Further Mathematics Past Questions

A circle with centre (4,5) passes through the y-intercept of the line 5x - 2y + 6 = 0. Find its equation.

Given that \(\sin x = \frac{5}{13}\) and \(\sin y = \frac{8}{17}\), where x and y are acute, find \(\cos(x+y)\).

If \(B = \begin{pmatrix}  2 & 5  \\  1 & 3  \end{pmatrix}\), find \(B^{-1}\).

\(\alpha\) and \(\beta\) are the roots of the equation \(2x^{2} - 3x + 4 = 0\). Find \(\frac{\alpha}{\beta} + \frac{\beta}{\alpha}\)

\(\alpha\) and \(\beta\) are the roots of the equation \(2x^{2} - 3x + 4 = 0\). Find \(\alpha + \beta\).

A straight line 2x+3y=6, passes through the point (-1,2). Find the equation of the line.

Express cos150° in surd form.

If \(\begin{pmatrix}  2  &  1 \\  4 & 3 \end{pmatrix}\)\(\begin{pmatrix}  5 \\ 4 \end{pmatrix}\)  = k\(\begin{pmatrix}  17.5 \\ 40.0 \end{pmatrix}\), find the value of k.

How many ways can 6 students be seated around a circular table?

Find the 21st term of the Arithmetic Progression (A.P.):  -4, -1.5, 1, 3.5,...

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

Given that \(\frac{6x+m}{2x^{2}+7x-15} \equiv \frac{4}{x+5} - \frac{2}{2x-3}\), find the value of m.

Given that \(f(x) = \frac{x+1}{2}\), find \(f^{1}(-2)\).

The function f: x \(\to \sqrt{4 - 2x}\) is defined on the set of real numbers R. Find the domain of f.

Find the coordinates of the centre of the circle \(3x^{2}+3y^{2} - 4x + 8y -2=0\)

If \(x^{2} - kx + 9 = 0\) has equal roots, find the values of k.

Simplify \(\frac{1}{(1-\sqrt{3})^{2}}\)

A binary operation \(\Delta\) is defined on the set of real numbers, R, by \(a \Delta b = \frac{a+b}{\sqrt{ab}}\), where a\(\neq\) 0, b\(\neq\) 0. Evaluate \(-3 \Delta -1\).

If \(log_{y}\frac{1}{8}\) = 3, find the value of y.