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Having learned a lot about the arithmetic and geometric sequences, most people are used to expressing the n^{th} term of a sequence un in the form u_{n}=u_{1}+d(n-1) for the arithm...

Before attempting to re-arrange the equation, we take an organic approach to looking at asymptotes:1) What happens to y when x=0 and when x -> infinity? What happens to x when y=0 and when y -> infi...

Solution: Let us consider the function f(k) = k^{2 }- k -12. Firstly, we want to find out the roots of this function. We calculate the discriminant: Δ = b^{2} – 4ac = 49 hence we ...

a) First we can rewrite y=arccos(x/2) as cosy = x/2 which allows us to use implicit differentiation to easily differentiate each side. Taking d/dx of each side gives u...

There is a total of 7! possible ways in which the seven children can be seated on the bench. The number of favourable arrangements when four boys are seated on one side and three girls on the other side i...