WAEC Further Mathematics 2019 Past Questions

Given that (\(_r^n\)) = \(^nC_r\), simplify (\(^{2x + 1}_{3}\)) - (\(^{2x - 1}_3\)) - 2(\(^x_2\))

Differentiate from first principles, with respect to x, (3x\(^2\) + 2x - 1) 

Find the equation of the circle centre (2. 3) which passes through the y - intercept of the line 3x  - 2y + 6 = 0

If \(\alpha\) and \(\beta\) are the roots of the equation 3x\(^2\) + 4x - 5 = 0, find the value of )\(\alpha - \beta\)), leaving the answer in surd form. 

Three soldies, X, Y and Z have probabilities \(\frac{1}{3}, \frac{1}{5}\) and \(\frac{1}{4}\) respectively of hitting a target. If each of them fires once, find, correct to two decimal places, the probability that only one of them hits the target 

The distribution of the masses of a group of persons is shown in the following table

Draw a histogram for the distribution

Find the angle between \(\over {OP}\) = (\(^{-3}_{-4}\)) and \(\over{OQ}\) = (\(^8_{-15}\))

In the diagram, a mass of 12kg hanging from a light inextensible string is pulled aside by a horizontal force, R, such that the string is inclined at 45\(^o\) to the vertical. If the system is in equilibrium, calculate the;

(a) tension in the string;

(b) value of R 

(a).  \(\frac{T}{\sin 90^o}\) = \(\frac{120}{sin 135^o}\) and found T = 169.71N

(b) \(\frac{R}{\sin 135^o}\) = \(\frac{120}{\sin 135^o}\)

R = 120N

(a) If sin p = \(\frac{1}{2}\) and cos q = \(\frac{1}{3}\), evaluate sin(p - q), where 0\(^o\) \(\geq\) p \(\geq\) 90\(^o\) and 90\(^o\) \(\geq\) q \(\geq\) 180\(^o\)

b) Using trapezum rule with seven ordinates, evaluate \(\int^4_1\frac{2}{\sqrt{x + 3}}\)dx

Using determinants, solve the following equations simultaneously.

5x — 6y + 4z = 15

7x + 4y — 3z = 19

2x + y + 6z = 46 
 

The table shows the distribution of masks obtained by students in an examination. 

Using an assumed mean of 67, calculate, correct to one decimal place. the

a) Mean

b) Standard deviation of the distribution 
 

(a) In a bakery, 30% of loaves of bread produced are of bad quality. If twelve loaves are selected at random from the bakery, calculate, correct to four decimal places. the probabshty of getting 

(i) exactly 6 bad ones:

(ii) at least 4 bad ones;

(ii) no bad one.

(b) A group consists of 8 boys and 5 girls. A committee of 7 members is chosen from the group. Find the probability that the committee is made up of 4 boys and 3 girls. 
 

(a) P(-1, 4), Q(2, 3), R(x, y) and S(-2, 3) are the verticles of a parallelogram. Find the value of x and y. 

(b) A particle starts from rest and moves in a straight line. It attains a velocity of 20ms\(^{-1}\) after travelling a distance of 8 metres. Calculate;

(ii) Iis acceleration

(ii) the time taken to travel 40 metres

Forces(5N, 030\(^o\)), (PN, 060\(^o\)), (QN, 150\(^o\)), (3N, 180\(^o\)) and (5N, 270\(^o\)) act on a body . If the system is in quilibrium, find, correct to one decimal place, the values of P and Q

(a) Find the coordinates of the point which divides the line joining (7, -5) and (-2, 7) externally in the ration 3 : 2.

(b) Without using calculators or mathematical tables, evaluate \(\frac{2}{1 + \sqrt{2}}\) - \(\frac{2}{2 + \sqrt{2}}\), leaving the answer in the form p + q\(\sqrt{n}\), where p, q and n are integers. 

How many terms of the series -3 -1 + 1 +..... add up to 165?

If sin x \(\frac{P - Q}{P + Q}\), where 0\(^o\) \(\leq\) x \(\leq\) 90\(^o\), find 1 - tan\(^2\)x

Three forces N, 14N and 16N acting on a particle keep it in equilibrium. Find the angle between the forces 10N and 16N.

A uniform beam, WX, of length 90 cm and weight 50N is suspended on a pivot, 35 cm from W. It is kept in equilibrum by a means of forces T and 20N applied at Y and Z respectively. |WY| = 10cm and |XZ| = 10cm. Find the value of T 

The table shows the age distribution in years of a group of people 

Using an assume mean of 13 years, find the mean age of the people. 

Two fair dice are thrown together two times. Find the probability of obtaining a sum of seven in the first throw and a sum of four in the second throw. 

The curve y = 7 - \(\frac{6}{x}\) and the line y + 2x - 3 = 0 intersect at two point. Finf the;

(a) coordinates of the two points

(b) equation of the perpendicular bisector of the line joining the two points 

(a) Find the range of value of p for which 4x\(^2\) - px + 1 = 0 

(b)(i) Expand (1 + 3x)\(^6\) in ascending powers of x

(ii) Using the expression in 10

(ii) find, correct to four significant figures, the value of (1.03)\(^6\)

In an examination, 60% of the candidates passed. If 10 candidates are selected at random, find the probability that;

(1) at least two of the, failed

(2) exactly half of them passed 

(3) at most two of them failed 

In a research to determine the relationship between performance of students in an entrance examination and subsequent school performance, the results of ten randomly selected students wre obtained as follows;

1, Calculate the spearman's rank correlation coefficient

2. What would be the researcher's from the result in a?

A body, moving at 20ms\(^{-1}\) accelerates uniformly at 2\(\frac{1}{2}ms^{-2}\) for 4 seconds. It continues the journey at this speed for 8 seconds, before coming to rest seconds at tseconds after with uniform retardation. If the ratio of the acceleration to retardation is 3 : 4

(a( sketch the velocity - times graph of the journey

(b) find t

(c) find the total distance of the journey

(a) Given that m = i - i, n = 2i + 3j and 2m + n - r = 0, find |r|

(b) The distance, S metres of a moving particle at any time tseconds is given by

S = 3t - \(\frac{t^3}{3}\) + 9

Find the;

(i) time

(ii) distance travelled

When the particle is momentarily at rest