WAEC SSCE - Further Mathematics - 2014 (Objective)

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).

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

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

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

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

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

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

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.

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

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

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

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

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

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

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

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

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

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.

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

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.

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

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

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

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

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

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 which group is the upper quartile?

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

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 \((1.98)^{6}\).

What is the class mark of the median class?

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

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

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.

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

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

Find the mean of the distribution.

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

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.