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Find the equation of a circle with centre (-3, -8) and radius \(4\sqrt{6}\).
Evaluate \(\frac{1}{1 - \sin 60°}\), leaving your answer in surd form.
The fourth term of a geometric sequence is 2 and the sixth term is 8. Find the common ratio.
If \(\begin{pmatrix} 3 & 2 \\ 7 & x \end{pmatrix} \begin{pmatrix} 2 \\ 3 \end{pmatrix} = \begin{pmatrix} 12 \\ 29 \end{pmatrix} \), find x.
The inverse of a function is given by \(f^{-1} : x \to \frac{x + 1}{4}\).
Solve \(9^{2x + 1} = 81^{3x + 2}\)
A line is perpendicular to \(3x - y + 11 = 0\) and passes through the point (1, -5). Find its equation.
If \(y^{2} + xy - x = 0\), find \(\frac{\mathrm d y}{\mathrm d x}\).
Find \(\lim \limits_{x \to 3} \frac{x + 3}{x^{2} - x - 12}\)
\(f(x) = (x^{2} + 3)^{2}\) is defines on the set of real numbers, R. Find the gradient of f(x) at x = \(\frac{1}{2}\).
The sum and product of the roots of a quadratic equation are \(\frac{4}{7}\) and \(\frac{5}{7}\) respectively. Find its equation.
\(f(x) = p + qx\), where p and q are constants. If f(1) = 7 and f(5) = 19, find f(3).
The equation of a circle is \(3x^{2} + 3y^{2} + 6x - 12y + 6 = 0\). Find its radius
Solve \(3x^{2} + 4x + 1 > 0\)
Simplify \(\sqrt[3]{\frac{8}{27}} - (\frac{4}{9})^{-\frac{1}{2}}\)
A function is defined by \(f(x) = \frac{3x + 1}{x^{2} - 1}, x \neq \pm 1\). Find f(-3).
Find the remainder when \(5x^{3} + 2x^{2} - 7x - 5\) is divided by (x - 2).
Evaluate \(\cos (\frac{\pi}{2} + \frac{\pi}{3})\)
If \(\log_{9} 3 + 2x = 1\), find x.
Express 75° in radians, leaving your answer in terms of \(\pi\).