WAEC Mathematics 1998 Past Questions

A, B and C are subsets of the universal set U such that : \(U = {0, 1, 2, 3,..., 12}; A = {x : 0 \leq x \leq 7}; B = {4, 6, 8, 10, 12}; C = {1 < y < 8}\), where y is a prime number.

(a) Draw a venn diagram to illustrate the information given above;

(b) Find: (i) \((B \cup C)'\); (ii) \(A' \cap B \cap C\).

(a) Given that \(\log_{10} 2 = 0.3010, \log_{10} 7 = 0.8451\) and \(\log_{10} 5 = 0.6990\), evaluate without using logarithm tables:

(i) \(\log_{10} 35\); (ii) \(\log_{10} 2.8\).

(b) Given that \(N^{0.8942} = 2.8\), use your result in (a)(ii) to find the value of N.

(a) The value of the expression \(2Ax - Kx^{2}\) is 7 when x = 1 and 4 when x = 2. Find the values of the constants A and K.

(b) Solve the equation \(x^{2} - 3x - 1 = 0\), giving your answers correct to 1 decimal place.

The area of a rectangular floor is 13.5m\(^{2}\). One side is 1.5m longer than the other.

(a) Calculate the dimensions of the floor ;

(b) If it costs N250.00 per square metre to carpet the floor and only N2,000.00 is available, what area of the floor can be covered with carpet?

(a) A number is selected at random from each of the sets {2, 3, 4} and {1, 3, 5}. What is the probability that the sum of the two numbers will be less than 7 but greater than 3?

(b) In the diagram, ABCD is a circle. DAE, CBE, ABF and DCF are straight lines. If y + m = 90°, find the value of x.

The third term of a Geometric Progression (G.P) is 360 and the sixth term is 1215. Find the 

(a) common ratio;

(b) first term ;

(c) sum of the first four terms.

(a) A radio which a dealer bought for N6,000.00 and marked to give a profit of 30% was reduced in a sales by 10%. Find : (i) the final sales price ; (ii) the percentage profit.

(b) Solve the equation : \(2^{(2x + 1)} - 9(2^{x}) + 4 = 0\).

(a) Copy and complete the table of values for the relation \(y = 5 - 7x - 6x^{2}\) for \(-3 \leq x \leq 2\).

(b) Using a scale of 2cm to 1 unit on the x- axis and 2cm to 5 units on the y- axis, draw the :

(i) graph of \(y = 5 - 7x - 6x^{2}\) ; (ii) line \(y = 3\) on the same axis.

(c) Use your graph to find the : (i) roots of the equation \(2 - 7x - 6x^{2} = 0\) ; (ii) maximum value of \(y = 5 - 7x - 6x^{2}\).

Using a ruler and a pair of compasses only, construct (a) triangle QRT with |QR| = 8cm, |RT| = 6cm and |QT| = 4.5cm.

(b) a quadrilateral QRSP which has a common base QR with \(\Delta\)QRT such that QTP is a straight line, PQ || SR, |QP| = 9cm and |RS| = 4.5cm.

(i) Measure |PS| ; (ii) Find the perpendicular distance between RS and PQ ; (iii) What is QRSP?

A surveyor standing at a point X sights a pole Y due east of him and a tower Z of a building on a bearing of 046°. After walking to a point W, a distance of 180m in the South- East direction, he observes the bearing of Z and Y to be 337° and 050° respectively.

(a) Calculate, correct to the nearest metre : (i) |XY| ; (ii) |ZW| 

(b) If N is on XY such that XZ = ZN, find the bearing of Z from N.

In the diagram, ASRTB represents a piece of string passing over a pulley of radius 10cm in a vertical plane. O is the centre of the pulley and AMB is a horizontal straight line touching the pulley at M. Angle SAB = 90° and angle TBA = 60°. 

(a) Calculate (i) the obtuse angle SOT ; (ii) arc SRT ; (iii) |BT| 

(b) Find, correct to the nearest cm, the length of the string. (Take \(\pi = \frac{22}{7}\)).

The table below shows the number of eggs laid by the chickens in a man's farm in a year.

(a) Draw a cumulative frequency curve for the distribution.

(b) Use your graph to find the interquartile range.

(c) If a woman buys a chicken from the farm, what is the probability that the chicken lays at least 60 eggs in a year?