Which of the following is a factor of the polynomial \(6x^{4} + 2x^{3} + 15x + 5\)?
Odpověď
(A)
3x + 1
10
Given that \(f : x \to \frac{2x - 1}{x + 2}, x \neq -2\), find \(f^{-1}\), the inverse of f.
Odpověď
(A)
\(f^{-1} : x \to \frac{1+2x}{2-x}, x \neq 2\)
11
If \(36, p, \frac{9}{4}, q\) are consecutive terms of an exponential sequence (G.P.). Find the sum of p and q.
Odpověď
(D)
\(9\frac{9}{16}\)
12
Find the minimum value of \(y = x^{2} + 6x - 12\).
Odpověď
(A)
-21
13
A line passes through the origin and the point \((1\frac{1}{4}, 2\frac{1}{2})\), what is the gradient of the line?
Odpověď
(B)
2
14
A line passes through the origin and the point \((1\frac{1}{4}, 2\frac{1}{2})\). Find the y-coordinate of the line when x = 4.
Odpověď
(D)
8
15
In how many ways can a committee of 5 be selected from 8 students if 2 particular students are to be included?
Odpověď
(A)
20
16
If \(x = i - 3j\) and \(y = 6i + j\), calculate the angle between x and y.
Odpověď
(C)
81°
17
The gradient of a curve at the point (-2, 0) is \(3x^{2} - 4x\). Find the equation of the curve.
Odpověď
(D)
\(y = x^{3} - 2x^{2} + 16\)
18
If \(\alpha\) and \(\beta\) are the roots of \(x^{2} + x - 2 = 0\), find the value of \(\frac{1}{\alpha^{2}} + \frac{1}{\beta^{2}}\).
Odpověď
(A)
\(\frac{5}{4}\)
19
Given that \(x^{2} + 4x + k = (x + r)^{2} + 1\), find the value of k and r.
Odpověď
(B)
k = 5, r = 2
20
Given the statements:
p : the subject is difficult
q : I will do my best
Which of the following is equivalent to 'Although the subject is difficult, I will do my best'?
Odpověď
(D)
\( p \wedge q\)
21
Given that \(r = 2i - j\), \(s = 3i + 5j\) and \(t = 6i - 2j\), find the magnitude of \(2r + s - t\).
Odpověď
(D)
\(\sqrt{26}\)
22
Marks
0
1
2
3
4
5
Number of candidates
6
4
8
10
9
3
The table above shows the distribution of marks scored by students in a test. How many candidates scored above the median score?
Odpověď
(B)
12
23
Marks
0
1
2
3
4
5
Number of candidates
6
4
8
10
9
3
The table above shows the distribution of marks scored by students in a test. Find the interquartile range of the distribution.
Odpověď
(B)
3
24
A mass of 75kg is placed on a lift. Find the force exerted by the floor of the lift on the mass when the lift is moving up with constant velocity. \([g = 9.8ms^{-2}]\)
Odpověď
(C)
735N
25
Each of the 90 students in a class speak at least Igbo or Hausa. If 56 students speak Igbo and 50 speak Hausa, find the probability that a student selected at random from the class speaks Igbo only.
Odpověď
(B)
\(\frac{4}{9}\)
26
If \(\begin{vmatrix} 1+2x & -1 \\ 6 & 3-x \end{vmatrix} = -3 \), find the values of x.
Find the coordinates of the point which divides the line joining P(-2, 3) and Q(4, 6) internally in the ratio 2 : 3.
Odpověď
(D)
\((\frac{2}{5}, 4\frac{1}{5})\)
29
A particle starts from rest and moves in a straight line such that its acceleration after t seconds is given by \(a = (3t - 2) ms^{-2}\). Find the other time when the velocity would be zero.
Odpověď
(C)
\(\frac{4}{3} seconds\)
30
A particle starts from rest and moves in a straight line such that its acceleration after t secs is given by \(a = (3t - 2) ms^{-2}\). Find the distance covered after 3 secs.
Odpověď
(D)
\(\frac{9}{2} m\)
31
Given that \(y = 4 - 9x\) and \(\Delta x = 0.1\), calculate \(\Delta y\).
Odpověď
(D)
-0.9
32
Four fair coins are tossed once. Calculate the probability of having equal heads and tails.
Odpověď
(B)
\(\frac{3}{8}\)
33
In calculating the mean of 8 numbers, a boy mistakenly used 17 instead of 25 as one of the numbers. If he obtained 20 as the mean, find the correct mean.
Odpověď
(C)
21
34
Simplify: \(^{n}C_{r} ÷ ^{n}C_{r-1}\)
Odpověď
(D)
\(\frac{n+1-r}{r}\)
35
If \(2\sin^{2} \theta = 1 + \cos \theta, 0° \leq \theta \leq 90°\), find the value of \(\theta\).
