Mathematics Past Questions and Answers

(a) If \(2^{x + y} = 16\) and \(4^{x - y} = \frac{1}{32}\), find the value of x and y.
(b) P, Q and R are related in such a way that \(P \propto \frac{Q^{2}}{R}\). When P = 36, Q = 3 and R = 4. Calculate Q when P = 200 and R = 2.

(a) Solve, correct to two decimal places, the equation \(4x^{2} = 11x + 21\).
(b) A man invests £1500 for two years at compound interest. After one year, his money amounts to £1560. Find the :
(i) rate of interest ; (ii) interest for the second year.
(c) A car costs N300,000.00. It depreciates by 25% in the first year and 20% in the second year. Find its value after 2 years.

The ages, in years, of 50 teachers in a school are given below :
21 37 49 27 49 42 26 33 46 40 50 29 23 24 29 31 36 22 27 38 30 26 42 39 34 23 21 32 41 46 46 31 33 29 28 43 47 40 34 44 26 38 34 49 45 27 25 33 39 40
(a) Form a frequency distribution table of the data using the intervals : 21 - 25, 26 - 30, 31 - 35 etc.
(b) Draw the histogram of the distribution
(c) Use your histogram to estimate the mode
(d) Calculate the mean age.

(a) The triangle ABC has sides AB = 17m, BC = 12m and AC = 10m. Calculate the :
(i) largest angle of the triangle ; (ii) area of the triangle.
(b) From a point T on a horizontal ground, the angle of elevation of the top R of a tower RS, 38m high is 63°. Calculate, correct to the nearest metre, the distance between T and S.

(a) Using ruler and a pair of compasses only, construct :
(i) a quadrilateral PQRS such that /PQ/ = 7 cm, < QPS = 60°, /PS/ = 6.5 cm, < PQR = 135° and /QS/ = /QR/ ;
(ii) locus, \(l_{1}\) of points equidistant from P and Q ;
(iii) locus, \(l_{2}\) of points equidistant from P and S.
(b)(i) Label the point T where \(l_{1}\) and \(l_{2}\) intersect. (ii) With center T and radius /TP/, construct a circle \(l_{3}\).