What’s that, you cry? Algebra was bad enough, without throwing fractions into the mix? Well, unfortunately for you, it’s on the Edexcel Unit 3 spec., and you’re going to have to learn it. To find out about algebraic fractions, simplifying before multiplying, and calculations involved, read on…

Yikes. Probably the fusion of some of the nastier topics on the GCSE Maths course – trigonometry, and graphs. And you have to know how they transform, as well! But not to fear, this article is here to tell you all you need to know about trigonometric graphs – and how they transform, using the handy rules in this article here (best read that before this article). Ready? Then let’s get these graphs going on…

You might have thought transformations was as simple as translating, enlarging, rotating and reflecting. Well, maybe it is – in Year 7. For the Edexcel GCSE Maths course, you need to learn about transforming any graph – known as transforming **functions**. Confused? Don’t panic, we’re going to explain this all here – so let’s give it a go!

You’ll have almost certainly seen this stuff somewhere before – probably around Year 7, 8 or even earlier. But heading back to translations, enlargements, rotations and reflections is all important for getting those easy marks in the Edexcel Unit 3 exam – so we’re going to cover it. Ready? Then let’s go for it…

You might have thought this was done, with a quick article on simple simultaneous equations a while back. But no, they’re back, and they’re back with a vengeance. Ready to take the plunge? Here we go…

Proportion is an easy topic, and nowhere near as frightening as it looks. Well, not normally any way. There are two (reasonably) simple formulas you must learn for proportion – one for direct proportion, and one for indirect proportion. But first, some definitions:

Directly Proportional –This is when ‘as one thing goes up, so does another’. For example, the amount of money you earn is proportional to the number of hours you work – the more hours you work, the more money you receive.

Inversely Proportional –This is when ‘as one thing goes up, another goes down’. For example. my laptop’s battery level is inversely proportional to the number of hours I spend using it. The higher the number of hours used, the lower the battery level.

When you’re answering a simultaneous equations question, you’ll actually be given two equations to work with – and there’s a good reason for this: both equations have two unknown variables in (variables are *x’s* and *y’s*), meaning that we can’t solve them individually.

Instead, we have to use both equations to figure out an answer!

And you thought normal, straightforward, rational numbers were hard enough. Then surds came along – nasty, recurring decimals; square and cube roots, and goodness knows what else. It’s understandable that you’d be feeling a little unsure of what to do now. But really, surds are all about knowing how to manipulate them – a few handy tricks I’m going to show you here. Ready? Then let’s begin…

So, factorising something basically means to put it inside of brackets. Sometimes you’ll get a simple question with simple factors, other times you’ll get a tricky question with multiple factors.

Did I tell you that factors can be numbers **and **letters?

**So, what is trial and improvement?**

*Well, it’s definitely not trial and error… It’s trial and error’s mathematical cousin, trial and improvement.* In all seriousness though, the exam boards are very picky with this kind of thing, and it’s “trial and

**improvement**” – Think positive!

So? What is trial and improvement? Put simply, it’s mostly common sense… You’ll get given a question something like this:

Prove that

xhas a solution between two and three. correct to one decimal place.^{3}– 6x + 1 = 0