Browsing category core 3

James Bloody Grime and his blasted logarithms

It's typical of James Grime to ask a really interesting question just as I'm going to bed. I was going to sleep like a log, but suddenly I was awake liking logarithms. I've been asked, for what base a does the equation $\log_a(x) = a^x$ have only one solution. If

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How to do calculus with $a^x$

Every time you're asked to differentiate $a^x$ and you say $xa^{x-1}$, a kitten dies. A kitten that had been raised lovingly by an orphan, her only friend in the whole wide word - DEAD, just because you couldn't be bothered to learn how to do calculus properly. I hope the

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How to do… R-sin-alpha questions

There's a very typical question in C3 papers that looks something like: "Express $3 \sin (x) + 5 \cos (x)$ in the form $R \sin (x + \alpha)$." (Sometimes it's a different trig function, or it may have a minus sign in it, but the same principle works for any

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