WAEC SSCE - Further Mathematics - 2013 (Objective)

The function \(f : F \to R\) 

= \(f(x) = \begin{cases} 3x + 2 : x > 4 \\ 3x - 2 : x = 4 \\ 5x - 3 : x < 4 \end{cases}\). Find f(4) - f(-3).

Evaluate \(\int_{0}^{2} (8x - 4x^{2}) \mathrm {d} x\).

Find the coordinates of the point which divides the line joining P(-2, 3) and Q(4, 9) internally in the ratio 2 : 3.

Find the equation of the line that is perpendicular to \(2y + 5x - 6 = 0\) and bisects the line joining the points P(4, 3) and Q(-6, 1).

Find the third term in the expansion of \((a - b)^{6}\) in ascending powers of b.

Find the upper quartile of the following scores: 41, 29, 17, 2, 12, 33, 45, 18, 43 and 5.

Find the range of values of x for which \(x^{2} + 4x + 5\) is less than \(3x^{2} - x + 2\)

The sales of five salesgirls on a certain day are as follows; GH¢ 26.00, GH¢ 39.00, GH¢ 33.00, GH¢ 25.00 and GH¢ 37.00. Calculate the standard deviation if the mean sale is GH¢ 32.00. 

A binary operation * is defined on the set of real numbers, R, by \(x * y = x + y - xy\). If the identity element under the operation * is 0, find the inverse of \(x \in R\).

If \(s = 3i - j\) and \(t = 2i + 3j\), find \((t - 3s).(t + 3s)\).

Express \(\frac{x^{2} + x + 4}{(1 - x)(x^{2} + 1)}\) in partial fractions.

An object is thrown vertically upwards from the top of a cliff with a velocity of \(25ms^{-1}\). Find the time, in seconds, when it is 20 metres above the cliff. \([g = 10ms^{-2}]\).

If \(g(x) = \frac{x + 1}{x - 2}, x \neq -2\), find \(g^{-1}(2)\).

If \(\alpha\) and \(\beta\) are the roots of the equation \(2x^{2} - 6x + 5 = 0\), evaluate \(\frac{\beta}{\alpha} + \frac{\alpha}{\beta}\).

Given that \(f(x) = 2x^{3} - 3x^{2} - 11x + 6\) and \(f(3) = 0\), factorize f(x).

Solve: \(\sin \theta = \tan \theta\)

Two out of ten tickets on sale for a raffle draw are winning tickets. If a guest bought two tickets, what is the probability that both tickets are winning tickets?

A circular ink blot on a piece of paper increases its area at the rate \(4mm^{2}/s\). Find the rate of the radius of the blot when the radius is 8mm. \([\pi = \frac{22}{7}]\).

Given that \(P = \begin{pmatrix} 3 & 4 \\ 2 & x \end{pmatrix}; Q = \begin{pmatrix} 1 & 3 \\ -2 & 4 \end{pmatrix}; R = \begin{pmatrix} -5 & 25 \\ -8 & 26 \end{pmatrix}\)  and PQ = R, find the value of x.

The equation of a circle is \(x^{2} + y^{2} - 8x + 9y + 15 = 0\). Find its radius.

The angle subtended by an arc of a circle at the centre is \(\frac{\pi}{3} radians\). If the radius of the circle is 12cm, calculate the perimeter of the major arc.

A particle is acted upon by two forces 6N and 3N inclined at an angle of 120° to each other. Find the magnitude of the resultant force.

If \(\frac{^{n}C_{3}}{^{n}P_{2}} = 1\), find the value of n.

If \(2\sin^{2}\theta = 1 + \cos \theta, 0° \leq \theta \leq 90°\), find \(\theta\).

The fourth term of an exponential sequence is 192 and its ninth term is 6. Find the common ratio of the sequence.

Given that \(P = \begin{pmatrix} y - 2 & y - 1 \\ y - 4 & y + 2 \end{pmatrix}\) and |P| = -23, find the value of y.

If \(\sqrt{x} + \sqrt{x + 1} = \sqrt{2x + 1}\), find the possible values of x.

Calculate the mean deviation of 1, 2, 3, 4, 5, 5, 6, 7, 8, 9.

Forces 50N and 80N act on a body as shown in the diagram. Find, correct to the nearest whole number, the horizontal component of the resultant force.

A body is kept at rest by three forces \(F_{1} = (10N, 030°), F_{2} = (10N, 150°)\) and \(F_{3}\). Find \(F_{3}\).

Differentiate \(x^{2} + xy - 5 = 0\).

Two bodies of masses 3kg and 5kg moving with velocities 2 m/s and V m/s respectively in opposite directions collide. If they move together after collision with velocity 3.5 m/s in the direction of the 5kg mass, find the value of V.

A committee consists of 5 boys namely: Kofi, John, Ojo, Ozo and James and 3 girls namely: Rose, Ugo and Ama. In how many ways can a sub-committee consisting of 3 boys and 2 girls be chosen, if Ozo must be on the sub-committee?

Given that \(a^{\frac{5}{6}} \times a^{\frac{-1}{n}} = 1\), solve for n.

P and Q are the points (3, 1) and (7, 4) respectively. Find the unit vector along PQ.

Given that \(\frac{\mathrm d y}{\mathrm d x} = \sqrt{x}\), find y.

Find the equation of the straight line that passes through (2, -3) and perpendicular to the line 3x - 2y + 4 = 0.

If \(V = \begin{pmatrix} -2 \\ 4 \end{pmatrix}\) and \(U = \begin{pmatrix} -1 \\ 5 \end{pmatrix}\), find \(|U + V|\).

If \(f(x) = x^{2}\)  and \(g(x) = \sin x\), find g o f.

Express \(\log \frac{1}{8} + \log \frac{1}{2}\) in terms of \(\log 2\).