Via @DrTrapezio, an interesting question: Year 13 curve sketching challenge: y = | | | |x| - 1| - 1| - 1| — Luciano Rila (@DrTrapezio) July 14, 2016 Where do you even start with that mess? The answer to that, my friend, is you start in the middle and

Read More →
Posted in core 3, trigonometry.

"Hm," I thought, "that's odd." I don't often work in degrees, but the student's syllabus insisted. And $\sin(50º)$ came up. It's 0.7660, to four decimal places. But... I know that $\sin\left(\frac 13 \pi\right)$, er, sorry, $\sin(60º)$ is 0.8660 -- a difference that's pretty close to $\frac 1{10}$. Which got me

Read More →
Posted in ask uncle colin, core 3, trigonometry.

Ask Uncle Colin is a chance to ask your burning, possibly embarrassing, maths questions -- and to show off your skills at coming up with clever acronyms. Send your questions to colin@flyingcoloursmaths.co.uk and Uncle Colin will do what he can. Dear Uncle Colin, I've been given a trigonometry problem I

Read More →
Posted in core 2, core 3, geometry, trigonometry.

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

Read More →
Posted in core 3, inequalities, modulus.

Solve $\sqrt{|x|-3} > x-4$ Difficult, as the man said. Difficult, difficult, lemon difficult. It’s not that it’s tricky to solve it - it’s just… fiddly. Let’s start by drawing the graphs. The right-hand side is easy enough: it’s a straight line with gradient 1, through the point $(0,-4)$. The left-hand

Read More →
Posted in circles, core 3, geometry, trigonometry.

Ask virtually any maths teacher what $\sec(\alpha)$ means, the chances are they'll say "it's $\frac{1}{\cos(\alpha)}$," without missing a beat. Ask them what it means geometrically... well, I don't want to speak for the teaching profession as a whole, but I'd have been stumped until the other day. As with the

Read More →
Posted in calculus, core 3, pirate maths.

"Yarr!" said the Mathematical Pirate, chopping his way through the piles of papers strewn around the classroom. The student looked unimpressed. "How do you differentiate $y = \sec^2(3x)$?" she asked. The Mathematical Ninja would have discerned that she'd just read the question without trying to solve it, but the Mathematical

Read More →A reader asks: how do you do the chain rule? The chain rule was always my least favourite of the differentiation rules - although the quotient rule has now replaced it as an unnecessary evil. I suspect I didn't like it when I learnt it because I learnt it more

Read More →
Posted in core 3.

These are my barely-edited, initial thoughts on today's controversial EdExcel Core 3 paper. Nothing is meant as an attack on anyone - except, of course, for Mr Gove, who must be used to it by now. UPDATED June 14: The legendary Arsey at TSR has worked solutions for the paper

Read More →