formulae

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 [pmath]{1}/{x^7}[/pmath] is rewritten as [pmath]x^-7[/pmath])

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

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?

We have discussed about Simple And Compound Interest using 2 case studies previously based on concepts understanding. Now we have introduced formulaes which will make your calculation faster and easier :)

To find the Total Amount based on Simple Interest, this is the formuale you can use:
$A_n=P(1+\frac{r}{100}n)$

An : Total Amount after n years

P: Original Principal Amount

r: Simple Interest Rate

n: Number of Years

To find the Total Amount based on Compound Interest, this is the formuale you can use:
$A_n=P(1+\frac{r}{100})^n<br>$

An : Total Amount after n years

P: Original Principal Amount

r: Compound Interest Rate

n: Number of Years

Apply these formulaes to the case studies we have discussed, did you get the same answer?

Congrats!Now you have 2 different approaches, the formulae way or the conventional way to solve all Interest questions.

Keep using the strategies learnt so that you get better and better.

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

Formulae Usage On Simple And Compound Interest