# The Flying Colours Maths Blog: Latest posts

## The trig identities you need to know for integration

There is one big-daddy among the trig identities that you need to learn right now, if you don't know it already: $$\sin^2(x) + \cos^2(x) = 1$$ This is the identity that nearly all of the others spring from. There are some more definitions: $tan(x) = \frac{\sin(x)}{\cos(x)}$, which is one of

## Free-for-all Friday!

It's that time of the week again! What's been on your mind? What's giving you a headache? As always, drop your questions in the comments box and I'll get back to you as swiftly as I can!

## The maths of the decathlon

While I'm quite steadfastly refusing to be swept along with either Olympics fever or anti-games grumbling, I stumbled across the Wikipedia page for the decathlon in a moment of nostalgia for my 1980s childhood tapping the keys of the ZX Spectrum - a system that was kind of like an

## The crazy way you have to integrate logs

When you learn how to integrate by parts, you're probably told that a good rule of thumb is that if you have a power of $x$, that's going to be the thing you differentiate. That's a pretty good heuristic, but there are two places it breaks down: one, if you're

## Free for all Friday

Frankly, the first free-for-all-Friday of February! Fandabbydozy. You know the drill: whatever questions you've got about any part of A-level maths - AS, A2, further, whatever you like - bring 'em on. Something your teacher rushed through, or something you don't understand why... ask away!

## Why SOH CAH TOA is stupid (and what you can do instead)

My dad tells me that, above the blackboard in his 1960s Scottish high school, was a banner with the letters 'SOH CAH TOA' written out on it. Any questions about the banner were brushed off with a smile and 'you're not old enough to learn about SOH CAH TOA yet."

## Questions with only one answer

There are many questions with only one answer. Or at least, one sensible answer. If someone asks you "Are you dead?", the only possible answer you can give is "no". "Does my bum look big in this?" "Of course not, dear, it looks lovely". And if you say "Is there

## Free for all Friday

Well... it's not really a free-for-all Friday as I'm on a train to Bristol, but you can still leave me questions here and I'll respond when I'm back in front of a computer. Any A-level maths topics - including Further Maths - you're struggling with, I'll be happy to help

## The Line of Best Fit (Linear Regression)

Have a look at this picture. What do you notice? "It's a straight line, Colin!" Very good. You could get a ruler out and draw a straight line through the points. Why would you bother doing such a thing? Well, the idea is that if you can model a data