Further Mathematics Past Questions and Answers

A polynomial is defined by \(f(x + 1) = x^{3} + px^{2} - 4x + 2\), find f(2).

The equation of a circle is \(3x^{2} + 3y^{2} + 24x - 12y = 15\). Find its radius.

If the midpoint of the line joining (1 - k, -4) and (2, k + 1) is (-k, k), find the value of k.

Evaluate \(\int_{-2}^{3} (3x^{2} - 2x - 12) \mathrm {d} x\)

If \(y = x^{3} - x^{2} - x + 6\), find the values of x at the turning point.