Author: Colin

Ask Uncle Colin: Completing the Square

Dear Uncle Colin, I was asked to complete the square on $f(x) = 2x^2 + 13x + 20$. I started by halving everything, which makes it cleaner, but the solution manual disagrees. What gives? - Have Always Loathed Functions Hi, HALF, and thanks for your message! Dividing a quadratic by

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Wrong, But Useful: Episode 53

In this month's episode of Wrong But Useful (#53), brought to you by the power of Lemsip and a day in bed, Colin and Dave are joined by Special Guest Co-Hosts @sean_jamshidi and #NikiWithoutTwitter, who are Sean Jamshidi and Niki Kalaydzhieva from Chalkdust Magazine1 in real life. Niki is an

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Daylight, Durlston Castle, and Where is Hamburg?

"Is Hamburg that much further north than London?" I furrowed my brow. Hamburg, to the best of my knowledge, is not that much further north than London. But here it was, written in stone (on the side of Durlston Castle in Swanage.) (I've transcribed the sign at the bottom of

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Ask Uncle Colin: What is $\cos(72º)$?

Dear Uncle Colin, How would you calculate $\cos(72º)$ by hand? - Pointless Historical Inquiry Hi, PHI, and thanks for your message. There seems to be an awful lot of degree use around at the moment, and I'm not very happy about it. But still, in the spirit of answering what

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An “Impossible” New Zealand exam: Part II

Last time, we looked at an 'impossible' question from a New Zealand exam, which was (of course) nothing of the sort. The second question highlighted as a brute was this one: (Full exam is here.) But, you see, I look at that and think... part (iv) isn't straightforward on its

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Ask Uncle Colin: A Plane-teaser

Dear Uncle Colin, In a recent contest, I was told that $a$, $b$ and $c$ were real numbers such that $a-7b+8c=4$ and $8a + 4b -c = 7$. I had to find $a^2 - b^2 + c^2$ and couldn't see a way in. Can you? - Puzzle Lacks Answer -

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An “Impossible” New Zealand exam: Part I

To-may-to / tomato; potato / po-tah-to; impossible exam / underprepared students. This time it's the hapless Kiwis who are making Downfall parody videos and complaining that their practice papers hadn't prepared them for stuff on the syllabus. Never mind; the formidable @solvemymaths has picked out the two most-complained-about questions, and

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Ask Uncle Colin: Horizontal Asymptotes

Dear Uncle Colin, I'm working on finding horizontal asymptotes for rational functions. I normally do that by division, but my teacher wants me to do it by rearranging - and I don't really know what's going on there! Can you explain? - Horizontal Asymptotes Leaving Me Outwitted Somehow Hi, HALMOS,

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The Mathematical Ninja and $\sin(15º)$

The Mathematical Ninja sniffed. "$4\sin(15º)$? Degrees? In my classroom?" "Uh uh sorry, sensei, I mean $4\sin\br{\piby{12}}$, obviously, I was just reading from the textmmmff." "Don't eat it all at once. Now, $4\sin\br{\piby{12}}$ is an interesting one. You know all about Ailes' Rectangle, of course, so you know that $\sin\br{\piby{12}}=\frac{\sqrt{6}-\sqrt{2}}{4}$, which

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Ask Uncle Colin: A mental quotient

Dear Uncle Colin, I have to work out $851 \div 37$ without pen, paper or calculator. How would you do it? - Simple Mental Arithmetic Looks Easy Hi, SMALE, and thanks for your message! I have three ways to tackle it. Brute force and estimation It's fairly obvious that the

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