WAEC SSCE - Further Mathematics - 2019 (Objective)
Ibeere 2 Ìròyìn
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.
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Ibeere 3 Ìròyìn
A linear transformation is defined by T: (x, y) \(\to\) (-x + y, -4y). Find the image, Q`, of Q(-3, 2) under T
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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).
Ibeere 4 Ìròyìn
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"?
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Ibeere 5 Ìròyìn
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.
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Ibeere 7 Ìròyìn
Find the coefficient of the term in the binomial expansion of [2x + \(\frac{3y}{4}\)]\(^3\) in descending powers of x.
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Ibeere 8 Ìròyìn
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
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Ibeere 10 Ìròyìn
Find the coordinates of the centre of the circle 3x\(^2\) + 3y\(^2\) - 6x + 9y - 5 = 0
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Ibeere 11 Ìròyìn
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.
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Ibeere 12 Ìròyìn
Find the constant term in the binomial expansion of (2x\(^2\) + \(\frac{1}{x^2}\))\(^4\)
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Ibeere 13 Ìròyìn
Find the sum of the first 20 terms of the sequence -7-3, 1, ......
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Ibeere 14 Ìròyìn
If y = (5 - x)\(^{-3}\), and \(\frac{dy}{dx}\)
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Ibeere 15 Ìròyìn
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
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Ibeere 16 Ìròyìn
Calculate the distance between points (-2, -5) and (-1, 3)
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Ibeere 17 Ìròyìn
Evaluate: \(^{lim}_{x \to 1} \begin{pmatrix} \frac{1 - x}{x^2 - 3x + 2} \end {pmatrix}\)
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Ibeere 18 Ìròyìn
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)
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Ibeere 19 Ìròyìn
Find the value of x for which 6\(\sqrt{4x^2 + 1}\) = 13x, where x > 0
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Ibeere 20 Ìròyìn
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.
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Ibeere 21 Ìròyìn
Solve; \(\frac{P}{2} + \frac{k}{3}\) = 5 and 2p = k = 6 simultaneously
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Ibeere 22 Ìròyìn
Which of the following vectors is perpendicular to \(\begin{pmatrix} -1 & 3 \end{pmatrix}\)?
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Ibeere 24 Ìròyìn
Calculate the mean deviation of 5, 8, 2, 9 and 6
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Ibeere 25 Ìròyìn
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.
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Ibeere 26 Ìròyìn
Given that P and Q are non-empty subsets of the universal set, U. Find P \(\cap\) (Q U Q`).
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Ibeere 27 Ìròyìn
Solve, correct to three significant figures, (0.3)\(^x\) = (0,5)\(^8\)
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Ibeere 28 Ìròyìn
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
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Ibeere 29 Ìròyìn
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.
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Ibeere 30 Ìròyìn
If g : r \(\to\) 5 - 2r, r is a real number, find the image of -3
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Ibeere 31 Ìròyìn
Evaluate tan 75\(^o\); leaving the answer in surd form (radicals)
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Ibeere 32 Ìròyìn
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.
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Ibeere 34 Ìròyìn
Find correct to the nearest degree,5 the angle between p = 12i - 5j and q = 4i +3j
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Ibeere 35 Ìròyìn
If the mean of 2, 5, (x + 1), (x + 2), 7 and 9 is 6, find the median.
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Ibeere 36 Ìròyìn
Find the area between line y = x + 1 and the x-axis from x = -2 to x = 0.
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Ibeere 38 Ìròyìn
Given that g ; x \(\to\) 3x and f ; x \(\to\) cos x. Find the value of g\(^o\) f(20\(^o\))
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Ibeere 39 Ìròyìn
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?
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Ibeere 40 Ìròyìn
A 35 N force acts on a body of mass 5 kg for 2 seconds. Calculate the change in momentum of the body.
