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Evaluate: 2\(\sqrt{28} - 3\sqrt{50} + \sqrt{72}\)
If 6, P, and 14 are consecutive terms in an Arithmetic Progression (AP), find the value of P.
If 23\(_y\) = 1111\(_{\text{two}}\), find the value of y
Evaluate; \(\frac{\log_3 9 - \log_2 8}{\log_3 9}\)
If T = {prime numbers} and M = {odd numbers} are subsets of \(\mu\) = {x : 0 < x ≤ 10} and x is an integer, find (T\(^{\prime}\) n M\(^{\prime}\)).
If 7 + y = 4 (mod 8), find the least value of y, 10 \(\leq y \leq 30\)
Simplify, correct to three significant figures, (27.63)\(^2\) - (12.37)\(^2\)
Solve: \(\frac{y + 1}{2} - \frac{2y - 1}{3}\) = 4
Evaluate: (0.064)\(^{-\frac{1}{3}}\)
Express, correct to three significant figures, 0.003597.
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 \(\frac{\mathrm d^2 y}{\mathrm d x^2}\).