$y$ is directly proportional to $x^3$, you say? And when $x = 4$, $y = 72$? Well, then. The traditional method is to say: $y = kx^3$ and substitute in what you know. $72 = 64k$ $k = \frac{72}{64} = \frac{9}{8}$ That gives $y = \frac98 x^3$. Easy enough. But

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Posted in featuring peter rowlett, podcasts.

A special anniversary episode where @reflectivemaths (Dave Gale) and I pick the brains of two special guests: Abel prize nominee @samuel_hansen (Samuel Hansen) and @peterrowlett (Dr Peter Rowlett, surprisingly). “I think we should conclude that an argument has gone on long enough when Samuel Hansen is the voice of conciliation”

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Posted in geometry, ninja maths.

@srcav wasn’t going to take that argument lying down! The Ninja looked smug. He thought that was it, game over. I thought it had been a sneaky trick he’d pulled with the Ninja Bread, but I couldn’t change it now. I finally pulled my mouth apart and took a big

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Posted in ninja maths.

“Who DARES to challenge the Mathematical Ninja?” he bellowed. “It is I,” said the challenger. “@srcav, but Cav in real life.” “Oh!” said the Mathematical Ninja. “Hello there, old chap, I was expecting someone else. Come in, I’ll put the kettle on.” “Much obliged,” said Cav. The challenge, which Cav

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Posted in gcse, triangles, trigonometry.

There’s a natural question, when you learn about the sine and cosine rules: “Is there a tan rule?” The answer to that is yes – yes, there is a tan rule. The natural follow-up is “Why don’t we learn it?” Let me explain why not! Here’s the tangent rule in

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Posted in gcse, triangles, trigonometry.

There’s a natural question, when you learn about the sine and cosine rules: “Is there a tan rule?” The answer to that is yes – yes, there is a tan rule. The natural follow-up is “Why don’t we learn it?” Let me explain why not! Here’s the tangent rule in

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Posted in gcse, triangles, trigonometry.

There’s a natural question, when you learn about the sine and cosine rules: “Is there a tan rule?” The answer to that is yes – yes, there is a tan rule. The natural follow-up is “Why don’t we learn it?” Let me explain why not! Here’s the tangent rule in

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Posted in basic maths skills.

Every so often, a question that comes up that looks incredibly trivial, but – no matter how much each side protests that the preference doesn’t really matter – sets down clear divides in the maths community. My podcasting partner in crime-fighting @reflectivemaths (Dave Gale in real life) stumble upon such

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Posted in probability, sport.

There are six minutes to play in the last Autumn international, and Australia are leading Wales by 30 points to 26. Australia, however, have just conceded a penalty in front of the posts, leaving the Welsh captain, Sam Warburton, with a dilemma: should he kick at goal (and take a

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Posted in quadratics.

A student asks: I’m currently preparing for my GCSE mocks. I started looking over quadratic expressions and factorisation and it just blew me away – I get stuck trying to work it out with negatives! First things first: thanks for asking for help. You’re not alone: factorising quadratics can be

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