Further Mathematics Past Questions and Answers

A binary operation ,*, is defined on the set R, of real numbers by \(a * b = a^{2} + b + ab\). Find the value of x for which \(5 * x = 37\).

Find the coefficient of \(x^{4}\) in the binomial expansion of \((1 - 2x)^{6}\).

Find the derivative of \(3x^{2} + \frac{1}{x^{2}}\)

Find the equation of the line passing through (0, -1) and parallel to the y- axis.

The coefficient of the 5th term in the binomial expansion of \((1 + kx)^{8}\), in ascending powers of x is \(\frac{35}{8}\). Find the value of the constant k.