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1. We first use the identity sin²x+cos²x=1  to substitute for sin^2 in terms of cos. 

          sin^2(x)=1-cos^2(x)  ------------->  -4cos^2(x)+8cosx-3=0

How do you show that (x+2) is a factor of f(x) = x^3 - 19x - 30, and then factorise f(x) completely?

f(x) = 2x^3 – 7x^2 + 4x + 4 (a) Use the factor theorem to show that (x – 2) is a factor of f(x). (2) (b) Factorise f(x) completely.

Consider a cone of vertical height H (in metres) and base radius R (in metres) which is full with water. The cone, at time t=0, starts to leak such that it loses water at a rate of k m^3 per second. Give an expression for the rate of change of H.

Integrate the following function: f(x) = ln(x)