WAEC SSCE - Further Mathematics - 2019 (Objective)

An operation (*) is defined on the set T = {-1, 0, ...., 5} by x * y = x + y - xy. Which of the following operation(s) will give an image which is an element of T?

I. 2(*)5 II. 3(*)5 III. 3(*)4 

A particle starts from rest and moves in a straight line such that its velocity, V ms\(^{-1}\), at time t second is given by V = 3t\(^2\) - 6t. Calculate the acceleration in the 3rd second. 

If \(^nC_2\) = 15, find the value of n

Given that P and Q are non-empty subsets of the universal set, U. Find P \(\cap\) (Q U Q`).

The second and fourth terms of an exponential sequence (G.P) are \(\frac{2}{9}\) and \(\frac{8}{81}\) respectively. Find the sixth term of the sequence 

Given that \(\frac{1}{x^2 - 4} = \frac{p}{(x + 2)} + \frac{Q}{(x - 2})\)

x \(\neq \pm 2\)

Find the value of (P + Q)

Point X and Y are on the same horizontal base as the foot of a building such that X is 96m due east of the building and Y is due west. If the angle of elevation of the top of that building from X is 30\(^o\) and that of Y is 50\(^o\), calculate the distance of Y from the base of the building.

How many numbers greater than 200 can be formed from the digits 1,2,3,4, 5 if no digit is to be repeated in any particular number? 

A particle starts from rest and moves in a straight line such that its velocity, V ms\(^{-1}\), at time t second is given by V = 3t\(^2\) - 6t. Calculate the acceleration in the 3rd second. 

Which of the following vectors is perpendicular to \(\begin{pmatrix} -1 & 3 \end{pmatrix}\)?

The probabilities that John and Jane will pass an examination are 0.9 and 0.7 respectively. Find the probability that at least one of them will pass the examination.

Find the coefficient of the term in the binomial expansion of [2x + \(\frac{3y}{4}\)]\(^3\) in descending powers of x.

Find the sum of the first 20 terms of the sequence -7-3, 1, ......

A linear transformation is defined by T: (x, y) \(\to\) (-x + y, -4y). Find the image, Q`, of Q(-3, 2) under T

Solve, correct to three significant figures, (0.3)\(^x\) =  (0,5)\(^8\)

A uniform beam, PQ. is 100 m long and weighs 35 N. It is placed on a support at a point 40 cm from P. If weights of 54 N and FN are attached at P and Q respectively in order to keep it in a horizontal position, calculate, correct to the nearest whole number, the value of F.

Given that g ; x \(\to\) 3x and f ; x \(\to\) cos x. Find the value of g\(^o\) f(20\(^o\)) 

Find the constant term in the binomial expansion of (2x\(^2\) +  \(\frac{1}{x^2}\))\(^4\)

Which of these inequalities is represented by the shaded portion of the graph? 

Evaluate \(\int^0_0 \sqrt{x} dx\)

If P = \(\begin {pmatrix} 2 & 3\\  -4 & 1 \end {pmatrix}\), Q = \(\begin{pmatrix} 6 \\ 8 \end {pmatrix}\) and PQ = k \(\begin {pmatrix} 45\\ -20 \end {pmatrix}\). Find the value of k.

A 35 N force acts on a body of mass 5 kg for 2 seconds. Calculate the change in momentum of the body.

The function f : x \(\to\) x\(^2\) + px + q has turning point when x = -3 and remainder of -6 when divided by (x + 2). Find the value of q.

Calculate the mean deviation of 5, 8, 2, 9 and 6

If y = (5 - x)\(^{-3}\), and \(\frac{dy}{dx}\)

Consider the following statements:

p: Birds fly

q: The sky is blue

r: The grass is green
What is the symbolic representation of "If the grass is green and the sky is not blue, then the birds do not fly"?

If g : r \(\to\) 5 - 2r, r is a real number, find the image of -3

Find the coordinates of the point in the curve y = 3x\(^2\) - 2x - 5 where the tangent is parallel to the line y = - 5 = 8x

Solve; \(\frac{P}{2} + \frac{k}{3}\) = 5 and 2p = k = 6 simultaneously

Evaluate: \(^{lim}_{x \to 1} \begin{pmatrix} \frac{1 - x}{x^2 - 3x + 2} \end {pmatrix}\)

Solve: 8\(^{x - 2}\) = 4\(^{3x}\)

Find the area between line y = x + 1 and the x-axis from x = -2 to x = 0. 

Find correct to the nearest degree,5 the angle between p = 12i - 5j and q = 4i +3j

Given that X and Y are independent events such that P(X) = 0.5, P(Y) = m and P(X U Y) = 0.75, find the value of m. 

Calculate the distance between points (-2, -5) and (-1, 3) 

Find the value of x for which 6\(\sqrt{4x^2 + 1}\) = 13x, where x > 0

Find the coordinates of the centre of the circle 3x\(^2\) + 3y\(^2\) - 6x + 9y - 5 = 0

Rationalize; \(\frac{1}{\sqrt{2 + 1}}\)

If the mean of 2, 5, (x + 1), (x + 2), 7 and 9 is 6, find the median.

Evaluate tan 75\(^o\); leaving the answer in surd form (radicals)