(a) Given that \((\sqrt{3} - 5\sqrt{2})(\sqrt{3} + \sqrt{2}) = a + b\sqrt{6}\), find a and b. (b) If \(\frac{2^{1 - y} \times 2^{y - 1}}{2^{y + 2}} = 8^{2 -...

(a) If \(\log 5 = 0.6990, \log 7 = 0.8451\) and \(\log 8 = 0.9031\), evaluate \(\log (\frac{35 \times 49}{40 \div 56})\). (b) For a musical show, x children ...

(a) A woman looking out from the window of a building at a height of 30m, observed that the angle of depression of the top of a flag pole was 44°. If the foo...

The table shows the number of children per family in a community. No of children 0 1 2 3 4 5 No of families 3 5 7 4 3 2 (a) Find the : (i) mode ; (ii) third ...

(a) Simplify \(\frac{x + 2}{x - 2} - \frac{x + 3}{x - 1}\) (b) The graph of the equation \(y = Ax^{2} + Bx + C\) passes through the point (0, 0), (1, 4) and ...

(a) If \(9 \cos x - 7 = 1\) and \(0° \leq x \leq 90°\), find x. (b) Given that x is an integer, find the three greatest values of x which satisfy the inequal...

(a) Out of 30 candidates applying for a post, 17 have degrees, 15 have diplomas and 4 neither degree nor diploma. How many of them have both? (b) In triangle...

In the diagram, ABCDEF is a triangular prism. < ABC = < DEF = 90°, /AB/ = 24 cm, /BC/ = 7 cm and /CD/ = 40 cm. Calculate : (a) /AC/ ; (b) the total surface a...

The marks scored by 50 students in a Geography examination are as follows : 60 54 40 67 53 73 37 55 62 43 44 69 39 32 45 58 48 67 39 51 46 59 40 52 61 48 23 ...