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…

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!

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