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 →
Posted in ask uncle colin, complex numbers

Dear Uncle Colin, I've been given $u = (2\sqrt{3} - 2\i)^6$ and been told to express it in polar form. I've got as far as $u=54 -2\i^6$, but don't know where to take it from there! - Not A Problem I'm Expecting to Resolve Hello, NAPIER, and thanks for your

Read More →
Posted in proof

Someone recently asked me where I get enough ideas for blog posts that I can keep up such a 'prolific' schedule. (Two posts a week? Prolific? If you say so.) The answer is straightforward: Twitter Reddit One reliable source of interesting stuff is @WWMGT - What Would Martin Gardner Tweet?

Read More →