Parallel and Perpendicular Lines

Get some practise in on finding perpendicular lines!

When it comes to perpendicular gradients, the key rule is that the gradients have a product of -1.

So, this means that if you know one gradient, the perpedicular gradient comes from changing the sign and inverting it - for example, a gradient of 2 is perpendicular to -1/2.

A couple more -

A gradient of -3 is perpendicular to a gradient of 1/3
A gradient of 2/3 is perpendicular to a gradient of -3/2

Still not sure? Take a look at this tutorial from Corbett Maths.

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).

Rearranging Formulae- Higher and Foundation

Today my year 11 higher classes and C MTG have been revising Rearranging Formulae. Remember to take each step carefully.

Corbett maths exam questions can be found here: 

Corbett exam questions Higher 
Corbett maths exam questions Foundation

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

Circle Theorems

A nice single sheet covering the key CIRCLE THEOREMS. Remember that the specific wording is really important!!!

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. 

Paper Puzzle

Two rectangles lay on top of each other at diagonals as shown. What are the dimensions of the purple rectangle? (credit: this weekend's Guardian)