(a) Solve the following pair of simultaneous equations: \(2x + 5y = 6\frac{1}{2} ; 5x - 2y = 9\) (b) If \(\log_{10} (2x + 1) - \log_{10} (3x - 2) = 1\), fin...

(a) If \(17x = 375^{2} - 356^{2}\), find the exact value of x. (b) If \(4^{x} = 2^{\frac{1}{2}} \times 8\), find x. (c) The sum of the first 9 terms of an A....

(a) Calculate the area of the shaded segment of the circle shown in the diagram [Take \(\pi = \frac{22}{7}\)] (b) A tin has radius 3cm and height 6cm. Find t...

(a) Copy and complete the following table for the relation \(y = \frac{5}{2} + x - 4x^{2}\) x -2.0 -1.5 -1.0 -0.5 0 0.5 1 1.5 2.0 y -15.5 1 2.5 (b) Using a s...

(a) The angle of a sector of a circle radius 7cm is 108°. Calculate the perimeter of the sector. [Take \(\pi = \frac{22}{7}\)] (b) A boat is on the same hori...

(a) In a game, a fair die is rolled once and two unbiased coins are tossed at once. What is the probability of obtaining 3 and a tail? (b) A box contains 10 ...

(a) The sides PQ and PR of \(\Delta\) PQR are produced to T and S respectively, such that TQR = 131° and < QRS = 98°. Find < QPR. (b) The circumference of a ...

(a) If \(9^{2x - 1} = \frac{81^{x - 2}}{3^{x}}\), find x. (b) Without using Mathematical Tables, evaluate: \(\sqrt{\frac{0.81 \times 10^{-5}}{2.25 \times 10^...

(a) Using a ruler and a pair of compasses only, construct: (i) a triangle ABC such that |AB| = 5cm, |AC| = 7.5cm and < CAB = 120°; (ii) the locus \(l_{1}\) o...