Posted in calculus, core 3, graphs, 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

Read More →
Posted in calculus, core 3, logarithms.

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

Read More →
Posted in core 3, trigonometry.

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

Read More →