WAEC Further Mathematics 2017 Past Questions

(a) If \(f(x) = \frac{4 - 5x}{2}\), and \(g(x) = x + 6, x \in R\), find \(f \circ g^{-1}\).

(b) P(x, y) divides the line joining (7, -5) and (-2, 7) internally in 5 : 4. Find the coordinates of P.

Evaluate : \(\int_{1}^{3} (\frac{x - 1}{(x + 1)^{2}}) \mathrm {d} x\).

(a) Given that \(\log_{10} p = a, \log_{10} q = b\) and \(\log_{10} s = c\), express \(\log_{10} (\frac{p^{\frac{1}{3}}q^{4}}{s^{2}}\) in terms of a, b and c.

(b) The radius of a circle is 6cm. If the area is increasing at the rate of 20\(cm^{2}s^{-1}\), find, leaving the answer in terms of \(\pi\), the rate at which the radius is increasing.

If (x + 1) and (x - 2) are factors of the polynomial \(g(x) = x^{4} + ax^{3} + bx^{2} - 16x - 12\), find the values of a and b.

Bottles of the same sizes produced in a factory are packed in boxes. Each box contains 10 bottles. If 8% of the bottles are defective, find, correct to two decimal places, the probability that box chosen at random contains at least 3 defective bottles.

The table shows the heights in cm of some seedlings in a certain garden.

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

(b) Using the curve in (a), find thesemi-interquartile range.

A parallelogram MNQR has vertices M(4, -6), N(10, 2), Q(8, 16) and R(x, y). Find the coordinates of R.

Forces \(F_{1} (18N, 330°), F_{2} (10N, 090°)\) and \(F_{3} (25N, 180°)\) act on a body at rest. Find, correct to one decimal place, the magnitude and direction of the resultant force.

(a) Simplify : \(\frac{1}{1 - \cos \theta} + \frac{1}{1 + \cos \theta}\) and leave your answer in terms of \(\sin \theta\).

(b) Find the equation of the line joining the stationary points of \(y = x^{2} (x - 3)\) and the distance between them.

(a) If \(f(x) = \frac{2x - 3}{(x^{2} - 1)(x + 2)}\)

(i) find the values of x for which f(x) is undefined.

(ii) express f(x) in partial fractions.

(b) A circle with centre (-3, 1) passes through the point (3, 1). Find its equation.

(a) If \(f(x) = \int (4x - x^{2}) \mathrm {d} x\) and f(3) = 21, find f(x).

(b) The second, fourth and eigth terms of an Arithmetic Progression (A.P) form the first three consecutive terms of a Geometric Progression (G.P). The sum of the third and fifth terms of the A.P is 20, find the :

(i) first four terms of the A.P

(ii) sum of the first ten terms of the A.P

(a) In a school, the ratio of those who passed to those who failed in a History test is 4 : 1. If 7 students are selected at random from the school, find, correct to two decimal places, the probability that :

(i) at least 3 passed the test ; (ii) between 3 and 6 students failed the test.

(b) A fair die is thrown five times; find the probability of obtaining a six three times.

The table shows the frequency distribution of the ages of patients in a clinic.

(a) Draw a histogram for the distribution

(b) Find, correct to two decimal places, the mean age of the patients.

(a) A body P of mass q kg is suspended by two light inextensible strings AB and DB attached to a horizontal table. The strings are inclined at 30° and 60° respectively to the horizontal and the tension in AB is 48N. If the system is in equilibrium :

(i) sketch a diagram to represent the information ; (ii) calculate the tension in DB ; 

(a) Given that \(m = (6i + 8j)\) and \(n = (-8i + \frac{7}{3}j)\), find the :

(i) magnitudes and direction of m and n ; (ii) angle between m and n.

(b) The position vectors of points P, Q, R and S are \(\begin{pmatrix} -2 \\ 3 \end{pmatrix}, \begin{pmatrix} 10 \\ 4 \end{pmatrix}, \begin{pmatrix} 3 \\ 12 \end{pmatrix}\) and \(\begin{pmatrix} 4 \\ 0 \end{pmatrix}\) respectively. Show that \(\overrightarrow{PQ}\) is perpendicular to \(\overrightarrow{RS}\).