# The Flying Colours Maths Blog: Latest posts

## A GCSE surprise

Some time ago, I was surprised to see the following question in a predicted GCSE paper: Solve for $x$: $\frac{2x}{3x+2} \leq \frac{3}{4x+1}$ Give your answers to two decimal places (3 marks) Why surprised? Surprised because the techniques you need to solve it correctly are Further Maths A-level, rather than

## Ask Uncle Colin: A Pair of Vectors

Dear Uncle Colin, The question says "Under what circumstances does $|\mathbf{a} + \mathbf{b} | = | \mathbf{a} | + | \mathbf{b} |$ and I don’t have a clue. Can you help? Sines? Cosines? Angle Leaves A Residue Hi, SCALAR, and thanks for your message! I have several ways to approach

## Proofs

A question that comes up a lot in class is, “how do you get good at proofs?” (It’s usually framed as “I don’t like proofs”, but we’re not having any of that negativity here, thank you very much.) I don’t have a silver bullet for that. I do have some

## Ask Uncle Colin: A horrible CDF

Dear Uncle Colin I have the set-up below - how do I find the cumulative density function for $d^2$? - Circles Don’t Fit Hi, CDF, and thanks for your message! Before I start, I’m going to make two simplifying assumptions that don’t change anything1 - that the radius of the

## Dictionary of Mathematical Eponymy: Noether’s Theorem

We’ve just reached the halfway point of the Dictionary of Mathematical Eponymy project, and it’s time for a fairly famous one (and again, one I’ve been meaning to understand better). What is Noether’s Theorem? Emmy Noether has several theorems named for her, but the first (and probably most important) can

## Ask Uncle Colin: Dividing by halves

Dear Uncle Colin, Why is dividing by a half the same as doubling? - How Arithmetic Leverages Fractions Hi, HALF, and thanks for your message! I’m going to give a couple of reasons: first, the algebra of it, then the logic. Algebra Let’s set this up as $\frac{x}{\br{\frac{1}{2}}} = y$

## “How many days old are you?”

“How old are you?” asked young Fred. (This is not, technically, an ‘Ask Uncle Colin’. It’s an ‘Ask Daddy’.) “I’m 42, buddy.” “42 days?” “No, 42 years!” “Oh. But how many days is that?” It is not quite 7:15am on New Year’s Day. I have not yet had my coffee.

## Wrong, but Useful: Episode 75

In episode 75 of Wrong, but Useful, we talk with @astrastefania, who is Stefania Delprete in real life. We discuss: Dreams about Maths and doing Maths in lucid dreams Goodreads maths reading challenge Newsletters I like: Stuff Evelyn Wants You To Read by @evelynjlamb and and Fair Warning by @SophieWarnes