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Evaluate \(\int_{-1}^{0} (x+1)(x-2) \mathrm{d}x\)
If \(y = \frac{1+x}{1-x}\), find \(\frac{dy}{dx}\).
Given that \(f(x) = 5x^{2} - 4x + 3\), find the coordinates of the point where the gradient is 6.
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 \(\frac{1}{(1-\sqrt{3})^{2}}\)