Further Mathematics Past Questions and Answers

p and q are statements such that \(p \implies q\). Which of the following is a valid conclusion from the implication?

The roots of a quadratic equation are -3 and 1. Find its equation.

The derivative of a function f with respect to x is given by \(f'(x) = 3x^{2} - \frac{4}{x^{5}}\). If \(f(1) = 4\), find f(x).

Simplify \((216)^{-\frac{2}{3}} \times (0.16)^{-\frac{3}{2}}\)

Given that \(\log_{3}(x - y) = 1\) and \(\log_{3}(2x + y) = 2\), find the value of x.