# Browsing category core 2

## A MathsJam Masterclass

At the East Dorset MathsJam Christmas party, @jussumchick (Jo Sibley in real life) posed the following question: There are two ways to draw a 16-gon with rotational symmetry of order 8 inside a unit circle, as shown. What's the ratio of their areas? Typically, I look at this sort of

## HOW much rice?

There's a legend, so well-known that it's almost a cliche, about the wise man who invented chess. When asked by the great king what reward he wanted, he replied that he'd be satisfied by a chessboard full of rice: one grain on the first square, two on the second, four

## The Mathematical Pirate’s Guide to Factorising Cubics

“Yarr,” said the Mathematical Pirate. “Ye’ll have plundered a decent calculator, of course?” “Er… well, I bought it from Argos, but… aye, cap’n! A Casio fx-83 GT PLUS!” “A fine calculator,” said the Mathematical Pirate. “One that offers you at least three ways to factorise cubics.” “Really!? I thought you

## Quotients and remainders

A few months ago, I wrote a post about replacing long division with a coefficient-matching process. That's brilliant for C2, but what happens if you're looking at a C4 question that wants a quotient and a remainder? Well, it gets a bit more complicated, that's what happens. But it's not

## Why I don’t buy that $1 + 2 + 3 + … = -\frac{1}{12}$

Thanks to Robert Anderson for the question. I told him that the sum of an infinite number of terms of the series: 1 + 2 + 3 + 4 + · · · = −1/12 under my theory. If I tell you this you will at once point out to

## There’s More Than One Way To Do It: Algebraic Division

Doing long division is like going to watch Raith Rovers play: you can force yourself do it, but why would you? I'm not going to show you the long division way. It's too much fuss to set out, and frankly I can't be bothered with it. There's a way I

## There’s More Than One Way To Do It: Equations of a circle

Depending on your AS-level maths exam board, you might encounter the equation of a circle in C1 (OCR) or C2 (everyone else). It's really just a restatement of Pythagoras' Theorem: saying $(x-a)^2 + (y-b)^2 = r^2$ is the same as saying "the square of the horizontal distance between $(a,b)$ and

## Two trains and a fly

There's a classic maths puzzle that goes something like this: Two trains start 20 miles apart, and travel towards each other at 10 miles per hour. Just as they start, a fly takes off from the front of one train, flies at 15mph directly to the other, turns around, flies

## Why the binomial expansion is stupid and you shouldn’t use it

The Mathematical Ninja looked offended. For once, it wasn't a student that was the guilty party, it was me. "You're considering a series on the WHAT?!" "The binomial expansion," I said, brightly. "Drivel!" said the Mathematical Ninja "Drivel, piffle and poppycock! Newtonian claptrap, not worth the space made for it

## Core 2 basics revision quiz

I'm going to run a little experiment for a while. Every Tuesday until the exams, I'm going to put out a ten-question quiz on one of the A-level modules. I'd love to have feedback on whether you find them useful, how I can make them better, and what else I