WAEC SSCE - Further Mathematics - 2018 (Objective)

Out of 70 schools, 42 of them can be attended by boys and 35 can be attended by girls. If a pupil is selected at random from these schools, find the probability that he/ she is from a mixed school.

The marks scored by 4 students in Mathematics and Physics are ranked as shown in the table below

Calculate the Spearmann's rank correlation coefficient.

Given that \(a = i - 3j\) and \(b = -2i + 5j\) and \(c = 3i - j\), calculate \(|a - b + c|\).

The general term of an infinite sequence 9, 4, -1, -6,... is \(u_{r} = ar + b\). Find the values of a and b.

The midpoint of M(4, -1) and N(x, y) is P(3, -4). Find the coordinates of N.

Find the domain of \(g(x) = \frac{4x^{2} - 1}{\sqrt{9x^{2} + 1}}\)

If \(\overrightarrow{OX} = \begin{pmatrix} -7 \\ 6 \end{pmatrix}\) and \(\overrightarrow{OY} = \begin{pmatrix} 16 \\ -11 \end{pmatrix}\), find \(\overrightarrow{YX}\).

A particle starts from rest and moves through a distance \(S = 12t^{2} - 2t^{3}\) metres in time t seconds. Find its acceleration in 1 second.

Find the constant term in the binomial expansion \((2x^{2} + \frac{1}{x})^{9}\)

Find the stationary point of the curve \(y = 3x^{2} - 2x^{3}\).

A body of mass 28g, initially at rest is acted upon by a force, F Newtons. If it attains a velocity of \(5.4ms^{-1}\) in 18 seconds, find the value of F.

Two functions f and g are defined on the set of real numbers by \(f : x \to x^{2} + 1\) and \(g : x \to x - 2\). Find f o g.

\(P = {1, 3, 5, 7, 9}, Q = {2, 4, 6, 8, 10, 12}, R = {2, 3, 5, 7, 11}\) are subsets of \(U = {1, 2, 3, ... , 12}\). Which of the following statements is true?

How many numbers greater than 150 can be formed from the digits 1, 2, 3, 4, 5 without repetition?

Find the coefficient of \(x^{3}\) in the binomial expansion of \((x - \frac{3}{x^{2}})^{9}\).

A binary operation * is defined on the set of real numbers, by \(a * b = \frac{a}{b} + \frac{b}{a}\). If \((\sqrt{x} + 1) * (\sqrt{x} - 1) = 4\), find the value of x. 

Evaluate \(\int_{-1}^{1} (x + 1)^{2}\mathrm {d} x\). 

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

What is the probability of obtaining a head and a six when a fair coin and and a die are tossed together? 

If the determinant of the matrix \(\begin{pmatrix} 2 & x \\ 3 & 5 \end{pmatrix} = 13\), find the value of x.

Express \(\frac{13}{4}\pi\) radians in degrees.

Given that \(y = x(x + 1)^{2}\), calculate the maximum value of y.

Resolve \(\frac{3x - 1}{(x - 2)^{2}}, x \neq 2\) into partial fractions.

If \(\begin{vmatrix}  k & k \\ 4 & k \end{vmatrix} + \begin{vmatrix}  2 & 3 \\ -1 & k \end{vmatrix} = 6\), find the value of the constant k, where k > 0.

If \(\log_{3}a - 2 = 3\log_{3}b\), express a in terms of b.

Solve \(\log_{2}(12x - 10) = 1 + \log_{2}(4x + 3)\).

If \(\sin\theta = \frac{3}{5}, 0° < \theta < 90°\), evaluate \(\cos(180 - \theta)\).

Calculate the standard deviation of 30, 29, 25, 28, 32 and 24.

If \(4x^{2} + 5kx + 10\) is a perfect square, find the value of k.

Find the radius of the circle \(x^{2} + y^{2} - 8x - 2y + 1 = 0\).

If \(\alpha\) and \(\beta\) are the roots of the equation \(2x^{2} + 5x + n = 0\), such that \(\alpha\beta = 2\), find the value of n.

If the polynomial \(f(x) = 3x^{3} - 2x^{2} + 7x + 5\) is divided by (x - 1), find the remainder.

The first term of a Geometric Progression (GP) is \(\frac{3}{4}\), If the product of the second and third terms of the sequence is 972, find its common ratio.

In how many ways can the letters of the word 'ELECTIVE' be arranged?

Find the angle between forces of magnitude 7N and 4N if their resultant has a magnitude of 9N.

A car is moving at 120\(kmh^{-1}\). Find its speed in \(ms^{-1}\).

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

If \(\alpha\) and \(\beta\) are the roots of \(2x^{2} - 5x + 6 = 0\), find the equation whose roots are \((\alpha + 1)\) and \((\beta + 1)\).

Given that \(f(x) = 3x^{2} -  12x + 12\) and \(f(x) = 3\), find the values of x.

Find the equation to the circle \(x^{2} + y^{2} - 4x - 2y = 0\) at the point (1, 3).