WAEC SSCE - Further Mathematics - 2014 (Objective)

Given that \(AB = \begin{pmatrix} 4 \\ 3 \end{pmatrix}\) and \(AC = \begin{pmatrix} 2 \\ -3 \end{pmatrix}\), find |BC|.

Given that \(x * y = \frac{x + y}{2}, x \circ y = \frac{x^{2}}{y}\) and \((3 * b) \circ 48 = \frac{1}{3}\), find b, where b > 0.

A particle accelerates at 12\(ms^{-2}\) and travels a distance of 250m in 6 seconds. Find the initial velocity of the particle.

Express (14N, 240°) as a column vector.

A function is defined by \(h : x \to 2 - \frac{1}{2x - 3}, x \neq \frac{3}{2}\). Find \(h^{-1}(\frac{1}{2})\).

A function is defined by \(h : x \to 2 - \frac{1}{2x - 3}, x \neq \frac{3}{2}\). Find \(h^-1\), the inverse of h.

Using the binomial expansion \((1+x)^{6} = 1 + 6x + 15x^{2} + 20x^{3} + 15x^{4} + 6x^{5} + x^{6}\), find, correct to 3 dp, the value of \((1.98)^{6}\).

If a fair coin is tossed four times, what is the probability of obtaining at least one head?

If \(2, (k+1), 8,...\) form an exponential sequence (GP), find the values of k.

Find the equation of a circle with centre (2, -3) and radius 2 units.

Find \(\lim\limits_{x \to 3} (\frac{x^{3} + x^{2} - 12x}{x^{2} - 9})\)

A ball is thrown vertically upwards with a velocity of 15\(ms^{-1}\). Calculate the maximum height reached. \([g = 10ms^{-2}]\)

Evaluate \(\frac{\tan 120° + \tan 30°}{\tan 120° - \tan 60°}\)

The first term of a linear sequence is 9 and the common difference is 7. If the nth term is 380, find the value of n.

Find the distance between the points (2, 5) and (5, 9).

If \(Px^{2} + (P+1)x + P = 0\) has equal roots, find the values of P.

Forces 90N and 120N act in the directions 120° and 240° respectively. Find the resultant of these forces.

Integrate \((x - \frac{1}{x})^{2}\) with respect to x.

Find the coefficient of \(x^3\) in the binomial expansion of \((3x + 4)^4\) in ascending powers of x.

Find the derivative of \(\sqrt[3]{(3x^{3} + 1}\) with respect to x.

Simplify \(\frac{1 + \sqrt{8}}{3 - \sqrt{2}}\).

Simplify: \((1 - \sin \theta)(1 + \sin \theta)\).

Find the variance of 1, 2, 0, -3, 5, -2, 4.

In which group is the upper quartile?

A box contains 5 red and k blue balls. A ball is selected at random from the box. If the probability of selecting a blue ball is \(\frac{2}{3}\), find the value of k.

If \(\frac{1}{5^{-y}} = 25(5^{4-2y})\), find the value of y.

Find the mean of the distribution.

What is the class mark of the median class?

If the points (-1, t -1), (t, t - 3) and (t - 6, 3) lie on the same straight line, find the values of t.

If \(T = \begin{pmatrix} -2 & -5 \\ 3 & 8 \end{pmatrix}\), find \(T^{-1}\), the inverse of T.

For what values of m is \(9y^{2} + my + 4\) a perfect square?

The radius of a sphere is increasing at a rate \(3cm s^{-1}\). Find the rate of increase in the surface area, when the radius is 2cm. 

In how many ways can 9 people be seated on a bench if only 3 places are available?

The deviations from the mean of a set of numbers are \((k+3)^{2}, (k+7), -2, \text{k and (} k+2)^{2}\), where k is a constant. Find the value of k.

Find the angle between \((5i + 3j)\) and \((3i - 5j)\).

Given that \(3x + 4y + 6 = 0\) and \(4x - by + 3 = 0\) are perpendicular, find the value of b.

If \((x + 2)\) and \((3x - 1)\) are factors of \(6x^{3} + x^{2} - 19x + 6\), find the third factor.

If \(8^{x} ÷ (\frac{1}{4})^{y} = 1\) and \(\log_{2}(x - 2y) = 1\), find the value of (x - y).

If \(\frac{x + P}{(x - 1)(x - 3)} = \frac{Q}{x - 1} + \frac{2}{x - 3}\), find the value of (P + Q).

If \(f(x) = 3x^{3} + 8x^{2} + 6x + k\) and \(f(2) = 1\), find the value of k.