WAEC - Further Mathematics (2019)

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

Trả lời
(B)
-1
2
Solve; \(\frac{P}{2} + \frac{k}{3}\) = 5 and 2p = k = 6 simultaneously
Trả lời
(C)
p = 6, k = 6
3
Evaluate tan 75\(^o\); leaving the answer in surd form (radicals)
Trả lời
(D)
\(\sqrt{3 - 2}\)
4
Rationalize; \(\frac{1}{\sqrt{2 + 1}}\)
Trả lời
(A)
\(\sqrt{2}\) - 1
5
If \(^nC_2\) = 15, find the value of n
Trả lời
(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
Trả lời
(B)
II only
7
Given that g ; x \(\to\) 3x and f ; x \(\to\) cos x. Find the value of g\(^o\) f(20\(^o\))
Trả lời
(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
Trả lời
(A)
Q`(5, -8)
9
If g : r \(\to\) 5 - 2r, r is a real number, find the image of -3
Trả lời
(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"?
Trả lời
(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)
Trả lời
(D)
0
12
Find the sum of the first 20 terms of the sequence -7-3, 1, ......
Trả lời
(A)
620
13
Find the value of x for which 6\(\sqrt{4x^2 + 1}\) = 13x, where x > 0
Trả lời
(A)
\(\frac{6}{5}\)
14
Calculate the distance between points (-2, -5) and (-1, 3)
Trả lời
(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.
Trả lời
(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
Trả lời
(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.
Trả lời
(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
Trả lời
(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.
Trả lời
(A)
6.5
20
Calculate the mean deviation of 5, 8, 2, 9 and 6
Trả lời
(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.
Trả lời
(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.
Trả lời
(C)
6 ms\(^{-2}\)
23
Find the constant term in the binomial expansion of (2x\(^2\) + \(\frac{1}{x^2}\))\(^4\)
Trả lời
(B)
12
24

Which of these inequalities is represented by the shaded portion of the graph?
Trả lời
(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.
Trả lời
(A)
70 kg ms\(^{-1}\)
26
Solve, correct to three significant figures, (0.3)\(^x\) = (0,5)\(^8\)
Trả lời
(A)
4.61
27
Given that P and Q are non-empty subsets of the universal set, U. Find P \(\cap\) (Q U Q`).
Trả lời
(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.
Trả lời
(B)
\(\frac{27}{8}\)y\(^2\)
29
Find the coordinates of the centre of the circle 3x\(^2\) + 3y\(^2\) - 6x + 9y - 5 = 0
Trả lời
(C)
(1, - \(\frac{3}{2}\))
30
Evaluate \(\int^9_0 \sqrt{x} dx\)
Trả lời
(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.
Trả lời
(B)
2
32
If y = (5 - x)\(^{-3}\), and \(\frac{dy}{dx}\)
Trả lời
(C)
\(\frac{3}{(5 - x)^4}\)
33
Which of the following vectors is perpendicular to \(\begin{pmatrix} -1 & 3 \end{pmatrix}\)?
Trả lời
(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
Trả lời
(A)
59\(^o\)
35
Find the area between line y = x + 1 and the x-axis from x = -2 to x = 0.
Trả lời
(C)
2 square units