The Flying Colours Maths blog has been running posts twice weekly since 2012, covering maths from the basics to… well, the most advanced stuff I have a clue about.
Here they all are, sorted by date. Some day, other ways to filter them will be possible.
It’s that time of the week again! What’s been on your mind? What’s giving you a headache? As always, drop your questions in the comments box and I’ll get back to you as swiftly as I can!
Science is the belief in the ignorance of experts. - Richard Feynman
This is a follow-up to Monday’s post about the smart way to do the binomial expansion. In this one, we’re going to look at how to do C4 binomial expansions - ones with crazy powers like $-3$ or $\frac{3}{2}$. This bit is very important: you should COMPLETELY ignore the formula in the …
Ah, the binomial expansion. The scourge of my A-level: the sum that was always wider than the paper, and always had one more minus sign than I’d allowed for. A crazy, pointless exercise in arithmetic, if you ask me, only really useful for finding square roots in your head (of which more …
End of the week again already? Fantastic. That means it’s time for free-for-all Friday! Did you get any Valentine’s cards? Did you send any? Did you fall in love with maths? Of course you did. Tell me about it here… or ask anything that’s on your mind. There’s even a …
When you integrate a function - for instance, $\cos(3x)$, you probably have to stop for a moment and think: “Do you multiply by 3 or divide when you integrate?” Some people don’t even get that far, and just say “Oh, it must be $\sin(3x)$”, and all of us can just sigh at …
There is one big-daddy among the trig identities that you need to learn right now, if you don’t know it already: $$\sin^2(x) + \cos^2(x) = 1$$ This is the identity that nearly all of the others spring from. There are some more definitions: $tan(x) = \frac{\sin(x)}{\cos(x)}$, which is one of …
It’s that time of the week again! What’s been on your mind? What’s giving you a headache? As always, drop your questions in the comments box and I’ll get back to you as swiftly as I can!
While I’m quite steadfastly refusing to be swept along with either Olympics fever or anti-games grumbling, I stumbled across the Wikipedia page for the decathlon in a moment of nostalgia for my 1980s childhood tapping the keys of the ZX Spectrum - a system that was kind of like an XBOX, but …
When you learn how to integrate by parts, you’re probably told that a good rule of thumb is that if you have a power of $x$, that’s going to be the thing you differentiate. That’s a pretty good heuristic1, but there are two places it breaks down: one, if you’re doing …
Frankly, the first free-for-all-Friday of February! Fandabbydozy. You know the drill: whatever questions you’ve got about any part of A-level maths - AS, A2, further, whatever you like - bring ’em on. Something your teacher rushed through, or something you don’t understand …
My dad tells me that, above the blackboard in his 1960s Scottish high school, was a banner with the letters ‘SOH CAH TOA’ written out on it. Any questions about the banner were brushed off with a smile and ‘you’re not old enough to learn about SOH CAH TOA yet." Which, I …
There are many questions with only one answer. Or at least, one sensible answer. If someone asks you “Are you dead?”, the only possible answer you can give is “no”. “Does my bum look big in this?” “Of course not, dear, it looks lovely”. And if you say …
Well… it’s not really a free-for-all Friday as I’m on a train to Bristol, but you can still leave me questions here and I’ll respond when I’m back in front of a computer. Any A-level maths topics - including Further Maths - you’re struggling with, I’ll be …
Have a look at this picture. What do you notice? “It’s a straight line, Colin!” Very good. You could get a ruler out and draw a straight line through the points. Why would you bother doing such a thing? Well, the idea is that if you can model a data set - come up with a formula …
Every time you’re asked to differentiate $a^x$ and you say $xa^{x-1}$, a kitten dies. A kitten that had been raised lovingly by an orphan, her only friend in the whole wide word - DEAD, just because you couldn’t be bothered to learn how to do calculus properly. I hope the image of tears …
It’s Friday, which means… It’s free for all Friday time! Any questions you’ve got, about maths or anything else, pop them in the comments. I’m in the middle of the deadline doldrums (the next Dummies book won’t write itself, you know!) but I’ll pop in once …
If I could wave a magic wand and overhaul just one thing to make the world a better place, I’d have a tough choice. Would I get rid of the QWERTY keyboard in favour of a more sensible layout? Would I make the English language fonetik? Would I take maths notation and make it a bit more obvious? …
There’s a very typical question in C3 papers that looks something like: “Express $3 \sin (x) + 5 \cos (x)$ in the form $R \sin (x + \alpha)$.” (Sometimes it’s a different trig function, or it may have a minus sign in it, but the same principle works for any type of question …
It’s C1 day (and C2 for many)! I hope it’s gone well if you were sitting it today. Anything that bothered you about the paper? It’s your chance to pick my brain about whatever’s on your mind about maths. Got a question you’ve been struggling with? Got a topic you just …
Today’s big question is about poker. For some reason, statistics books shy away from gambling, reasoning that it’s somehow harmful or evil. It’s true, it can be addictive (although so can, for instance, using the computer or reading books) but it’s actually the whole reason …
Part I: Basic shapes of Core 1 graphs There are a handful of basic shapes of graphs you need to know about for C1, namely: - reciprocal graphs ($y = \frac{1}{x}$) - reciprocal-square graphs ($y = \frac{1}{x^2}$) - straight line graphs ($y = x$) - you know this one, right? - quadratic graphs ($y = …
Part I: Basic shapes of Core 1 graphs There are a handful of basic shapes of graphs you need to know about for C1, namely: - reciprocal graphs ($y = frac{1}{x}$) - reciprocal-square graphs ($y = frac{1}{x^2}$) - straight line graphs ($y = x$) - you know this one, right? - quadratic graphs ($y = …
Welcome to the first FFAF of the new year! It’s your chance to pick my brain about whatever’s on your mind about maths. Got a question you’ve been struggling with? Got a topic you just can’t get your head around? Found a great maths resource I might not have seen? Pop it in …
I turned over the paper and froze. Up until that point I’d been convinced that maths was, and always would be, easy. As such, I’d done next to no revision for this paper, which I needed to do well in to qualify for my next year of studies. This, I realised, was what they meant by maths …
If you’re sitting your first AS-level maths modules next week, you’re probably in one of two camps about Core 1: The not-worried camp, thinking “I’ll just wing it - I understood most of the stuff from last term, so I should be OK” The frenzied panic camp, thinking …
OK! This is the official first Flying Colours Free-for-all Friday! Cue fanfare! It’s your chance to pick my brain about whatever’s on your mind about maths. Got a question you’ve been struggling with? Got a topic you just can’t get your head around? Found a great maths …
When you’ve got a maths exam coming up, you need to study for it. Trouble is, you don’t know how. Here are a few tips and tricks that can help you improve - as Katrina says: I got my results back. My previous exam, i did really badly, but by doing your methods, I improved by 24 marks! I …