Question 1
Simplify \(\frac{\sqrt{3}}{\sqrt{3} -1} + \frac{\sqrt{3}}{\sqrt{3} + 1}\)
Objective
WAEC Further Mathematics 2018 Past Questions
Practice each question, then open it to see the full details.
Question 1
If \(\begin{vmatrix} x - 3 & -4 & 3 \\ 5 & 2 & 2 \\ 2 & -4 & 6 - x \end{vmatrix} = -24 \), find the values of x.
Theory
Question 2
Find the domain of \(g(x) = \frac{4x^{2} - 1}{\sqrt{9x^{2} + 1}}\)
Objective
Question 2
Given that \(\log_{3} x - 3\log_{x} 3 + 2 = 0\), find the values of x.
Theory
Question 3
Given that \(f(x) = 3x^{2} - 12x + 12\) and \(f(x) = 3\), find the values of x.
Objective
Question 3
(a) Using the substitution \(u = x - 2\), write \(\frac{x^{3} + 5}{(x - 2)^{4}}\) as an expression in terms of u.
(b) Using the answer in (a), express \(\frac{x^{3} + 5}{(x - 2)^{4}}\) in partial fractions.
Theory
Question 4
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.
Objective
Question 4
The sum of the first twelve terms of an Arithmetic Progression is 168. If the third term is 7, find the values of the common difference and the first term.
Theory
Question 5
If \(4x^{2} + 5kx + 10\) is a perfect square, find the value of k.
Objective
Question 5
Two panel of judges, X and Y, rank 8 brands of cooking oil as follows :
| Cooking oil type | A | B | C | D | E | F | G | H |
| X | 8 | 5 | 1 | 7 | 2 | 6 | 3 | 4 |
| Y | 6 | 3 | 4 | 8 | 5 | 7 | 1 | 2 |
Calculate the Spearmann's rank correlation coefficient.
Theory
Question 6
If the polynomial \(f(x) = 3x^{3} - 2x^{2} + 7x + 5\) is divided by (x - 1), find the remainder.
Objective
Question 6
(a) The probability that Kunle solves a particular question is \(\frac{1}{3}\) while that of Tayo is \(\frac{1}{5}\). If both of them attempt the question, find the probability that only one of them will solve the question.
(b) A committee of 8 is to be chosen from 10 persons. In how many ways can this be done if there is no restriction?
Theory
Question 7
\(P = {1, 3, 5, 7, 9}, Q = {2, 4, 6, 8, 10, 12}, R = {2, 3, 5, 7, 11}\) are subsets of \(U = {1, 2, 3, ... , 12}\). Which of the following statements is true?
Objective
Question 7
Given that \(m = 3i - 2j ; n = 2i - 3j\) and \(p = -i + 6j\), find \(4m + 2n - 3p\).
Theory
Question 8
If \(\log_{3}a - 2 = 3\log_{3}b\), express a in terms of b.
Objective
Question 8
A body of mass 20kg moving with a velocity of 80ms\(^{-1}\) collides with another body of mass 30kg moving with a velocity of 50ms\(^{-1}\). If they both moved in the same direction after collision, find their common velocity if they moved in the :
(a) same direction before collision ; (b) opposite direction before collision.
Theory
Question 9
If \(\alpha\) and \(\beta\) are the roots of \(2x^{2} - 5x + 6 = 0\), find the equation whose roots are \((\alpha + 1)\) and \((\beta + 1)\).
Objective
Question 9
A circle is drawn through the points (3, 2), (-1, -2) and (5, -4). Find the :
(a) coordinates of the centre of the circle ;
(b) radius of the circle ;
(c) equation of the circle.
Theory
Question 10
Resolve \(\frac{3x - 1}{(x - 2)^{2}}, x \neq 2\) into partial fractions.
Objective
Question 10
(a) Solve : \(2^{3y + 2} - 7(2^{2y + 2}) - 31(2^{y}) - 8 = 0, y \in R\).
(b) Find \(\int (\sqrt{x^{2} + 1}) xdx\).
Theory
Question 11
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.
Objective
Question 11
(a)(i) Write down the binomial expansion of \((2 - \frac{1}{2}x)^{5}\) in ascending powers of x.
(ii) Using the expansion in (a)(i), find, correct to two decimal places, the value of \((1.99)^{5}\).
(b) The polynomial \(x^{3} + qx^{2} + rx + 9\), where q and r are constants, has (x + 1) as a factor and has a remainder -17 when divided by (x + 2). Find the values of q and r.
