Further Mathematics Past Questions

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

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 locus of points which is equidistant from P(4, 5) and Q(-6, -1).

Two statements are represented by p and q as follows:

p : He is brilliant; q : He is regular in class

Which of the following symbols represent "He is regular in class but dull"?

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.