WAEC Mathematics 1992 Past Questions

(a) If \(9^{2x - 1} = \frac{81^{x - 2}}{3^{x}}\), find x.

(b) Without using Mathematical Tables, evaluate: \(\sqrt{\frac{0.81 \times 10^{-5}}{2.25 \times 10^{7}}}\)

(a) Solve the following pair of simultaneous equations: \(2x + 5y = 6\frac{1}{2} ; 5x - 2y = 9\)

(b) If \(\log_{10} (2x + 1) - \log_{10} (3x - 2) = 1\), find x.

(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 horizontal level as the foot of a cliff, and the angle of depression of the boat from the top of the cliff is 30°. If the boat is 120m away from the foot of the cliff, find the height of the cliff correct to three significant figures.

(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 circular track is 400m. Find its radius, correct to the nearest metre. [Take \(\pi = \frac{22}{7}\)]

(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 marbles, 7 of which are black and 3 are red. Two marbles are drawn one after the other without replacement. Find the probability of getting:

(i) a red, then a black marble ; (ii) two black marbles.

(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.P is 72 and the sum of the next 4 terms is 71, find the A.P.

(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 \(l_{1}\) of points equidistant from A and B; (iii) the locus \(l_{2}\) of points equidistant from AB and AC which passes through triangle ABC .

(b) Label the point P where \(l_{1}\) and \(l_{2}\) intersect.

(c) Measure |CP|.

(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 the (i) total surface area of the tin ; (ii) volume, in litres, that will fill the tin to capacity, correct to two decimal places. 

[Take \(\pi = \frac{22}{7}\)]

(a) Copy and complete the following table for the relation \(y = \frac{5}{2} + x - 4x^{2}\)

(b) Using a scale of 2cm to 1 unit on the x- axis and 2cm to 5 units on the y- axis, draw the graph of the relation for \(-2.0 \leq x \leq 2.0\).

(c) What is the maximum value of y?

(d) From your graph, obtain the roots of the equation \(8x^{2} - 2x - 5 = 0\)

(a) The distribution of junior workers in an institution is as follows: Clerks - 78, Drivers - 36, Typists - 44, Messengers - 52, Others - 30. Represent the above information by a pie chart.

(b) The table below shows the frequency distribution of marks scored by 30 candidates in an aptitude test.

Find the mean score to the nearest whole number.

Three towns P, Q and R are such that the distance between P and Q is 50km and the distance between P and R is 90km. If the bearing of Q from P is 075° and the bearing of R from P is 310°, find the :

(a) distance between Q and R ;

(b) baering of R from Q.

The table below shows the weekly profit in naira from a mini-market.

(a) Draw the cumulative frequency curve of the data;

(b) From your graph, estimate the :  (i) median ; (ii) 80th percentile

(c) What is the modal weekly profit?