WAEC - Further Mathematics (2012)

1
Which of the following sets is equivalent to \((P \cup Q) \cap (P \cup Q')\)?
Jibu
(A)
P
2
Simplify: \(\frac{\cos 2\theta - 1}{\sin 2\theta}\)
Jibu
(A)
\(-\tan \theta\)
3
Solve the inequality \(x^{2} - 2x \geq 3\)
Jibu
(B)
\(x \geq 3\) and \(x \leq -1\)
4
Given that \(\sqrt{6}, 3\sqrt{2}, 3\sqrt{6}, 9\sqrt{2},...\) are the first four terms of an exponential sequence (G.P), find in its simplest form the 8th term.
Jibu
(C)
\(81\sqrt{2}\)
5
Given that \(\sin x = \frac{-\sqrt{3}}{2}\) and \(\cos x > 0\), find x.
Jibu
(A)
300°
6
Evaluate \(\log_{10}(\frac{1}{3} + \frac{1}{4}) + 2\log_{10} 2 + \log_{10} (\frac{3}{7})\)
Jibu
(B)
0
7
QRS is a triangle such that \(\overrightarrow{QR} = (3i + 2j)\) and \(\overrightarrow{SR} = (-5i + 3j)\), find \(\overrightarrow{SQ}\).
Jibu
(A)
8i + j
8
If (x + 1) is a factor of the polynomial \(x^{3} + px^{2} + x + 6\). Find the value of p.
Jibu
(B)
-4
9
A polynomial is defined by \(f(x + 1) = x^{3} + px^{2} - 4x + 2\), find f(2).
Jibu
(C)
2
10
The equation of a circle is \(3x^{2} + 3y^{2} + 24x - 12y = 15\). Find its radius.
Jibu
(D)
5
11
If the midpoint of the line joining (1 - k, -4) and (2, k + 1) is (-k, k), find the value of k.
Jibu
(D)
-1
12
Evaluate \(\int_{-2}^{3} (3x^{2} - 2x - 12) \mathrm {d} x\)
Jibu
(A)
-30
13
If \(y = x^{3} - x^{2} - x + 6\), find the values of x at the turning point.
Jibu
(C)
\(1, -\frac{1}{3}\)
14
Given that \(P = \begin{pmatrix} 2 & 1 \\ 5 & -3 \end{pmatrix}\) and \(Q = \begin{pmatrix} 4 & -8 \\ 1 & -2 \end{pmatrix}\), Find (2P - Q).
Jibu
(D)
\(\begin{pmatrix} 0 & 10 \\ 9 & -4 \end{pmatrix}\)
15
A binary operation, \(\Delta\), is defined on the set of real numbers by \(a \Delta b = a + b + 4\). Find the identity element.
Jibu
(D)
-4
16
The marks obtained by 10 students in a test are as follows: 3, 7, 6, 2, 8, 5, 9, 1, 4 and 10. Find the mean mark.
Jibu
(B)
5.50
17
The marks obtained by 10 students in a test are as follows: 3, 7, 6, 2, 8, 5, 9, 1, 4 and 10. Find the variance.
Jibu
(A)
8.25
18
If r denotes the correlation coefficient between two variables, which of the following is always true?
Jibu
(D)
\(-1 \leq r \leq 1\)
19
A stone is dropped from a height of 45m. Find the time it takes to hit the ground. \([g = 10 ms^{-2}]\)
Jibu
(A)
3.0 seconds
20
Differentiate \(\frac{x}{x + 1}\) with respect to x.
Jibu
(B)
\(\frac{1}{(x + 1)^{2}}\)
21
Two forces 10N and 6N act in the directions 060° and 330° respectively. Find the x- component of their resultant.
Jibu
(A)
\(5\sqrt{3} - 3\)
22
Find the unit vector in the direction of the vector \(-12i + 5j\).
Jibu
(C)
\(\frac{-12i}{13} + \frac{5j}{13}\)
23
In computing the mean of 8 numbers, a boy mistakenly used 17 instead of 25 as one of the numbers and obtained 20 as the mean. Find the correct mean
Jibu
(B)
21
24
Given that \(^{n}P_{r} = 90\) and \(^{n}C_{r} = 15\), find the value of r.
Jibu
(B)
3
25
Which of the following is nor a measure of central tendency?
Jibu
(B)
Variance
26
A fair die is tossed twice. Find the probability of obtaining a 3 and a 5.
Jibu
(D)
\(\frac{1}{36}\)
27
If P(x - 3) + Q(x + 1) = 2x + 3, find the value of (P + Q).
Jibu
(C)
2
28
Find the values of x at the point of intersection of the curve \(y = x^{2} + 2x - 3\) and the lines \(y + x = 1\).
Jibu
(D)
(1, -4)
29
Find the constant term in the binomial expansion of \((2x - \frac{3}{x})^{8}\).
Jibu
(A)
90720
30
A straight line makes intercepts of -3 and 2 on the x- and y- axes respectively. Find the equation of the line.
Jibu
(D)
-2x + 3y - 6 =0
31
Find the number of different arrangements of the word IKOTITINA.
Jibu
(A)
30240
32
Find the acute angle between the lines 2x + y = 4 and -3x + y + 7 = 0.
Jibu
(C)
45°
33
A box contains 4 red and 3 blue identical balls. If two are picked at random, one after the other without replacement, find the probability that one is red and the other is blue.
Jibu
(A)
\(\frac{4}{7}\)
34
The distance s in metres covered by a particle in t seconds is \(s = \frac{3}{2}t^{2} - 3t\). Find its acceleration.
Jibu
(C)
\(3 ms^{-2}\)
35
The angle of a sector of a circle is 0.9 radians. If the radius of the circle is 4cm, find the length of the arc of the sector.
Jibu
(A)
3.6 cm