WAEC SSCE - Further Mathematics - 2019 (Objective)
Vraag 1 Verslag
A linear transformation is defined by T: (x, y) \(\to\) (-x + y, -4y). Find the image, Q`, of Q(-3, 2) under T
Antwoorddetails
To find the image, Q`, of point Q(-3, 2) under the linear transformation T, we need to apply the transformation matrix to the coordinates of Q.
T: (x, y) → (-x + y, -4y)
So, we have:
T(Q) = (-(-3) + 2, -4(2)) = (5, -8)
Therefore, the image, Q`, of Q(-3, 2) under T is (5, -8).
Explanation: A linear transformation is a function that maps vectors to other vectors while preserving some properties such as linearity and proportionality. In this case, the linear transformation T takes a vector (x, y) and maps it to a new vector (-x + y, -4y). To find the image of a point under T, we simply plug in the coordinates of the point into the transformation matrix and apply the transformation. In this case, we plugged in the coordinates of Q(-3, 2) and found that the image is (5, -8).
Vraag 2 Verslag
If the mean of 2, 5, (x + 1), (x + 2), 7 and 9 is 6, find the median.
Antwoorddetails
Vraag 3 Verslag
Find the constant term in the binomial expansion of (2x\(^2\) + \(\frac{1}{x^2}\))\(^4\)
Antwoorddetails
Vraag 5 Verslag
If g : r \(\to\) 5 - 2r, r is a real number, find the image of -3
Antwoorddetails
Vraag 6 Verslag
Evaluate: \(^{lim}_{x \to 1} \begin{pmatrix} \frac{1 - x}{x^2 - 3x + 2} \end {pmatrix}\)
Antwoorddetails
Vraag 8 Verslag
A 35 N force acts on a body of mass 5 kg for 2 seconds. Calculate the change in momentum of the body.
Antwoorddetails
Vraag 11 Verslag
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"?
Antwoorddetails
Vraag 12 Verslag
Which of the following vectors is perpendicular to \(\begin{pmatrix} -1 & 3 \end{pmatrix}\)?
Antwoorddetails
Vraag 13 Verslag
Find correct to the nearest degree,5 the angle between p = 12i - 5j and q = 4i +3j
Antwoorddetails
Vraag 14 Verslag
Find the coefficient of the term in the binomial expansion of [2x + \(\frac{3y}{4}\)]\(^3\) in descending powers of x.
Antwoorddetails
Vraag 16 Verslag
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
Antwoorddetails
Vraag 17 Verslag
Solve, correct to three significant figures, (0.3)\(^x\) = (0,5)\(^8\)
Antwoorddetails
Vraag 18 Verslag
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)
Antwoorddetails
Vraag 19 Verslag
Given that P and Q are non-empty subsets of the universal set, U. Find P \(\cap\) (Q U Q`).
Antwoorddetails
Vraag 20 Verslag
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.
Antwoorddetails
Vraag 21 Verslag
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.
Antwoorddetails
Vraag 22 Verslag
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
Antwoorddetails
Vraag 23 Verslag
Find the coordinates of the centre of the circle 3x\(^2\) + 3y\(^2\) - 6x + 9y - 5 = 0
Antwoorddetails
Vraag 24 Verslag
Calculate the mean deviation of 5, 8, 2, 9 and 6
Antwoorddetails
Vraag 25 Verslag
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.
Antwoorddetails
Vraag 26 Verslag
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.
Antwoorddetails
Vraag 27 Verslag
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?
Antwoorddetails
Vraag 28 Verslag
Given that g ; x \(\to\) 3x and f ; x \(\to\) cos x. Find the value of g\(^o\) f(20\(^o\))
Antwoorddetails
Vraag 29 Verslag
Find the area between line y = x + 1 and the x-axis from x = -2 to x = 0.
Antwoorddetails
Vraag 30 Verslag
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.
Antwoorddetails
Vraag 31 Verslag
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.
Antwoorddetails
Vraag 33 Verslag
If y = (5 - x)\(^{-3}\), and \(\frac{dy}{dx}\)
Antwoorddetails
Vraag 34 Verslag
Calculate the distance between points (-2, -5) and (-1, 3)
Antwoorddetails
Vraag 35 Verslag
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.
Antwoorddetails
Vraag 36 Verslag
Which of these inequalities is represented by the shaded portion of the graph?
Antwoorddetails
Vraag 37 Verslag
Find the value of x for which 6\(\sqrt{4x^2 + 1}\) = 13x, where x > 0
Antwoorddetails
Vraag 38 Verslag
Solve; \(\frac{P}{2} + \frac{k}{3}\) = 5 and 2p = k = 6 simultaneously
Antwoorddetails
Vraag 39 Verslag
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
Antwoorddetails
Vraag 40 Verslag
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.
