# April, 2014

## Simplifying algebraic fractions (GCSE algebra)

Towards the end of a GCSE paper, you're quite frequently asked to simplify an algebraic fraction like: $\frac{4x^2 + 12x - 7}{2x^2 + 5x - 3}$ Hold back the tears, dear students, hold back the tears. These are easier than they look. There's one thing you need to know: algebraic

## Simplifying algebraic fractions (GCSE algebra)

Towards the end of a GCSE paper, you're quite frequently asked to simplify an algebraic fraction like: $\frac{4x^2 + 12x - 7}{2x^2 + 5x - 3}$ Hold back the tears, dear students, hold back the tears. These are easier than they look. There's one thing you need to know: algebraic

## A student asks: Why does variance do THAT?

A student asks: The mark scheme says $Var(2 - 3X) = 9 Var(X)$. Where on earth does that come from? Great question, which I'm going to answer in two ways. Firstly, there's the instinctive reasoning; secondly, there's the maths behind it, just to make sure. Instinctively Well, instinctively, you'd think

## Book review: Vedic Mathematics

I wanted - I really, really wanted - to like this book. On the surface, it's exactly my cup of tea: a whole book of tricks to make mental arithmetic easy. Sadly, there's so much about it that's dreadful that the nuggets inside it are hardly worth the effort. The

## The Sausage Rule: Secrets of the Mathematical Ninja

The student stared, blankly, at the sine rule problem in front of him. $\frac{15}{\sin(A)} = \frac{20}{\sin(50^º)}$ "I don't know where to st," he started whining as something flew past his head. He knew better than to turn and look at whatever implement of death and destruction he had dodged. "I

## Dealing with nasty powers

There's nearly always a question on the non-calculator GCSE paper about Nasty Powers. I'm not talking about the Evil Empire or anything, I just mean powers that aren't nice - we can all deal with positive integer powers, it's the zeros, the negatives and the fractions that get us down.

## The square root of three: Secrets of the Mathematical Ninja

"$45 \cos($ thir... I mean $\frac{\pi}{6})$," said the student, catching himself just before the axe reached his shoulder." "Thirty-nine," said the Mathematical Ninja, without a pause. "A tiny bit less." The student raised an eyebrow as a request to check on the calculator, and the Mathematical Ninja nodded in assent.

## The semicircle puzzle

In a recent episode of Wrong, But Useful, I asked: A square is inscribed within a circle of radius $r$. A second square is inscribed within a semicircle of the same radius. What is the ratio of the areas of the squares? It's easy enough to find the side length

## How to remember which way the skewness goes

OK, this is a quick and dirty trick of the sort that I love and the Mathematical Ninja hates. He doesn't have much time for stats at all, truth be told, least of all skewness. However, I've had several students struggle to remember 'which way is which' when it comes

## How The Mathematical Ninja Divides By 49

"... which works out to be $\frac{13}{49}$," said the student, carefully avoiding any calculator use. "Which is $0.265306122...$", said the Mathematical Ninja, with the briefest of pauses after the 5. "I presume you could go on?" "$...448979591...$" "All right, all right, all right. I suppose you're going to tell me