# January, 2014

## 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

## Wrong, But Useful – Episode 11

The first non-trivial palindromic episode of Wrong, But Useful, in which Colin gets a touch of the Samuel Hansens and starts picking fights, and Dave does his best to calm things down. Fight #1, with loyal listener @srcav about which form of a straight line is better. The opposite of

## Proving three points lie on a straight line (GCSE vectors)

Need help with problem-solving? Fill out the short blue form on the left and get free tips on how to approach maths questions - delivered direct to your inbox twice a week → If you ever study GCSE vectors questions, you'll spot a pattern: there's normally a (relatively) straightforward first

## Proving three points lie on a straight line (GCSE vectors)

If you ever study GCSE vectors questions, you'll spot a pattern: there's normally a (relatively) straightforward first part which involves writing down a few vectors, and then something like "show that points $O$, $X$ and $Y$ lie on a straight line." Pretty much every student I've ever worked with on

## Why the maths of infinite sums is dangerous

This is a follow-up to last week's piece on the Numberphile video claiming that $1 + 2 + 3 + 4 + ... = -\frac{1}{12}$. I mentioned something in the last article about certain1 infinite sums not being well-defined, and wanted to add some examples to show how they can

## 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

## Inverse sines near a half: Secrets of the Mathematical Ninja

"So, $\sin(x) = 0.53$," said the student. "32 degrees," said the Mathematical Ninja. The student frowned - the Mathematical Ninja's showing off was starting to wear her down - and typed it into the calculator to check. "$32.005^º$, actually." "I'll take that," said the Mathematical Ninja. "How did you guess

## Dealing with M1 vectors

OK, so you've got to grips with the SUVAT equations, you're on top of resolving forces, you understand that $F=ma$ and you have M1 under control... only for them to start throwing $\bi$s and $\bj$s around. Who ordered those? Maybe you have a vague recollection of vectors from GCSE -

## Wrong, But Useful: Episode 10

This month, @reflectivemaths (Dave Gale in real life) and I discuss: The birth of baby Bill (d'aww) Dave's loyalty to More or Less, and nappies WBU ultra-loyalist 's comments on Episode 9 and a plea for reviews Whether to up our podcasting output in an attempt to outdo Math/Maths and

## The Compulsory New Year’s Resolution post

A big hello to 2014! Last year was a fantastic year for me: I spoke at the Edinburgh festival, I ran the Berlin marathon, I had crosswords published in 1 Across... oh, and I became a dad for the first time. Cracking year. 2014 is going to struggle to top