Further Mathematics Past Questions

The mean age of 15 pupils in a class is 14.2 years. One new pupil joined the class and the mean changed to 14.1 years. Calculate the age of the new pupil.

Find the equation of the tangent to the curve \(y = 4x^{2} - 12x + 7\) at point (2, -1).

Find the axis of symmetry of the curve \(y = x^{2} - 4x - 12\).

The third of geometric progression (G.P) is 10 and the sixth term is 80. Find the common ratio.

Given that \(P = {x : \text{x is a factor of 6}}\) is the domain of \(g(x) = x^{2} + 3x - 5\), find the range of x.

If \(\begin{vmatrix} 3 & x \\ 2 & x - 2 \end{vmatrix} = -2\), find the value of x.

Evaluate \(\int_{1}^{2} \frac{4}{x^{3}} \mathrm {d} x\)

Calculate, correct to one decimal place, the acute angle between the lines 3x - 4y + 5 = 0 and 2x + 3y - 1 = 0.

If \(y = 2(2x + \sqrt{x})^{2}\), find \(\frac{\mathrm d y}{\mathrm d x}\).

Calculate, correct to one decimal place, the length of the line joining points X(3, 5) and Y(5, 1).

For what values of x is \(\frac{x^{2} - 9x + 18}{x^{2} + 2x - 35}\) undefined?

If \(\sin x = -\sin 70°, 0° < x < 360°\), determine the two possible values of x.

If (x - 3) is a factor of \(2x^{2} - 2x + p\), find the value of constant p.

The roots of a quadratic equation are \((3 - \sqrt{3})\) and \((3 + \sqrt{3})\). Find its equation.

The coefficient of the 7th term in the binomial expansion of \((2 - \frac{x}{3})^{10}\) in ascending powers of x is

Simplify \(\frac{\log_{5} 8}{\log_{5} \sqrt{8}}\).

If \(16^{3x} = \frac{1}{4}(32^{x - 1})\), find the value of x.

If \(\frac{5}{\sqrt{2}} - \frac{\sqrt{8}}{8} = m\sqrt{2}\), where m is a constant. Find m.

Find the value of \(\cos(60° + 45°)\) leaving your answer in surd form.