Attack of the Mathematical Zombies: Calc vs non-calc | Colin

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 the distant horde. “Calculator…”

The first sighed. Bang bang.

“How on earth do you get through eleven years of schooling and believe that?” muttered the second.

“Beats me.” Bang bang.

“It’s as if they think the point of maths is following recipes to get a number.”

“There’s…

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Ask Uncle Colin: A STEP in the right direction | Colin

Ask Uncle Colin is a chance to ask your burning, possibly embarrassing, maths questions — and to show off your skills at coming up with clever acronyms. Send your questions to colin@flyingcoloursmaths.co.uk and Uncle Colin will do what he can.

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 question!

This is an absolute biter that took me several attempts to get under control. The key was…

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A curve-sketching masterclass | Colin

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 call DATAS:
Domain: where is the function defined?
Axes: where does the function cross them?
Turning points: where are the function’s critical points?
Asymptotes: what happens when $x$ or $y$ get really big?
Shape: what does the graph look like overall?

As it turns out, this approach is almost entirely useless…

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Ask Uncle Colin: fourth roots | Colin

Ask Uncle Colin is a chance to ask your burning, possibly embarrassing, maths questions — and to show off your skills at coming up with clever acronyms. Send your questions to colin@flyingcoloursmaths.co.uk and Uncle Colin will do what he can.

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 clever stuff with calculus.”

Without a…

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Wrong, But Useful: Episode 45 | Colin

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 rather than trillions, and sometimes transposes the 7 and 9 at the end. The fool.)
Alison is NOT a trainspotter, but has just been to visit the new Cambridge North station and Shippea Hill, just to mess with statistics. See All The Stations for more! Rule 135
Dave has no qualms about owning his…

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Some Thoughts On EdExcel 9-1 GCSE Paper 1 | Colin

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 questions used. However, I’m treating the topics and techniques as fair game.

I once claimed not to be very competitive. My friends looked at me askance and told me I was one of the most competitive people they knew, and I said “What do you mean, one of the most?”

So, when @christianp tweeted about having a sub-20 minute record for a…

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Ask Uncle Colin: about Chebyshev’s Equation | Colin

Ask Uncle Colin is a chance to ask your burning, possibly embarrassing, maths questions — and to show off your skills at coming up with clever acronyms. Send your questions to colin@flyingcoloursmaths.co.uk and Uncle Colin will do what he can.

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 + on top. Where have I gone wrong?

– Can’t Have…

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