(a) Given that \(3 \times 9^{1 + x} = 27^{-x}\), find x. (b) Evaluate \(\log_{10} \sqrt{35} + \log_{10} \sqrt{2} - \log_{10} \sqrt{7}\)

A bag contains 12 white balls and 8 black balls, another contains 10 white balls and 15 black balls. If two balls are drawn, without replacement from each ba...

(a) Evaluate, without using mathematical tables, \(17.57^{2} - 12.43^{2}\). (b) Prove that angles in the same segment of a circle are equal.

(a) Using a ruler and a pair of compasses only, construct (i) a triangle XYZ in which /YZ/ = 8cm, < XYZ = 60° and < XZY = 75°. Measure /XY/; (ii) the locus \...

The table below gives the ages, to the nearest 5 years of 50 people. Age in years 10 15 20 25 30 No of people 8 19 10 7 6 (a) Construct a cumulative frequenc...

(a) If \(\log_{10} (3x - 1) - \log_{10} 2 = 3\), find the value of x. (b) Use logarithm tables to evaluate \(\sqrt{\frac{0.897 \times 3.536}{0.00249}}\), cor...

(a) Divide \(11111111_{two}\) by \(101_{two}\) (b) A sector of radius 6 cm has an angle of 105° at the centre. Calculate its: (i) perimeter ; (ii) area . [Ta...

(a) A tower and a building stand on the same horizontal level. From the point P at the bottom of the building, the angle of elevation of the top, T of the to...

The table below gives the frequency distribution of the marks obtained by some students in a scholarship examination. Scores (x) 15 25 35 45 55 65 75 Freq (f...