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1. Factorisation: x² - 5x + 6 = (x - 2)(x - 3) This method is the quickest to perform if the roots are simple but does rely on a bit of trial and error. The method lets you find the roots of...

First, we must find the two points at which the curve crosses the boundary. To do this, set y=0 and solve.0 = 5x - 2x² - 20 = (2x - 1)(-x+2)This gives that x = 0.5 and x = 2Next, we integrate w...

The derivative tells us how much the output of a function changes when we change the input by a tiny amount. For the function f(x) = x², we can think of the input as being a line of length x, a...

Let f(x)=y: y = e^(x²+4); To find the inverse of a function, you need to find x in terms of y. In this case, you need to bring the exponent to the base. So in order to bring x²+4 fro...

First, we note the centre of the circle is at the origin (0,0). Then we calculate the gradient of the line OP, the line connecting the origin to P. The gradient = change in y / change in x = (√7 - 0) / (3...