WAEC SSCE - Further Mathematics - 2010 (Objective)

A stone is thrown vertically upwards and its height at any time t seconds is \(h = 45t - 9t^{2}\). Find the maximum height reached.

Calculate, correct to one decimal place, the length of the line joining points X(3, 5) and Y(5, 1).

Find the domain of \(f(x) = \frac{x}{3 - x}, x \in R\), the set of real numbers.

Two particles are fired together along a smooth horizontal surface with velocities 4 m/s and 5 m/s. If they move at 60° to each other, find the distance between them in 2 seconds.

The roots of a quadratic equation are \((3 - \sqrt{3})\) and \((3 + \sqrt{3})\). Find its equation.

If \(\overrightarrow{OA} = 3i + 4j\) and \(\overrightarrow{OB} = 5i - 6j \) where O is the origin and M is the midpoint of AB, find OM.

Find the direction cosines of the vector \(4i - 3j\).

The initial velocity of an object is \(u = \begin{pmatrix} -5 \\ 3 \end{pmatrix} ms^{-1}\). If the acceleration of the object is \(a = \begin{pmatrix} 3 \\ -4 \end{pmatrix} ms^{-2}\) and it moved for 3 seconds, find the final velocity.

Find the axis of symmetry of the curve \(y = x^{2} - 4x - 12\).

The distance s metres of a particle from a fixed point at time t seconds is given by \(s = 7 + pt^{3} + t^{2}\), where p is a constant. If the acceleration at t = 3 secs is \(8 ms^{-2}\), find the value of p.

Given that \(P = {x : \text{x is a factor of 6}}\) is the domain of \(g(x) = x^{2} + 3x - 5\), find the range of x.

If \(16^{3x} = \frac{1}{4}(32^{x - 1})\), find the value of x.

Yomi was asked to label four seats S, R, P, Q. What is the probability he labelled them in alphabetical order?

In a class of 50 pupils, 35 like Science and 30 like History. What is the probability of selecting a pupil who likes both Science and History?

Evaluate \(\int_{1}^{2} \frac{4}{x^{3}} \mathrm {d} x\)

A company took delivery of 12 vehicles made up of 7 buses and 5 saloon cars for two of its departments; Personnel and General Administration. If the Personnel department is to have at least 3 saloon cars, in how many ways can these vehicles be distributed equally between the departments?

If \(\sin x = -\sin 70°, 0° < x < 360°\), determine the two possible values of x.

Find the least value of n for which \(^{3n}C_{2} > 0, n \in R\).

Simplify \(\frac{\log_{5} 8}{\log_{5} \sqrt{8}}\).

The mean age of 15 pupils in a class is 14.2 years. One new pupil joined the class and the mean changed to 14.1 years. Calculate the age of the new pupil.

Two forces (2i - 5j)N and (-3i + 4j)N act on a body of mass 5kg. Find in \(ms^{-2}\), the magnitude of the acceleration of the body.

If \(y = 2(2x + \sqrt{x})^{2}\), find \(\frac{\mathrm d y}{\mathrm d x}\).

For what values of x is \(\frac{x^{2} - 9x + 18}{x^{2} + 2x - 35}\) undefined?

The third of geometric progression (G.P) is 10 and the sixth term is 80. Find the common ratio.

If \(\begin{vmatrix} 3 & x \\ 2 & x - 2 \end{vmatrix} = -2\), find the value of x.

If \(h(x) = x^{3} - \frac{1}{x^{3}}\), evaluate \(h(a) - h(\frac{1}{a})\).

Find the value of \(\cos(60° + 45°)\) leaving your answer in surd form.

If \(\frac{5}{\sqrt{2}} - \frac{\sqrt{8}}{8} = m\sqrt{2}\), where m is a constant. Find m.

Simplify \((1 + 2\sqrt{3})^{2} - (1 - 2\sqrt{3})^{2}\)

What is the angle between \(a = (3i - 4j)\) and \(b = (6i + 4j)\)?

If (x - 3) is a factor of \(2x^{2} - 2x + p\), find the value of constant p.

Given that \(\frac{\mathrm d y}{\mathrm d x} = 3x^{2} - 4\) and y = 6 when x = 3, find the equation for y.

Calculate, correct to one decimal place, the acute angle between the lines 3x - 4y + 5 = 0 and 2x + 3y - 1 = 0.

P, Q, R, S are points in a plane such that PQ = 8i - 5j, QR = 5i + 7j, RS = 7i + 3j  and PS = xi + yj. Find (x, y).

Find the maximum value of \(2 + \sin (\theta + 25)\).

The probabilities that a husband and wife will be alive in 15 years time are m and n respectively. Find the probability that only one of them will be alive at that time.

Find the equation of the tangent to the curve \(y = 4x^{2} - 12x + 7\) at point (2, -1).

Two forces \(F_{1} = (7i + 8j)N\) and \(F_{2} = (3i + 4j)N\) act on a particle. Find the magnitude and direction of \(F_{1} - F_{2}\).

The coefficient of the 7th term in the binomial expansion of \((2 - \frac{x}{3})^{10}\) in ascending powers of x is

A bicycle wheel of diameter 70 cm covered a distance of 350 cm in 2 seconds. How many radians per second did it turn?