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,

Read More →
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

Read More →
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

Read More →
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

Read More →
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

Read More →
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

Read More →
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 +

Read More →
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

Read More →
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

Read More →