A binary operation * is defined on the set of real numbers, R, by \(x * y = x + y - xy\). If the identity element under the operation * is 0, find the inverse of \(x \in R\).
Trả lời
(A)
\(\frac{-x}{1 - x}, x \neq 1\)
2
Solve: \(\sin \theta = \tan \theta\)
Trả lời
(D)
0°
3
Given that \(a^{\frac{5}{6}} \times a^{\frac{-1}{n}} = 1\), solve for n.
Trả lời
(D)
1.20
4
Express \(\log \frac{1}{8} + \log \frac{1}{2}\) in terms of \(\log 2\).
Trả lời
(D)
-4 log 2
5
If \(f(x) = x^{2}\) and \(g(x) = \sin x\), find g o f.
Trả lời
(B)
\(\sin x^{2}\)
6
Find the third term in the expansion of \((a - b)^{6}\) in ascending powers of b.
Trả lời
(B)
\(15a^{4}b^{2}\)
7
If \(\sqrt{x} + \sqrt{x + 1} = \sqrt{2x + 1}\), find the possible values of x.
Trả lời
(D)
0 and -1
8
If \(\alpha\) and \(\beta\) are the roots of the equation \(2x^{2} - 6x + 5 = 0\), evaluate \(\frac{\beta}{\alpha} + \frac{\alpha}{\beta}\).
Trả lời
(B)
\(\frac{8}{5}\)
9
Given that \(f(x) = 2x^{3} - 3x^{2} - 11x + 6\) and \(f(3) = 0\), factorize f(x).
Trả lời
(C)
(x - 3)(x + 2)(2x -1)
10
Find the equation of the line that is perpendicular to \(2y + 5x - 6 = 0\) and bisects the line joining the points P(4, 3) and Q(-6, 1).
Trả lời
(D)
5y - 2x - 12 = 0
11
Differentiate \(x^{2} + xy - 5 = 0\).
Trả lời
(A)
\(\frac{-(2x + y)}{x}\)
12
The fourth term of an exponential sequence is 192 and its ninth term is 6. Find the common ratio of the sequence.
Trả lời
(B)
\(\frac{1}{2}\)
13
Find the range of values of x for which \(x^{2} + 4x + 5\) is less than \(3x^{2} - x + 2\)
Trả lời
(B)
\(x < \frac{-1}{2}, x > 3\)
14
Given that \(\frac{\mathrm d y}{\mathrm d x} = \sqrt{x}\), find y.
Trả lời
(B)
\(\frac{2}{3}x^{\frac{3}{2}} + c\)
15
Given that \(P = \begin{pmatrix} y - 2 & y - 1 \\ y - 4 & y + 2 \end{pmatrix}\) and |P| = -23, find the value of y.
Trả lời
(B)
-3
16
An object is thrown vertically upwards from the top of a cliff with a velocity of \(25ms^{-1}\). Find the time, in seconds, when it is 20 metres above the cliff. \([g = 10ms^{-2}]\).
Find the coordinates of the point which divides the line joining P(-2, 3) and Q(4, 9) internally in the ratio 2 : 3.
Trả lời
(B)
\((\frac{2}{5}, 5\frac{2}{5})\)
19
The angle subtended by an arc of a circle at the centre is \(\frac{\pi}{3} radians\). If the radius of the circle is 12cm, calculate the perimeter of the major arc.
A committee consists of 5 boys namely: Kofi, John, Ojo, Ozo and James and 3 girls namely: Rose, Ugo and Ama. In how many ways can a sub-committee consisting of 3 boys and 2 girls be chosen, if Ozo must be on the sub-committee?
Trả lời
(C)
18
22
Forces 50N and 80N act on a body as shown in the diagram. Find, correct to the nearest whole number, the horizontal component of the resultant force.
Trả lời
(A)
13N
23
The sales of five salesgirls on a certain day are as follows; GH¢ 26.00, GH¢ 39.00, GH¢ 33.00, GH¢ 25.00 and GH¢ 37.00. Calculate the standard deviation if the mean sale is GH¢ 32.00.
Trả lời
(B)
GH¢ 5.66
24
A circular ink blot on a piece of paper increases its area at the rate \(4mm^{2}/s\). Find the rate of the radius of the blot when the radius is 8mm. \([\pi = \frac{22}{7}]\).
Trả lời
(B)
0.08 mm/s
25
Express \(\frac{x^{2} + x + 4}{(1 - x)(x^{2} + 1)}\) in partial fractions.
Trả lời
(B)
\(\frac{3}{1 - x} + \frac{2x + 1}{x^{2} + 1}\)
26
Two bodies of masses 3kg and 5kg moving with velocities 2 m/s and V m/s respectively in opposite directions collide. If they move together after collision with velocity 3.5 m/s in the direction of the 5kg mass, find the value of V.
Trả lời
(B)
6.8 m/s
27
The equation of a circle is \(x^{2} + y^{2} - 8x + 9y + 15 = 0\). Find its radius.
Trả lời
(C)
\(\frac{1}{2}\sqrt{85}\)
28
A particle is acted upon by two forces 6N and 3N inclined at an angle of 120° to each other. Find the magnitude of the resultant force.
Trả lời
(D)
\(3\sqrt{3}\) N
29
If \(s = 3i - j\) and \(t = 2i + 3j\), find \((t - 3s).(t + 3s)\).
Find the upper quartile of the following scores: 41, 29, 17, 2, 12, 33, 45, 18, 43 and 5.
Trả lời
(B)
41
32
Given that \(P = \begin{pmatrix} 3 & 4 \\ 2 & x \end{pmatrix}; Q = \begin{pmatrix} 1 & 3 \\ -2 & 4 \end{pmatrix}; R = \begin{pmatrix} -5 & 25 \\ -8 & 26 \end{pmatrix}\) and PQ = R, find the value of x.
Trả lời
(D)
5
33
Two out of ten tickets on sale for a raffle draw are winning tickets. If a guest bought two tickets, what is the probability that both tickets are winning tickets?
Trả lời
(B)
\(\frac{1}{45}\)
34
P and Q are the points (3, 1) and (7, 4) respectively. Find the unit vector along PQ.
Trả lời
(C)
\(\begin{pmatrix} 0.8 \\ 0.6 \end{pmatrix}\)
35
If \(g(x) = \frac{x + 1}{x - 2}, x \neq -2\), find \(g^{-1}(2)\).
