What are some good results to know for an interview?

Question

For an undergraduate interview for university in maths & theoretical physics, what are some good results to have on hand and (where relevant) know the derivation of? e.g.: $$\frac{d}{dx}[x^x]=x^x(ln(x)+1)$$ $$\sum_{n=1}^\infty\frac{1}{n^2}=\frac{\pi^2}{6}$$ $${1+\frac{1}{1+\frac{1}{\ddots}}}=\phi$$ $$\frac{d^2x(t)}{dt^2}+\omega^2x(t)=0\Rightarrow x(t)=x_0cos(\omega t)+\frac{v_0}{\omega}sin(\omega t)$$ Additionally, are there any techniques that might be helpful to know, to answer questions with more sophistication than required for high-school exams? e.g.: the Laplace transform to answer questions on SHM.

Answer 1

If you are about to be interviewed as part of the application process to be admitted to university, make sure you are competent with differentiation in all its forms especially the Chain Rule, and Integration, especially recognising when to use the Chain Rule in reverse, or substitution, as opposed to Integration by Parts. You should also know all the main trig identities.

However, the most useful skill to acquire is the ability to sketch graphs: interviewers frequently ask candidates to sketch a perhaps unfamiliar graph because it is a good test of mathematical insight and general knowledge and of problem-solving skills.