A(x-1)(x+2)+B(x-1)+C[/pmath] for all values of x, find the value of A, of B and of C.

Let x = 1,

[pmath]3+1-2 = C[/pmath]

[pmath]C=2[/pmath]

Let x = -2,

[pmath]3(4)-2-2 = B(-3) + 2[/pmath]

[pmath]B= -2[/pmath]

Let x = 0,

[pmath]-2 = -2A+ 2 + 2[/pmath]

[pmath]A = 3[/pmath]

Thus A = 3, B = -2 and C = 2

Concept behind the Subsitution method: The value of x choosen will cause one or more of the unknowns to be "cancel off", leaving just 1 unknown left. For example, when I choose x = 1 in the first subsituition, A & B are eliminated, allowing me to find 'C'.

Comparing Coefficients Method

Given that [pmath]3x^2+x-2=A(x-1)(x+2)+B(x-1)+C[/pmath] for all values of x, find the value of A, of B and of C.

By comparing coefficient of [pmath]x^2[/pmath]:

LHS: 3 = A => A = 3

By comparing coefficient of [pmath]x[/pmath]:

LHS: 1 = 2A - A + B => B = -2

By comparing coefficient of [pmath]x^0[/pmath]:

LHS: -2 = -2A - B + C => C = 2

Thus A = 3, B = -2 and C = 2

Concept behind the Comparing Coefficient method: Expansion is usually required on one side of the equation. It takes up time. The reason for the insignificant working shown is due to the fact that the expansion is done mentally instead of written. This method is highly recommended if there is more than 1 unknown other than x on the left hand side of the equation. For example, there's an unknown 'D' on the left hand side of the equation.

Which method do you usually use? And which method does your school teach you? Leave me your answer in the comment section below.

Play The Tower of Hanoi - A Famous Mathematical Game

From Wikipedia:

The Tower of Hanoi or Towers of Hanoi (also known as The Towers of Brahma) is a mathematical game or puzzle. It consists of three rods, and a number of disks of different sizes which can slide onto any rod. The puzzle starts with the disks neatly stacked in order of size on one rod, the smallest at the top, thus making a conical shape.

The objective of the puzzle is to move the entire stack to another rod, obeying the following rules:

Only one disk may be moved at a time.
Each move consists of taking the upper disk from one of the rods and sliding it onto another rod, on top of the other disks that may already be present on that rod.
No disk may be placed on top of a smaller disk.

This might be a simple game but it is a great tool to train your logic thinking.

Play the game here: http://www.mazeworks.com/hanoi/index.htm

You can try it with different number of disks. They even added the challenge of completing the game in the minimum moves. Solution is also provided should you face challenges in completing!

Have Fun!

For those who are interested in the history of this games, read more here.

I will be back in the next post to discuss on different approaches to a Additional Mathematics on Identity which falls in the topic of Factor Remainder Theorem. Look out for the next post!

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