The Flying Colours Maths Blog: Latest posts

The Mathematical Ninja and Cosines

As the student was wont to do, he idly muttered "So, that's $\cos(10º)$…" The calculator, as calculators are wont to do when the Mathematical Ninja is around, suddenly went up in smoke. "0.985," with a heavy implication of 'you don't need a calculator for that'. As the student was wont

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Ask Uncle Colin: Factors!

Dear Uncle Colin, If you know all of the factors of $n$, can you use that to find all of the factors of $n^2$? For example, I know that 6 has factors 1, 2, 3 and 6. Its square, 36, has the same factors, as well as 4, 9, 12,

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A common problem: not reading carefully

I'm a big advocate of error logs: notebooks in which students analyse their mistakes. I recommend a three-column approach: in the first, write the question, in the second, what went wrong, and in the last, how to do it correctly. Oddly, that's the format for this post, too. The question

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Ask Uncle Colin: Trouble in Sector ABC

Dear Uncle Colin, I got stuck on this sector question, which asks for the radius of circle $P$, which touches sector $ABC$ as shown. I’m given that $ABC$ is a sector of a circle with centre $A$ with radius 12cm, and that angle $BAC$ is $\frac{\pi}{3}$. My answer was 3.8cm,

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Attack of the Mathematical Zombies: Calc vs non-calc

Another horde of zombies lumbered into view. "What are they saying?" asked the first, readying the shotgun as he'd done a hundred times before. "Something about the calculator exam," said the second. "It's hard to make out." He pulled some spare shells from his bag. "Calculator papers are easier!" groaned

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Ask Uncle Colin: A STEP in the right direction

Dear Uncle Colin, I'm struggling with a STEP question. Any ideas? Given: 1. $q^2 – pr = -3k$ 2. $r^2 – qp = -k$ 3. $p^2 – rq = k$ Find p, q and r in terms of k. – Simultaneous Triple Equation Problem Hi, STEP, and thanks for your

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A curve-sketching masterclass

An implicit differentiation question dealt with $y^4 – 2x^2 + 8xy^2 + 9 = 0$. Differentiating it is easy enough for a competent A-level student – but what does the curve look like? That requires a bit more thought. My usual approach to sketching a function uses a structure I

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Ask Uncle Colin: fourth roots

Dear Uncle Colin, How would you find $\sqrt[4]{923521}$ without a calculator? — Some Quite Recherché Technique Hi, SQRT! I have a few possible techniques here. The first is “do some clever stuff with logarithms”, the second is “do some clever stuff with known squares” and the last is “do some

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Wrong, But Useful: Episode 45

In this episode of Wrong, But Useful1: We're joined by @ajk_44, who is Alison Kiddle from NRICH in real life. We ask Alison: how long has NRICH been going? How do you tell which problems you've covered before? Colin's number of the podcast is 13,532,396,179 (he mistakenly calls it quadrillions

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Some Thoughts On EdExcel 9-1 GCSE Paper 1

I imagine, if one put one's mind to it, one could acquire copies of this year's paper online – however, many schools plan to use it as a mock for next year's candidates. In view of that, and at the request of my top-secret source, I'm not sharing the actual

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