Posted in ask uncle colin, integration.

Dear Uncle Colin, I've been set an evil integral: $\int_0^\piby{4} \frac{\sqrt{3}}{2 + \sin(2x)}\d x$. There is a hint to use the substitution $\tan(x) = \frac{1}{2}\left( -1 + \sqrt{3}\tan(\theta)\right)$, but I can't see how that helps in the slightest. -- Let's Integrate Everything! Hello, LIE, and thank you for your message!

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Posted in arithmetic.

Some time back in the olden days, @robeastaway posted this: My 11 year old's sample SATs papers found in his book bag. "Work out 1118÷43 (no calculator)." I wish all ministers had to take these tests. pic.twitter.com/dEOiLv2fsJ — Rob Eastaway (@robeastaway) March 22, 2017 Before I say anything else: I

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Posted in ask uncle colin.

Dear Uncle Colin, I'm revising for a high-stakes exam. I learn material, do the exercises and think I understand it - but when I revisit it a couple of weeks later, it feels like I'm starting from scratch. What can I do to remember things better? -- Failure Of Remembering

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Posted in podcasts.

This month's episode is the 2017 MathsJam special. What we talked about: Some tables Some talks we liked (featuring @reflectivemaths, @ajk_44, @zoelgriffifths (of whom more later), @macaronique, @chalkdustmag, @pecnut, @mscroggs, @televisionduck, Andrew Russell) Dave talks to @pecnut about his favourite bits, how to dress to give a lecture, Catchphrase1, oblongs,

Read More →Before I begin: this post involves a puzzle and my attempt at a solution; everything above the horizontal rule is spoiler-free, but go beyond that at your peril. Some days, you can almost hear @colinthemathmo's chuckle as he innocently poses a question such as: Find all configurations of 4 points

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Posted in ask uncle colin.

Dear Uncle Colin, When evaluating an expression, after you've dealt with brackets, powers and roots, do you deal with multiplication and division left to right, or does multiplication take precedence? - BIDMAS Idiocy Doesn't Make Any Sense Hi, BIDMAS, and thanks for your message! There are three answers to this.

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Posted in mathematical style.

Recently, @solvemymaths asked the rather leading question: is there a convincing argument for ever using the obelus (÷) for division rather than fractional notation? In my mind it makes things harder — solve my maths (@solvemymaths) June 16, 2017 As with pretty much all mathematical notation questions, I have exactly

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Posted in ask uncle colin, mechanics 1.

Dear Uncle Colin I have a conceptual problem with impulse. Suppose you have a collision where your particle (of mass 1 kg) has an approach speed of 4m/s, changes direction, and leaves with a speed of 3m/s. That's an impulse of -7 units, and the ball slows down from 4m/s

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Posted in inequalities, puzzles.

The square root of 2 is 1.41421356237... Multiply this successively by 1, by 2, by 3, and so on, writing down each result without its fractional part: 1 2 4 5 7 8 9 11 12... Beneath this, make a list of the numbers that are missing from the first

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Posted in ask uncle colin, surds.

Dear Uncle Colin How does $\sqrt{9 - \sqrt{17}} = \frac{\sqrt{34}-\sqrt{2}}{2}$? I tried applying a formula, but I couldn't make it work. - Roots Are Dangerous, It's Chaotic A-Level Simplification Hi, RADICALS, and thank you for your message! Square roots of square roots are not usually trivial, but this one can

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