Further Mathematics Past Questions

If \(P = \begin{pmatrix} 1 & -2 \\ 3 & 4 \end{pmatrix}\) and \(Q = \begin{pmatrix} -2 & 3 \\ 1 & 0 \end{pmatrix}\), find PQ.

Express \(\frac{7\pi}{6}\) radians in degrees.

A rectangle has a perimeter of 24m. If its area is to be maximum, find its dimension.

Evaluate \(\int_{1}^{2} (2 + 2x - 3x^{2}) \mathrm {d} x\).

What is the coordinate of the centre of the circle \(5x^{2} + 5y^{2} - 15x + 25y - 3 = 0\)?

Which of the following quadratic curves will not intersect with the x- axis?

If \(2\log_{4} 2 = x + 1\), find the value of x.

The polynomial \(2x^{3} + x^{2} - 3x + p\) has a remainder of 20 when divided by (x - 2). Find the value of constant p.

If \(f(x) = 2x^{2} - 3x - 1\), find the value of x for which f(x) is minimum.

The sum of the first n terms of a linear sequence is \(S_{n} = n^{2} + 2n\). Determine the general term of the sequence.

The sum of the first n terms of a linear sequence is \(S_{n} = n^{2} + 2n\). Find the common difference of the sequence.

A function f is defined on R, the set of real numbers, by: \(f : x \to \frac{x + 3}{x - 2}, x \neq 2\), find \(f^{-1}\).

Find the range of values of x for which \(2x^{2} + 7x - 15 > 0\).

Simplify \(\frac{\sqrt{3} + \sqrt{48}}{\sqrt{6}}\)

Three forces \(F_{1} = (8 N, 300°), F_{2} = (6 N, 090°)\) and \(F_{3} = (4 N, 180°)\) act on a particle. Find the vertical component of the resultant force.

A force of 30 N acts at an angle of 60° on a body of mass 6 kg initially at rest on a smooth horizontal plane. Find the distance covered in 10 seconds.

A group of 5 boys and 4 girls is to be chosen from a class of 8 boys and 6 girls. In how many ways can this be done?

Calculate, correct to one decimal place, the standard deviation of the numbers: -1, 5, 0, 2 and 9.

Given that \(R = (4, 180°)\) and \(S = (3, 300°)\), find the dot product.