WAEC SSCE - Further Mathematics - 2018 (Objective)

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.

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

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

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

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

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

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

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.

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

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.

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

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

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

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

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

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

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.

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

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

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

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

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.

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.

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

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.

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

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

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

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.

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

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

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

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

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

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

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

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

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

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