Posted in ask uncle colin, circles, geometry, radians.

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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Posted in zombies.

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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Posted in algebra, ask uncle colin.

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

Read More →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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Posted in arithmetic, ask uncle colin.

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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Posted in podcasts.

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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Posted in exam technique, gcse.

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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Posted in calculus.

Dear Uncle Colin, I’ve been asked to solve Chebyshev’s equation using a series expansion: $(1-x)\diffn{2}{y}{x} – x\dydx + p^2 y = 0$ assuming $y=C_0 + C_1 x + C_2 x^2 + …$. I end up with the relation $C_{N+2} = \frac{C_N \left(N^2 -p^2\right)}{(N+2)(N+1)}$, but the given answer has a +

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Posted in dialogue.

This is a rolling update post for responses to this morning’s post. The Admirable Adam Atkinson has emailed to suggest an answer I hadn’t considered: 100. “I could imagine many programming languages would say 100. You start with the first term, 100. discover that the “next” number, 101, is outside

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Posted in dialogue.

"Counting is hard. This is what I keep saying." – @realityminus3 It all stemmed from an arithmetic series problem with a known sum, but an unknown number of terms. As these things are prone to do, it led to a quadratic equation; as those things are prone to do, that

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