WAEC - Further Mathematics (2019)

1
Solve: 8\(^{x - 2}\) = 4\(^{3x}\)

پاسخ دهید
(B)
-1
2
Solve; \(\frac{P}{2} + \frac{k}{3}\) = 5 and 2p = k = 6 simultaneously
پاسخ دهید
(C)
p = 6, k = 6
3
Evaluate tan 75\(^o\); leaving the answer in surd form (radicals)
پاسخ دهید
(D)
\(\sqrt{3 - 2}\)
4
Rationalize; \(\frac{1}{\sqrt{2 + 1}}\)
پاسخ دهید
(A)
\(\sqrt{2}\) - 1
5
If \(^nC_2\) = 15, find the value of n
پاسخ دهید
(C)
6
6
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
پاسخ دهید
(B)
II only
7
Given that g ; x \(\to\) 3x and f ; x \(\to\) cos x. Find the value of g\(^o\) f(20\(^o\))
پاسخ دهید
(D)
2.82
8
A linear transformation is defined by T: (x, y) \(\to\) (-x + y, -4y). Find the image, Q`, of Q(-3, 2) under T
پاسخ دهید
(A)
Q`(5, -8)
9
If g : r \(\to\) 5 - 2r, r is a real number, find the image of -3
پاسخ دهید
(B)
11
10
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"?
پاسخ دهید
(C)
(r ^~ q) \(\to\) ~p
11
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)
پاسخ دهید
(D)
0
12
Find the sum of the first 20 terms of the sequence -7-3, 1, ......
پاسخ دهید
(A)
620
13
Find the value of x for which 6\(\sqrt{4x^2 + 1}\) = 13x, where x > 0
پاسخ دهید
(A)
\(\frac{6}{5}\)
14
Calculate the distance between points (-2, -5) and (-1, 3)
پاسخ دهید
(C)
\(\sqrt{65}\) units
15
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.
پاسخ دهید
(C)
\(\frac{4}{5}\)
16
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
پاسخ دهید
(D)
\(\frac{32}{729}\)
17
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.
پاسخ دهید
(B)
32m
18
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
پاسخ دهید
(D)
\(\begin{pmatrix} \frac{5}{3} &, 0 \end {pmatrix}\)
19
If the mean of 2, 5, (x + 1), (x + 2), 7 and 9 is 6, find the median.
پاسخ دهید
(A)
6.5
20
Calculate the mean deviation of 5, 8, 2, 9 and 6
پاسخ دهید
(D)
2
21
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.
پاسخ دهید
(B)
16m
22
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.
پاسخ دهید
(C)
6 ms\(^{-2}\)
23
Find the constant term in the binomial expansion of (2x\(^2\) + \(\frac{1}{x^2}\))\(^4\)
پاسخ دهید
(B)
12
24

Which of these inequalities is represented by the shaded portion of the graph?
پاسخ دهید
(B)
2y - x - 3 < 0
25
A 35 N force acts on a body of mass 5 kg for 2 seconds. Calculate the change in momentum of the body.
پاسخ دهید
(A)
70 kg ms\(^{-1}\)
26
Solve, correct to three significant figures, (0.3)\(^x\) = (0,5)\(^8\)
پاسخ دهید
(A)
4.61
27
Given that P and Q are non-empty subsets of the universal set, U. Find P \(\cap\) (Q U Q`).
پاسخ دهید
(A)
p
28
Find the coefficient of the third term in the binomial expansion of [2x + \(\frac{3y}{4}\)]\(^3\) in descending powers of x.
پاسخ دهید
(B)
\(\frac{27}{8}\)y\(^2\)
29
Find the coordinates of the centre of the circle 3x\(^2\) + 3y\(^2\) - 6x + 9y - 5 = 0
پاسخ دهید
(C)
(1, - \(\frac{3}{2}\))
30
Evaluate \(\int^9_0 \sqrt{x} dx\)
پاسخ دهید
(C)
18
31
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.
پاسخ دهید
(B)
2
32
If y = (5 - x)\(^{-3}\), and \(\frac{dy}{dx}\)
پاسخ دهید
(C)
\(\frac{3}{(5 - x)^4}\)
33
Which of the following vectors is perpendicular to \(\begin{pmatrix} -1 & 3 \end{pmatrix}\)?
پاسخ دهید
(A)
\(\begin{pmatrix} -3 & 1 \end{pmatrix}\)
34
Find correct to the nearest degree,5 the angle between p = 12i - 5j and q = 4i +3j
پاسخ دهید
(A)
59\(^o\)
35
Find the area between line y = x + 1 and the x-axis from x = -2 to x = 0.
پاسخ دهید
(C)
2 square units