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I would start off by asking them if they know the Pythagoras theorem. If they don't, I would refresh their memory and explain that its a²+b²=c² where...

To solve this you need to integrate by substitution. You can spot this because the differential of the bottom of the fraction is a multiple of the top part, showing this quickly; if u = x²  + 3...

The equation we use to integrate by parts is

y = uv - ∫ v(du/dx) dx + c

so we separate dy/dx into u=(3x-4) and dv/dx=(2x²+5)

however we still need to find du/dx an...

de Moivre worked out a brilliant and beautiful way to solve complex equations.

If you for example have z³= 1 and you want to find all real and complex z that satisfy thi...

expand the brackets to get x²-2x+3x-6=4x+22 bring all the terms to one side x²-2x+3x-6-4x-22=0 (remember:if you do something to one side, do the same thing to the other! e.g. -4x on ...