Further Mathematics Past Questions

Given that \(r = 2i - j\), \(s = 3i + 5j\) and \(t = 6i - 2j\), find the magnitude of \(2r + s - t\).

Given the statements:

p : the subject is difficult

q : I will do my best

Which of the following is equivalent to 'Although the subject is difficult, I will do my best'?

Given that \(x^{2} + 4x + k = (x + r)^{2} + 1\), find the value of k and r.

If \(\alpha\) and \(\beta\) are the roots of \(x^{2} + x - 2 = 0\), find the value of \(\frac{1}{\alpha^{2}} + \frac{1}{\beta^{2}}\).

The gradient of a curve at the point (-2, 0) is \(3x^{2} - 4x\). Find the equation of the curve.

If \(x = i - 3j\) and \(y = 6i + j\), calculate the angle between x and y.

In how many ways can a committee of 5 be selected from 8 students if 2 particular students are to be included?

A line passes through the origin and the point \((1\frac{1}{4}, 2\frac{1}{2})\). Find the y-coordinate of the line when x = 4.

A line passes through the origin and the point \((1\frac{1}{4}, 2\frac{1}{2})\), what is the gradient of the line?

Find the minimum value of \(y = x^{2} + 6x - 12\).

If \(36, p, \frac{9}{4}, q\) are consecutive terms of an exponential sequence (G.P.). Find the sum of p and q.

Given that \(f : x \to \frac{2x - 1}{x + 2}, x \neq -2\), find \(f^{-1}\), the inverse of f.

Which of the following is a factor of the polynomial \(6x^{4} + 2x^{3} + 15x + 5\)?

Given that \(P = \begin{pmatrix} -2 & 1 \\ 3 & 4 \end{pmatrix}\) and \(Q = \begin{pmatrix} 5 & -3 \\ 2 & -1 \end{pmatrix}\), find PQ - QP.

Given that \(\frac{2x}{(x + 6)(x + 3)} = \frac{P}{x + 6} + \frac{Q}{x + 3}\), find P and Q.

Given that \(f : x \to x^{2}\) and \(g : x \to x + 3\), where \(x \in R\), find \(f o g(2)\).

Find the 3rd term of \((\frac{x}{2} - 1)^{8}\) in descending order of x.

If \(\log_{3} x = \log_{9} 3\), find the value of x.

Solve: \(4(2^{x^2}) = 8^{x}\)