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Evaluate \(\frac{2\sin 30 + 5\tan 60}{\sin 60}\), leaving your answer in surd form.
If \(\sin x = \frac{4}{5}\), find \(\frac{1 + \cot^2 x}{\csc^2 x - 1}\).
Calculate the volume of the regular three dimensional figure drawn above, where < ABC = 90° (a right- angled triangle).
In the circle above, with centre O and radius 7 cm. Find the length of the arc AB, when < AOB = 57°.
The histogram above represents the number of candidates who did Further Mathematics examination in a school. How many candidates scored more than 40?
| Marks | 1 | 2 | 3 | 4 | 5 |
| Frequency | 2y - 2 | y - 1 | 3y - 4 | 3 - y | 6 - 2y |
The table above is the distribution of data with mean equals to 3. Find the value of y.
Find the equation of a line perpendicular to the line 4y = 7x + 3 which passes through (-3, 1)
Find the distance between the points C(2, 2) and D(5, 6).
Differentiate \(\frac{2x}{\sin x}\) with respect to x.
If y = 8x\(^3\) - 3x\(^2\) + 7x - 1, find \(\frac{\mathrm d^2 y}{\mathrm d x^2}\).
Given the matrix \(A = \begin{vmatrix} 3 & -2 \\ 1 & 6 \end{vmatrix}\). Find the inverse of matrix A.
If \(\begin{vmatrix} 2 & -5 & 3 \\ x & 1 & 4 \\ 0 & 3 & 2 \end{vmatrix} = 132\), find the value of x.
If 2x\(^2\) + x - 3 divides x - 2, find the remainder.
Find the polynomial if given q(x) = x\(^2\) - x - 5, d(x) = 3x - 1 and r(x) = 7.
Determine the values for which \(x^2 - 7x + 10 \leq 0\)
Find the value of x for \(\frac{2 + 2x}{3} - 2 \geq \frac{4x - 6}{5}\)
Evaluate \(\frac{2\log_{3} 9 \times \log_{3} 81^{-2}}{\log_{5} 625}\)
Find the value of k in the equation: \(\sqrt{28} + \sqrt{112} - \sqrt{k} = \sqrt{175}\)
In a committee of 5, which must be selected from 4 males and 3 females. In how many ways can the members be chosen if it were to include 2 females?
If the universal set μ = {x : 1 ≤ x ≤ 20} and
A = {y : multiple of 3}
B = |z : odd numbers}
Find A ∩ B