WAEC Mathematics 1995 Past Questions

(a) Factorise : \(px - 2px - 4qy + 2py\)

(b) Given that the universal set U = {1, 2, 3, 4,5, 6, 7, 8, 9, 10}, P = {1, 2, 4, 6, 10} and Q = {2, 3, 6, 9}; show that \((P \cup Q)' = P' \cap Q'\)

The quantity y is partly constant and partly varies inversely as the square of x.

(a) Write down the relationship between x and y.

(b) When x = 1, y = 11 and when x = 2, y = 5, find the value of y when x = 4.

(a) In the diagram, PQSR and SRYZ are parallelograms and PQYZ is a straight line. If /QY/ = 2cm and /RS/ = 3cm, find /PZ/.

(b) P and Q are two towns on the earth's surface on latitude 56°N. Thei longitudes are 25°E and 95°E respectively. Find the distance PQ along their parallel of latitude, correct to the nearest km. [Take radius of the earth as 6400km and \(\pi = \frac{22}{7}\)]

(a) A pack of 52 playing cards is shuffled and a card is drawn at random. Calculate the probability that it is either a five or a red nine.

[Hint : There are 4 fives and 2 red nines in a pack of 52 cards]

(b) P, Q and R are points in the same horizontal plane. The bearing of Q from P is 150° and the bearing of R from Q is 060°. If /PQ/ = 5m and /QR/ = 3m, find the bearing of R from P, correct to the nearest degree.

The frequency table shows the marks scored by 32 students in a test.

Find the :

(a)(i) mean ; (ii) median ; (iii) mode of the marks;

(b) percentage of the students who scored at least 8 marks.

(a) Using mathematical tables, find ; (i) \(2 \sin 63.35°\) ; (ii) \(\log \cos 44.74°\);

(b) Find the value of K given that \(\log K - \log (K - 2) = \log 5\);

(c) Use logarithm tables to evaluate \(\frac{(3.68)^{2} \times 6.705}{\sqrt{0.3581}}\)

(a) Given that \(p = x + ym^{3}\), find m in terms of p, x and y.

(b) Using the method of completing the square, find the roots of the equation \(x^{2} - 6x + 7 = 0\), correct to 1 decimal place.

(c) The product of two consecutive positive odd numbers is 195. By constructing a quadratic equation and solving it, find the two numbers.

(a) Copy and complete the table for the relation \(y = 2 \cos 2x - 1\).

(b) Using a scale of 2cm = 30° on the x- axis and 2cm = 1 unit on the y- axis, draw the graph of \(y = 2 \cos 2x - 1\) for \(0° \leq x \leq 180°\).

(c) On the same axis, draw the graph of \(y = \frac{1}{180} (x - 360)\)

(d) Use your graphs to find the : (i) values of x for which \(2 \cos 2x + \frac{1}{2} = 0\); (ii) roots of the equation \(2 \cos 2x - \frac{x}{180} + 1 = 0\).

(a) Using a ruler and a pair of compasses only, construct triangle ABC with /AB/ = 7.5cm, /BC/ = 8.1cm and < ABC = 105°.

(b) Locate a point D on BC such that /BD/ : /DC/ is 3 : 2.

(c) Through D, construct a line I perpendicular to BC.

(d) If the line I meets AC at P, measure /BP/.

(a) A man travels from a village X on a bearing of 060° to a village Y which is 20km away. From Y, he travels to a village Z, on a bearing of 195°. If Z is directly east of X, calculate, correct to three significant figures, the distance of :

(i) Y from Z ; (ii) Z from X .

(b) An aircraft flies due South from an airfield on latitude 36°N, longitude 138°E to an airfield on latitude 36°S, longitude 138°E. 

(i) Calculate the distance travelled, correct to three significant figures ; (ii) if the speed of the aircraft is 800km per hour, calculate the time taken, correct to the nearest hour.

[Take \(\pi = \frac{22}{7}\), R = 6400km].

The table shows the scores of 2000 candidates in an entrance examination into a private secondary school.

(a) Prepare a cumulative frequency table and draw the cumulative frequency curve for the distribution.

(b) Use your curve to estimate the : (i) cut off mark, if 300 candidates are to be offered admission ; (ii) probability that a candidate picked at random, scored at least 45%.

A box contains 5 blue balls, 3 black balls and 2 red balls of the same size. A ball is selected at random from the box and then replaced. A second ball is then selected. Find the probability of obtaining

(a) two red balls ;

(b) two blue balls or two black balls ;

(c) one black and one red ball in any order.