WAEC SSCE - Further Mathematics - 2014 (Objective)

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

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

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

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.

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

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

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

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

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

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.

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 \(h^-1\), 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 \((1.98)^{6}\).

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

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

What is the class mark of the median class?

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

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.

In which group is the upper quartile?

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.

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. 

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

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

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.

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

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

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

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

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

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

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.

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

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

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

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

Find the mean of the distribution.