Theory
Question 12
Solve \(\log_{2}(12x - 10) = 1 + \log_{2}(4x + 3)\).
Objective
Question 12
Ten coins were tossed together a number of times. The distribution of the number of heads obtained is given in the following table :
| No of heads | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Frequency | 2 | 7 | 23 | 36 | 11 | 61 | 100 | 12 | 8 | 5 | 3 |
Calculate, correct to three decimal places, the :
(a) mean number of heads ;
(b) probability of getting an even head ;
(c) probability of getting an odd number.
Theory
Question 13
Find the coefficient of \(x^{3}\) in the binomial expansion of \((x - \frac{3}{x^{2}})^{9}\).
Objective
Question 13
The probabilities that Ali, Baba and Katty will gain admission to college are \(\frac{2}{3}, \frac{3}{4}\) and \(\frac{4}{5}\) respectively. Find the probability that:
(a) only Katty and Baba will gain admission ;
(b) none of them will gain admission ;
(c) at most two of them will gain admission.
Theory
Question 14
The general term of an infinite sequence 9, 4, -1, -6,... is \(u_{r} = ar + b\). Find the values of a and b.
Objective
Question 14
The position vectors of points A, B and C with respect to the origin are (8i - 2j), (2i + 6j) and (-10i + 4j) respectively. If ABCN is a parallelogram, find :
(a) the position vector of N;
(b) AN and AB ;
(c) correct to two decimal place, the acute angle between AN and AB.
Theory
Question 15
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.
Objective
Question 15
A uniform beam, XY, 4m long and weighing 350N rests on two pivots P and Q. It is kept in equilibrium by weights of 80N attached at X and 1000N attached at a point between P and Q such that it is 0.6m from Q. If XP = 0.8m and PQ = 2.2m.
(a) calculate the reactions at P and Q ;
(b) if the 1000N weight is replaced with a 1200N weight, at what point from Q should it be placed in order to maintain the equilibrium.
Theory
Question 16
How many numbers greater than 150 can be formed from the digits 1, 2, 3, 4, 5 without repetition?
Objective
Question 17
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.
Objective
Question 18
If \(\sin\theta = \frac{3}{5}, 0° < \theta < 90°\), evaluate \(\cos(180 - \theta)\).
Objective
Question 19
Find the radius of the circle \(x^{2} + y^{2} - 8x - 2y + 1 = 0\).
Objective
Question 20
In how many ways can the letters of the word 'ELECTIVE' be arranged?
Objective
Question 21
If the determinant of the matrix \(\begin{pmatrix} 2 & x \\ 3 & 5 \end{pmatrix} = 13\), find the value of x.
Objective
Question 22
Express \(\frac{13}{4}\pi\) radians in degrees.
Objective
Question 23
Find the equation to the circle \(x^{2} + y^{2} - 4x - 2y = 0\) at the point (1, 3).
Objective
Question 24
Given that \(y = x(x + 1)^{2}\), calculate the maximum value of y.
Objective
Question 25
The midpoint of M(4, -1) and N(x, y) is P(3, -4). Find the coordinates of N.
Objective
Question 26
Find the stationary point of the curve \(y = 3x^{2} - 2x^{3}\).
Objective
Question 27
Evaluate \(\int_{\frac{1}{2}}^{1} \frac{x^{3} - 4}{x^{3}} \mathrm {d} x\).
Objective
Question 28
Calculate the standard deviation of 30, 29, 25, 28, 32 and 24.
Objective
Question 29
Evaluate \(\int_{-1}^{1} (x + 1)^{2}\mathrm {d} x\).
Objective
Question 30
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.
Objective
Question 31
The marks scored by 4 students in Mathematics and Physics are ranked as shown in the table below
| Mathematics | 3 | 4 | 2 | 1 |
| Physics | 4 | 3 | 1 | 2 |
Calculate the Spearmann's rank correlation coefficient.
Objective
Question 32
Given that \(a = i - 3j\) and \(b = -2i + 5j\) and \(c = 3i - j\), calculate \(|a - b + c|\).
Objective
Question 33
What is the probability of obtaining a head and a six when a fair coin and and a die are tossed together?
Objective
Question 34
If \(\overrightarrow{OX} = \begin{pmatrix} -7 \\ 6 \end{pmatrix}\) and \(\overrightarrow{OY} = \begin{pmatrix} 16 \\ -11 \end{pmatrix}\), find \(\overrightarrow{YX}\).
Objective
Question 35
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.
Objective