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This question often throws maths students off fairly easily as they are generally not taught the integral of lnx, and do not usually realise that integration by parts can be used for anything, as you can ...

Firstly, we need to differentiate the equation to find an equation for the gradient of the line.dy/dx = 6x-12We know the original graph was quadratic, and therefore only has one stationary point. This is ...

To get the smallest value of w-x we will need the smallest value of w and the largest value of x.Our smallest possible value of w=41.Our largest possible value of x=29.So the smallest value of w-x = 41-29...

(Suppose the coordinates of the point on the circle is (2, 3))To calculate the tangents equation we will first work out it's gradient. The tangent to a circle at a point is perpendicular to the radius of ...

Note that 1/4 as a decimal is 0.25, half of this is 1/8 which is 0.125.Multplying this by 5: we get 0.625