Tutor profile: Devin C.

How do I memorise trigonometric identities and know which ones to use in which situations? There's just so many of them!

For memorisation, the perspective is very important. Some people realise that there are not as many identities as you think - many of the identities are actually related to one another, for example the identities for $\sin 2x$ and $\sin (x+y)$. One the relationship between the identities are explored, we can get by with just remembering a few simple ones that make our work easier - for example $\sin^2 \theta + \cos^2 \theta \equiv 1$. Application of trig identities is a different story. It takes practice to spot which identities will simplify the work the most, and with some experience at tackling problems the perfect identity for each problem becomes clearer and clearer.

What is the derivative of $e^x$? Is it $xe^{x-1}$?

Short Answer: No, the derivative of $e^x$ is still $e^x$. Long Answer: When I receive a question like this, I immediately realise that my student does not understand what the derivative is, and thinks of differentiation as a mechanical process where one "moves the power down and reduces power by 1". Therefore, it is important that a student understands the actual meaning of things, as bringing formulae from other functions may not work.

Why is the product of two negative numbers a positive number?

We can think of numbers on a line, where positive numbers mean "to the right", and negative numbers mean "to the left". This gives a "direction" to each number. The basic idea is simple actually, multiplying by a negative number REVERSES THE DIRECTION of the original number. Therefore, multiplying two negative number reverses the direction twice, so the number goes back to the initial direction, which is positive.