Browsing category core 1

Brutal simultaneous equations

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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Ask Uncle Colin: about summation notation

Dear Uncle Colin, I'm having trouble getting my head around sum notation! I can't tell whether $\sum_{n=0}^{6}{5}$ means $0\times5 + 1\times 5 + ... + 6\times 5$ or $0 + 1 + 2 + ... + 6$ or $5 + 5 + 5 ... + 5$. Wolfram|Alpha just gives me

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Ask Uncle Colin: a disguised quadratic

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 and Uncle Colin will do what he can. Dear Uncle Colin, How do I solve $3x^{\frac{2}{3}} + x^{\frac{1}{3}}-2

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Are you A-level ready?

When you said you wanted to do maths A-level, I imagine people pursed their lips and said "oo, it's a big step up." They're right, to an extent: every October I get deluged with panicked students who realise that the 'coast through it all doing just enough' approach that served

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The Mathematical Pirate’s Guide to Factorising Cubics

“Yarr,” said the Mathematical Pirate. “Ye’ll have plundered a decent calculator, of course?” “Er… well, I bought it from Argos, but… aye, cap’n! A Casio fx-83 GT PLUS!” “A fine calculator,” said the Mathematical Pirate. “One that offers you at least three ways to factorise cubics.” “Really!? I thought you

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A student asks: How do you simplify surds?

A student asks: How could I simplify a sum like $(\sqrt 3+\sqrt 2)(\sqrt 3-\sqrt 2)$? Great question! The trick is to treat it like it's an algebraic bracket, like this: $(x + y)(x - y) = x^2 + yx - xy - y^2$ But then you've got $+yx -xy$ in

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There’s More Than One Way To Do It: Arithmetic Series

You've got the formulas in the book, of course. $u_n = a + (n-1)d$ $S_n = \frac n2 \left(a + L\right) = \frac n2 \left(2a + (n-1)d\right)$ This is somewhere the book and I have a serious disagreement: as a mathematical document, it ought to define its terms. $a$ is

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A student asks: Why is there a $+c$ when you integrate?

A student asks: We've just started integration and I don't understand why there's always a $+c$ - I understand it's a constant, I just don't understand why it's there! Great question! The simple answer is, because constants vanish when you differentiate, they have to appear when you integrate - it's

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The C1 Last-Minute Panic Checklist

OK, OK, stop screaming! I KNOW C1 is only a few days away, I know you're underprepared, but panicking isn't going to help anything. It's a pretty common - and heartbreaking - thing for tutors and teachers to see: a student who's waltzed through GCSE getting to the end of

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Dealing with nasty powers

There's nearly always a question on the non-calculator GCSE paper about Nasty Powers. I'm not talking about the Evil Empire or anything, I just mean powers that aren't nice - we can all deal with positive integer powers, it's the zeros, the negatives and the fractions that get us down.

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