WAEC Mathematics 2007 Past Questions

(a) Evaluate, without using mathematical tables or calculator, \((3.69 \times 10^{5}) \div (1.64 \times 10^{-3})\), leaving your answer in standard form.

(b) A man invested N20,000 in bank A and N25,000 in bank B at the beginning of the year. Bank A pays simple interest at a rate of y% per annum and B pays 1.5y% per annum. If his total interest at the end of the year from the two banks was N4,600, find the value of y.

(a) Simplify : \(\frac{x^{2} - 8x + 16}{x^{2} - 7x + 12}\).

(b) If \(\frac{1}{2}, \frac{1}{x}, \frac{1}{3}\) are successive terms of an arithmetic progression (A.P), show that \(\frac{2 - x}{x - 3} = \frac{2}{3}\).

The diagram shows the cross- section of a railway tunnel. If |AB| = 100m and the radius of the arc is 56m, calculate, correct to the nearest metre, the perimetre of the cross- section.

Y is 60 km away from X on a bearing of 135°. Z is 80 km away from X on a bearing of 225°. Find the :

(a) distance of Z from Y ;

(b) bearing of Z from Y.

Out of the 24 apples in a box, 6 are bad. If three apples are taken from the box at random, with replacement, find the probability that :

(a) the first two are good and the third is bad ;

(b) all three are bad ;

(c) all the three are good.

(a) Simplify : \(\frac{3\frac{1}{12} + \frac{7}{8}}{2\frac{1}{4} - \frac{1}{6}}\)

(b) If \(p = \frac{m}{2} - \frac{n^{2}}{5m}\) ; 

(i) make n the subject of the relation ;  (ii) find, correct to three significant figures, the value of n when p = 14 and m = -8.

(a) With the aid of four- figure logarithm tables, evaluate \((0.004592)^{\frac{1}{3}}\).

(b) If \(\log_{10} y + 3\log_{10} x = 2\), express y in terms of x.

(c) Solve the equations : \(3x - 2y = 21\)

                                        \(4x + 5y = 5\).

(a) A cylinder with radius 3.5 cm has its two ends closed, if the total surface area is \(209 cm^{2}\), calculate the height of the cylinder. [Take \(\pi = \frac{22}{7}\)].

(b)   In the diagram, O is the centre of the circle and ABC is a tangent at B. If \(\stackrel\frown{BDF} = 66°\) and \(\stackrel\frown{DBC} = 57°\), calculate, (i) \(\stackrel\frown{EBF}\) and (ii) \(\stackrel\frown{BGF}\).

(a) Using a ruler and a pair of compasses only, construc :

(i) a triangle PQR such that /PQ/ = 10 cm, /QR/ = 7 cm and < PQR = 90° ; (ii) the locus \(l_{1}\) of points equidistant from Q and R ; (iii) the locus \(l_{2}\) of points equidistant from P and Q.

(b) Locate the point O equidistant from P, Q and R.

(c) With O as centre, draw the circumcircle of the triangle PQR.

(d) Measure the radius of the circumcircle.

(a) Simplify : \(\frac{x^{2} - y^{2}}{3x + 3y}\)

(b) In the diagram, PQRS is a rectangle. /PK/ = 15 cm, /SK/ = /KR/ and <PKS = 30°. Calculate, correct to three significant figures : (i) /PS/ ; (ii) /SK/ and (iii) the area of the shaded portion.

(a) In the diagram, AOB is a straight line. < AOC = 3(x + y)°, < COB = 45°, < AOD = (5x + y)° and < DOB = y°. Find the values of x and y.

(b) From two points on opposite sides of a pole 33m high, the angles of elevation of the top of the pole are 53° and 67°. If the two points and the base are on te same horizontal level, calculate, correct to three significant figures, the distance between the two points.

(a) The 3rd and 8th terms of an arithmetic progression (A.P) are -9 and 26 respectively. Find the : (i) common difference ; (ii) first term.

(b) In the diagram \(\overline{PQ} || \overline{YZ}\), |XP| = 2cm, |PY| = 3 cm, |PQ| = 6 cm and the area of \(\Delta\) XPQ = 24\(cm^{2}\).Calculate the area of the trapezium PQZY.

In a college, the number of absentees recorded over a period of 30 days was as shown in the frequency distribution table

Calculate the : (a) Mean

(b) Standard deviation , correct to two decimal places.