Binomial Theorem came out as a 9 marks question in 2009 GCE ‘O’ Level Additional Mathematics Paper (Subject Code: 4038) so you know as well as I do the importance of Binomial.

Read about other useful posts on Binomial Theorems:

• Binomial Expansion Teaches how to choose the RIGHT partner (:

• A-Math Binomial Expansion: Finding Term Independent of x By A Shortcut Method

• Exam Question : Usage of Binomial Formula

I’m looking at the question now. It is testing on the usage of the Binomial formula, including the ‘n choose r’ formula. Many students call this sign: ‘!’ ‘exclamation mark’ which is known correctly as factorial.

I will be using the following question to illustrate how to simplify the ‘n choose r’ formula without memorizing. (I understand some schools want students to memorize)

Let’s begin by understanding what’s ‘n choose r’ all about:

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Do you know how to simplify ‘n choose 3′?

Here’s the question which requires us to apply what we have discussed. I would suggest you attempt it on your own before clicking here for the solution.

binomial-question

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In the earlier post on free Math Exam Papers, we received very good response. Almost 200 copies were downloaded in less than 7 days. We have a subscriber requesting for step by step solution for the questions though we have provided the answer keys. I am sorry I am unable to provide the step by step solutions due to my busy schedule. However, subscribers can email me their workings I can assist and advice you on the incorrect workings. I hope this would be useful. Moreover, by providing the step by step solution will also not be useful as most students will perhaps take the easy way out to just “read” the solution and think that they understand them. Mastery of Mathematics is not by “reading” but it’s the knowing and applying of the strategies.

I have picked up one question on Binomial Expansion (another tricky A-Math topic) for discussion. Specifically on finding Term Independent of x.

Allow me to discuss the common mistake that students make.

Most students will expand the expression term by term

Disadvantages:

• Too time consuming
• Higher tendency to make careless mistakes!

So the following step by step solution is what I taught my students during my A-Math Ultimate Leap Programme (For Sec 4s who still wish to join, call me @ 9685 7675. For Sec 3s, we are opening up the classes in March 2009! More info will be released in Feb. Keep reading this blog)

Features to take note:

• General Term is applied (No memorization is required, just refer to the formula sheet if you aren’t sure)
• Constant (numbers) & variable (which is x in the question) are separated. (so that we can focus on the important part first)
• Power of x is circled (in red) so that you focus all your attention on it. (Reduces careless mistakes too!)
• Since this is a 4 marks question, 4 minutes is the working time to complete the solution. (Time management is part of examination techniques)

Skills required:

• Understanding of Term Independent of x (i.e it’s x to the power of 0 NOT x is zero!)
• Usage of Binomial Formula
• Basic application of Indice law (Observe that is rewritten as )

Evaluate the term which is independent of x in the expansion of .

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Harry – a vivd reader of askalwayslovely.blogspot.com sent me an email asking about solving of the following question. He did it using trial and error. I believe it will take him some time. He felt that his approach was not the best so he emailed me asking for alternatives.

In fact for this question, there is a step by step way which will get us the answer in less than 8 minutes time.

Question: If the coefficient of and in the expansion of are equal, find

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I always like to share with my students what each Math topic has to do with their everyday life, particularly their future.

Yesterday, I did Binomial Expansion. It’s about finding the RIGHT partner (: It’s about mastering the skills of finding the correct match based on a set of factors.

Just like this question, you see that there are 2 brackets. 1st bracket is good for now. 2nd bracket needs us to do some expansion work by using the FORMULAE (It’s provided during GCE O Level Exams but some schools don’t seem to provide it for their mid year, strange)
Oh yar, there is NO need to remember the Binomial Expansion Formulae!

Then one of the questions that often pop up is ” When do we stop our expansion for [TEX](1+\frac {x}{3})^{12}[/TEX]?”

To answer this question, it depends on what type of partners you are looking for.

(more…)

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Additional Mathematics (A-Math) topics – Simultaneous Eqns, Vectors, Gradient of Normal, Binomial

binomial, Exam Questions, gradient of normal, simultaneous eqns, vectors Hide