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People doing mathematics at A-Level will be familiar with the concept of using x and y coordinates in the cartesian coordinate system. But introducing the idea of the polar coordinate system can be confusing...

When investigating graphs, you will often be asked to pick out features of the graph; stationary points being the most popular. You will need to know that a stationary point on f(x) can be found by solving t...

First we must consider for which values of x the equation: 3/(x+3) = (x-4)/x is undefined. In this case, x=-3, and x=0. Now we must consider each of the cases, x<-3, -3<x<0, 0<x Case 1 (x<-3):...

To find power we are going to need the equation: P = F v Where P is power, F is force and v is velocity Since the car is travelling at a constant speed up the slope, we know that velocity, v is positive 20 m...

Divide through by x so: (dy/dx) +2(y/x) = 4x Now multiply through by the intergrating factor: e^(| (2/x) dx) = e^(2.ln(x)) = x^2 so you get: (x^2)(dy/dx) + 2xy = 4(x^3) Now integrate the entire equation and ...