WAEC Mathematics 1994 Past Questions

(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) 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) 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 tower is 65°. From the top Q of the building, the angle of elevation of the point T is 25°. If the building is 20m high, calculate the distance PT.

(b) Hence or otherwise, calculate the height of the tower. [Give your answers correct to 3 significant figures].

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

The table below gives the frequency distribution of the marks obtained by some students in a scholarship examination.

(a) Calculate, correct to 3 significant figures, the mean mark.

(b) Find the : (i) mode ; (ii) range of the distribution.

(a) If \(\log_{10} (3x - 1) - \log_{10} 2 = 3\), find the value of x.

(b) Use logarithm tables to evaluate \(\sqrt{\frac{0.897 \times 3.536}{0.00249}}\), correct to 3 significant figures.

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 bag, find the probability that :

(a) all four balls are black ;

(b) exactly one of the four balls is white.

(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 \(l_{1}\) of points equidistant from Y and Z ; (iii) the locus \(l_{2}\) of points equidistant from XY and YZ.

(b) Measure QY where Q is the point of intersection of \(l_{1}\) and \(l_{2}\).

The table below gives the ages, to the nearest 5 years of 50 people.

(a) Construct a cumulative frequency table for the distribution.

(b) Draw a cumulative frequency curve (Ogive)

(c) From your Ogive, find the : (i) median age ; (ii) number of people who are at most 15 years of age ; (iii) number of people who are between 20 and 25 years of age.

(a) Copy and complete the following table of values for \(y = 2x^{2} - 9x - 1\).

(b) Using a scale of 2cm to represent 1 unit on the x- axis and 2cm to represent 5 units on the y- axis, draw the graph of \(y = 2x^{2} - 9x - 1\).

(c) Use your graph to find the : (i) roots of the equation \(2x^{2} - 9x = 4\), correct to one decimal place ; (ii) gradient of the curve \(y = 2x^{2} - 9x - 1\) at x = 3.

(a) The fourth term of an A.P is 37 and 6th term is 12 more than the fourth term . Find the first and seventh terms.

(b) If \(P = {1, 2, 3, 4}\) and \(Q = {3, 5, 6}\), find (i) \(P \cap Q\) ; (ii) \(P \cup Q\) ; (iii) \((P \cap Q) \cup Q\) ; (iv) \((P \cap Q) \cup P\).

(a) Two points X(32°N, 47°W) and Y(32°N, 25°E) are on the earth's surface. If it takes an aeroplane 11 hours to fly from X to Y along the parallel of latitude, calculate its speed, correct to the nearest kilometre per hour. [Radius of the earth = 6400km; \(\pi = \frac{22}{7}\)]

(b) Two observers P and Q, 15metres apart observe a kite (K) in the same vertical plane and from the same side of the kite. The angles of elevation of the kite from P and Q are 35° and 45° respectively. Find the height of the kite to the nearest metre.