Posted in number theory, surds.

Funny thing. Type $(2 + \sqrt{3})^{20}$ into Wolfram Alpha. (Or, if you're really lazy, click this link.). It's 274,758,382,273.999999999996 or so. The higher the power you pick, the closer $(2 + \sqrt{3})^n$ gets to an integer value -- although it never quite gets there, because $\sqrt{3}$ is irrational. So, how

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Posted in probability, sport.

Former Formula 1 driver @MBrundleF1 asks: These election opinion polls. I've never been approached, nor has anybody I know, about a poll on anything whatsoever. Who are these people? — Martin Brundle (@MBrundleF1) April 5, 2015 (Obviously, he didn't ask me specifically, but I thought it was a good question.)

Read More →My dear readers, it is not often I become angry. Rage is not an emotion that frequently troubles Flying Colours Towers. A sharp word for a student who is trying to wind me up, perhaps once in a while, but rarely a rant. As the man says, you wouldn't like

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Posted in calculus.

A challenge question: The curve with equation $y=e^{kx}$ is tangent to the curve with equation $y=x^2$. Find $k$. Curves tangent to other curves? Well, why not! Tangent just means 'touching' -- so as long as there's a point common to both curves where the gradients are the same, we're good.

Read More →At granny's house, it always seems to go the same way after lunch: Bill and his cousin chase each other around the dining room, while the adults try to make head or tail of their toys. This Sunday was no different: the toy in question comprised a large number of

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Posted in core 1.

When you said you wanted to do maths A-level, I imagine people pursed their lips and said "oo, it's a big step up." They're right, to an extent: every October I get deluged with panicked students who realise that the 'coast through it all doing just enough' approach that served

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Posted in ask uncle colin.

A student asks: "I've got my calculator paper coming up -- I'm not really struggling with anything, I just get nervous! How can I make sure I do as well as I know I can? That’s a great question! First up: keep reminding yourself that you don’t really struggle with

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Posted in gcse, probability, ranting.

Gosh, who would have thought it? 15,000 students (at the time of writing) have signed a petition to get EdExcel to change the grade boundaries for Thursday's non-calculator GCSE paper. Good luck with that. The boundaries will have been set using magic statistics, and either have been or will be

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Posted in podcasts.

In this month's thrilling instalment of the world's #1 maths chatter podcast, @reflectivemaths (Dave) and I discuss... The number of the podcast: 1000000000000066600000000000001, Belfigore's prime. The rollercoaster question and the role of common sense in exams Colin’s reading: The Trachtenberg Speed System of Basic Mathematics Traffic maths and simulations --

Read More →On Twitter, @tessmaths asks: What's the thing you will do in the last lesson before GCSE maths exam this week? #mathsTLP — Tess Maths (@tessmaths) May 31, 2015 ... which is such a good question, it would be rude not to answer. Here's what I'll be doing with my GCSE

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