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30
A-Math Binomial Expansion: Finding Term Independent of x By A Shortcut Method
8 Comments | Posted by alwaysLovely in A-Math, Weekly Question
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 ![clip_image002[4]](http://www.singaporeolevelmaths.com/wp-content/uploads/2009/01/clip-image0024.gif){kind=small}
.
So do you do your working in a similar manner or you have your own style? I would love to hear from you if you know how to do this question initially. If no, which part did you not understand?
Related Posts:
- The Exclamation Mark ! in Binomial Theorem
- Binomial Expansion Teaches how to choose the RIGHT partner (:
- Exam Question : Usage of Binomial Formula
- Simultaneous Eqns, Vectors, Gradient of Normal, Binomial
- Tips on Operations of Standard Forms
8 Comments for A-Math Binomial Expansion: Finding Term Independent of x By A Shortcut Method
Cindy | February 9, 2009 at 1:20 pm
huaan | March 21, 2009 at 9:20 pm
thanks Ms Ong! I am sec 4 now, and i guess this question is really a good revision for me!=0
Reza | June 3, 2009 at 12:25 am
Sry but i haven’t learned any of this at all in school since im following the Malaysian Add Maths Syllabus.
Could you please enlighten me on what is this Independent term thingy ?
Thanks in adv.
CombiStudent | September 14, 2009 at 7:28 am
How would I find the constant term in the expansion of:
(x^2 + (1/x^2) – 2)^10.
This is a trinomial, but is there a way I can manipulate the expression so I can use the binomial theorem? What we just did was expand it to the 5th power and then square that to find the constant term. So we did:
[(x^2 + (1/x^2) - 2)^5]^2.
=S It took a while, but at least we got some number :S.
gautam | October 28, 2009 at 4:49 am
Thanks for the alert… our teacher insrtucted us to do it in the sasme way bt thanks anyway :)
The Exclamation Mark ! in Binomial Theorem | February 25, 2010 at 11:40 pm
[...] A-Math Binomial Expansion: Finding Term Independent of x By A Shortcut Method [...]
Kim | March 11, 2010 at 2:30 am
I didn’t know how to do that sort of question before I read this because I missed lectures on binomial expansion and i understood it untill the very last line because I don’t understant why that term equals that specific number?
Hi Sir/Mdm,
I am doing the same way as what you are doing.?
Thanks for the alert.
Regards,
Cindy
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