WAEC SSCE - Further Mathematics - 2009 (Objective)

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.

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.

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.

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

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

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

Which of the following binary operations is not commutative?

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.

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.

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

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.

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

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.

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

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

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

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

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

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

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

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

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.

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.

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).

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

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

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.

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

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.

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

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

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. \([g = 10 ms^{-2}]\).

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

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

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?

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

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

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

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.