Year 12- Completing the Square

From the first test, completing the square was identified as an area to work on. If you are struggling, watch these videos and have a go at the questions. #

Exam questions 

Completing the square:

Using completing the square 

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.

Solving Trigonometric Equations

Let's take a look at a typical Core 2 question on solving trignomentric equations.

This is part (b), where part (a) asks you to show that the equation can be rewritten as

(1 - 5 cos 2x)( sin 2x) = 0.

A few exam tips when answering these:

1. Which trig identity should I use to simplify the equation? Is it a quadratic (using sine squared or cosine squared) or not?

2. Has the equation been factorised already? Can I see multiple solutions? Remember that if you square root, you need to use a positive and negative root.

3. Remember to find the range for 2x, or whichever function of x you find by removing the trig function.

4. Use a quick sketch of a trigonometric graph to help you remember how many solutions are in this range.

You can find worked solutions to this question, here for part a and here for part b.

There's plenty more exam questions where that came from - take a look at exam solutions, which can link you straight to this type of question for each past paper.