Proof By Induction

Proof by Induction is the domino run of the Further Maths world:

If one domino falls, and the next one definitely falls, they all will.

A nice introductory video from Khan Academy



Once you have looked through this you can attempt the questions on this sheet

Worksheet from Mr Barton's A-Level Maths site

Another worked example can be found on our Instagram feed:

Proof by Induction example for FP1

A photo posted by King Ed VII (@makerevision) on May 12, 2016 at 1:45am PDT

Trigonometry - Sine and Cosine Rule

A short video on historical use of Trigonometry in ancient Indian astronomical observatories...



When we aren't dealing with right angle triangles then the Sine Rule and Cosine Rule become very important:

For the Sine Rule we are dealing with a situation involving two sides and two angles (one of which will be unknown), for the Cosine Rule you need 3 sides and one angle (again one of which is unknown).

Using the Quadratic Formula

Whenever you're faced with a quadratic equation you have choice:

• Plot it and find the intercepts
• Factorise and solve (x+...)(x+...) etc. Each bracket =0 etc
• Complete the square and rearrange (see these older posts)
• Use the quadratic formula:

(More can be seen about the quadratic formula in this post)

You will have your own order of preference for the above methods, but one thing you can be certain of is that if there are real solutions, the formula will find them (factorising may not!).

Circle Theorems

This powerpoint is not perfect (it mentions worksheets which we don't have here) but it does outline the key theorems:

Circle theorem powerpoint from ebayliss

nth Term

There are a couple of different ways of finding the nth term. Here's a few examples.

Completing the Square

I've been working with a few students today on Completing the Square. Here's a quick video reminder for those that need it.