WAEC SSCE - Further Mathematics - 2009 (Objective)

Calculate, correct to the nearest degree, the angle between the vectors \(\begin{pmatrix} 13 \\ 1 \end{pmatrix}\) and \(\begin{pmatrix} 1 \\ 4 \end{pmatrix}\).

The roots of the quadratic equation \(2x^{2} - 5x + m = 0\) are \(\alpha\) and \(\beta\), where m is a constant. Find \(\alpha^{2} + \beta^{2}\) in terms of m.

A stone is projected vertically with a speed of 10 m/s from a point 8 metres above the ground. Find the maximum height reached. \([g = 10 ms^{-2}]\).

The gradient of point P on the curve \(y = 3x^{2} - x + 3\) is 5. Find the coordinates of P.

If \(P = \begin{vmatrix} 1 & 1 \\ 2 & 1 \end{vmatrix}\), find \((P^{2} + P)\).

In the diagram, a ladder PS leaning against a vertical wall PR makes angle x° with the horizontal floor. The ladder slides down to a point QT such that angle QTR = 30° and SNT = y°. Find the relation between x and y.

Express the force F = (8 N, 150°) in the form (a i + b j) where a and b are constants. 

Express \(\frac{2}{3 - \sqrt{7}} \text{ in the form} a + \sqrt{b}\), where a and b are integers.

A body is acted upon by forces \(F_{1} = (10 N, 090°)\) and \(F_{2} = (6 N, 180°)\). Find the magnitude of the resultant force.

If \(\frac{^{8}P_{x}}{^{8}C_{x}} = 6\), find the value of x.

Eight football clubs are to play in a league on home and away basis. How many matches are possible?

Find the coefficient of \(x^{4}\) in the binomial expansion of \((2 + x)^{6}\).

The position vectors of A and B are (2i + j) and (-i + 4j) respectively; find |AB|.

Which of the following binary operations is not commutative?

The line \(y = mx - 3\) is a tangent to the curve \(y = 1 - 3x + 2x^{3}\) at (1, 0). Find the value of the constant m.

Given that \(2^{x} = 0.125\), find the value of x.

Solve \(x^{2} - 2x - 8 > 0\).

An arc of length 10.8 cm subtends an angle of 1.2 radians at the centre of a circle. Calculate the radius of the circle.

Three men, P, Q and R aim at a target, the probabilities that P, Q and R hit the target are \(\frac{1}{2}\), \(\frac{1}{3}\) and \(\frac{3}{4}\) respectively. Find the probability that exactly 2 of them hit the target.

If (x + 3) is a factor of the polynomial \(x^{3} + 3x^{2} + nx - 12\), where n is a constant, find the value of n.

Given \(\sin \theta =  \frac{\sqrt{3}}{2}, 0° \leq \theta \leq 90°\), find \(\tan 2\theta\) in surd form.

A force F acts on a body of mass 12kg increases its speed from 5 m/s to 35 m/s in 5 seconds. Find the value of F.

The first term of a geometric progression is 350. If the sum to infinity is 250, find the common ratio.

If the mean of -1, 0, 9, 3, k, 5 is 2, where k is a constant, find the median of the set of numbers.

Two balls are drawn, from a bag containing 3 red, 4 white and 5 black identical balls. Find the probability that they are all of the same colour.

The ages, in years, of 5 boys are 5, 6, 6, 8 and 10. Calculate, correct to one decimal place, the standard deviation of their ages.

Which of the following is the semi- interquartile range of a distribution?

Evaluate \(\begin{pmatrix} 2 & 3 \\ 4 & 1 \end{pmatrix} \begin{pmatrix} 2 \\ 3 \end{pmatrix}\). 

The derivative of a function f with respect to x is given by \(f'(x) = 3x^{2} - \frac{4}{x^{5}}\). If \(f(1) = 4\), find f(x).

The roots of a quadratic equation are -3 and 1. Find its equation.

Three defective bulbs got mixed up with seven good ones. If two bulbs are selected at random, what is the probability that both are good?

p and q are statements such that \(p \implies q\). Which of the following is a valid conclusion from the implication?

Simplify \(2\log_{3} 8 - 3\log_{3} 2\)

Simplify \((216)^{-\frac{2}{3}} \times (0.16)^{-\frac{3}{2}}\)

In the diagram, a ladder PS leaning against a vertical wall PR makes angle x° with the horizontal floor. The ladder slides down to a point QT such that angle QTR = 30° and SNT = y°. Find an expression for tan y.

Given that \(\log_{3}(x - y) = 1\) and \(\log_{3}(2x + y) = 2\), find the value of x.

The coordinates of the centre of a circle is (-2, 3). If its area is \(25\pi cm^{2}\), find its equation. 

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

The velocity \(v ms^{-1}\) of a particle moving in a straight line is given by \(v = 3t^{2} - 2t + 1\) at time t secs. Find the acceleration of the particle after 3 seconds.

Two fair dices, each numbered 1, 2, ..., 6, are tossed together. Find the probability that they both show even numbers.