Angle Bisectors and Perpendicular Bisectors

Not sure about how to construct a bisector? Or not sure which one is which? Have a look at these two videos which show you the step-by-step instructions.

Angle Bisectors:

Perpendicular Bisectors:

Got the hang of it? Draw a few lines and angles and get some practice in! You'll need a pencil, ruler and compass for this - make sure you have them.

Writing and Solving Equations

You might not have to just solve equations in your exam - you might have to write them out first!

Remember an equation just says that two expressions are equal.

So you just need to write out the information you read, and make sure you include an '=' sign!

Here's an example:

"I think of a number, double it and add seven. My answer is 37.

A number we don't know is usually called x.

Double this number would be written as 2x.

Seven more than this must be 2x + 7.

We are told this equals 37, so we write 2x + 7 = 37.

Got the hang of it? Try writing an equation for each of these sentences:

Volume and Surface Area

Get some practise in finding the volume and surface area of 3D shapes!

Remember:

Volume is the space inside the shape

Surface area is the total of all the areas around the shape.

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.