The Flying Colours Maths Blog: Latest posts

Completing the square – the easy way

-or- matching coefficients for fun and profit I bluffed my way through completing the square at A-level. I guessed, dropped minus signs, and dropped marks all the way. It was only once I started teaching it that I figured out completing the square. Let me share it with you. Completing

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Secrets of the Mathematical Ninja: The surprising integration rule you don’t get taught in school

Difficulty: ** Impressiveness: **** If you do A-level maths, you do an awful lot of integration. You integrate polynomials, trig functions, partial fractions, exponentials, parametric curves, products of these... and get nice analytical answers. Here, let me provoke controversy: Unless you're going to be a pure mathematician or a maths

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Free for all Friday (Good Friday edition)

It's the Easter break, time to make good on all those promises to put the work in before the exams! How can I help you this week? What's bothering you? Where are you stuck? Let me know in the comments and I'll get back to you as soon as I

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The three secrets to successful revision

There's a dark cloud looming. It's already April and the AS and A2 maths exams are unusually early this year. So, the question is, what can you do to revise effectively without driving yourself crazy? Here are my top three tips for getting on top of the material rather than

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Secrets of the Mathematical Ninja: powers near 1

Difficulty: (simple version) *** (advanced version) ***** Impressiveness: ***** Accuracy: *** If you're a statistician, you quite often end up working out powers of numbers just a little less than 1. What's the probability of rolling a pair of dice ten times and never getting a double six? It's $\left(\frac{35}{36}\right)^{10}$.

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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!

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Quotable maths: Bohr

We all agree that your theory is crazy, but is it crazy enough? - Niels Bohr

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What is a circle? (and how do you answer C2 questions about it?)

A conjecture both deep and profound Needs a proof that the circle is round. In a paper by Erdős Written in Kurdish A counter-example is found. One of my favourite questions to ask students is "what's a circle?" because I get to play "so that means this is a circle!"

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Secrets of the mathematical ninja: Divisibility tricks

Some of the secrets of the mathematical ninja are pretty pointless, when you come down to it: after all, we have machines for most of these things. The divisibility tricks are useful (as far as I can see) only in a very specific circumstance: when you're deciding whether to cancel

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