Posted in ask uncle colin, geometry.

Dear Uncle Colin, I find it easier to remember trigonometric identities if I can 'see' how they fit together. I'm expected to know that $\sin(2x) \equiv 2\sin(x)\cos(x)$, but haven't been able to prove it. Any ideas? -- Geometry? Right Angles? How About Medians? Hi, GRAHAM! My favourite proof jumps out

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Posted in algebra, arithmetic, core 1, ninja maths.

I recently became aware of the IYGB papers, available from Madas Maths. Like the Solomon papers, they're intended to stretch you a bit -- they're ranked by difficulty from standard to extremely hard. My student, being my student, demanded we go through one of the extremely hard ones. There were

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Posted in algebra, ask uncle colin, cav being wrong.

Dear Uncle Colin, I've got a line with equation $10y+36x=16.5$. That equation has no negative numbers in it, yet its gradient is apparently negative. I don't understand why. -- Silly Line, Only Positive Equation Dear SLOPE, It looks like we're in misconception-land! In fact, you can write the equation of

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Posted in surds.

The estimable @solvemymaths tweeted, some time back: hmm, perhaps I'll keep this one as "sin(22)" pic.twitter.com/cT5IHonoyb — solve my maths (@solvemymaths) January 16, 2016 A sensible option? Perhaps. But Wolfram Alpha is being a bit odd here: that's something that can be simplified significantly. (One aside: I'm not convinced that

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Posted in ask uncle colin, logarithms.

Dear Uncle Colin, I get $-\frac{\ln(0.02)}{0.03}$ as my answer to a question. They have $\frac{100\ln(50)}{3}$. Numerically, they seem to be the same, but they look completely different. What gives? -- Polishing Off Weird Exponents, Really Stuck Dear POWERS, What you need here are the log laws (to show that $-\ln(0.02)=\ln(50)$,

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Posted in fractions.

Some while back, Ben Orlin of the brilliant Maths With Bad Drawings blog posted a puzzle he'd set for some eleven-year-olds: Which is larger, $\frac{3997}{4001}$ or $\frac{4996}{5001}$? Hint: they differ by less than 0.000 000 05. He goes on to explain how he solved it (by considering the difference between

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Posted in ask uncle colin, modulus.

Dear Uncle Colin, I have to solve the inequality $x^2 - \left|5x-3\right| \lt 2+x$. I rearranged to make it $x^2 - x - 2 \lt \left|5x-3\right|$ , but the final answer is eluding me. -- Put Right Inequality Muddle Hello, PRIM! You're off to a good start; the next thing

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Posted in ninja maths.

While I'm no Mathematical Ninja, it does amuse me to come up with mental approximations to numbers, largely to convince my students I know what I'm doing. One number I've not looked at much1 is $\sqrt{\frac{1}{3}}$, which comes up fairly frequently, as it's $\tan\left(\frac{\pi}{6}\right)$2 . Ninja-chops taught me all about

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Posted in ask uncle colin.

Dear Uncle Colin, My maths mock went terribly, and I got a U. Since then I've done some real revision and got a good grade on a paper I did off my own bat. However, I'm a long way behind on the new material and I feel like it's too

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Posted in fractions, ninja maths.

The Mathematical Ninja played an implausible trick shot, not only removing himself from a cleverly-plotted snooker, but potting a red his student had presumed safe and setting himself up on the black. Again. "One!" he said, brightly, and put some chalk on the end of his cue. The student sighed.

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