The Flying Colours Maths Blog: Latest posts

The smart way to do the binomial expansion (Part II)

This is a follow-up to Monday's post about the smart way to do the binomial expansion. In this one, we're going to look at how to do C4 binomial expansions - ones with crazy powers like $-3$ or $\frac{3}{2}$. This bit is very important: you should COMPLETELY ignore the formula

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The smart way to do the binomial expansion (Part 1)

Ah, the binomial expansion. The scourge of my A-level: the sum that was always wider than the paper, and always had one more minus sign than I'd allowed for. A crazy, pointless exercise in arithmetic, if you ask me, only really useful for finding square roots in your head (of

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Free for all Friday – Valentine’s week edition

End of the week again already? Fantastic. That means it's time for free-for-all Friday! Did you get any Valentine's cards? Did you send any? Did you fall in love with maths? Of course you did. Tell me about it here... or ask anything that's on your mind. There's even a

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Three good reasons you divide when you integrate

When you integrate a function - for instance, $\cos(3x)$, you probably have to stop for a moment and think: "Do you multiply by 3 or divide when you integrate?" Some people don't even get that far, and just say "Oh, it must be $\sin(3x)$", and all of us can just

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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

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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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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

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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

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