If \(\begin{vmatrix} 3 & x \\ 2 & x - 2 \end{vmatrix} = -2\), find the value of x.
Απάντηση
(A)
-8
16
Given that \(P = {x : \text{x is a factor of 6}}\) is the domain of \(g(x) = x^{2} + 3x - 5\), find the range of x.
Απάντηση
(D)
{-1, 5, 13, 49}
17
The third of geometric progression (G.P) is 10 and the sixth term is 80. Find the common ratio.
Απάντηση
(A)
2
18
Find the axis of symmetry of the curve \(y = x^{2} - 4x - 12\).
Απάντηση
(C)
x = 2
19
Find the equation of the tangent to the curve \(y = 4x^{2} - 12x + 7\) at point (2, -1).
Απάντηση
(C)
y - 4x + 9 = 0
20
The mean age of 15 pupils in a class is 14.2 years. One new pupil joined the class and the mean changed to 14.1 years. Calculate the age of the new pupil.
Απάντηση
(B)
12.6 years
21
The distance s metres of a particle from a fixed point at time t seconds is given by \(s = 7 + pt^{3} + t^{2}\), where p is a constant. If the acceleration at t = 3 secs is \(8 ms^{-2}\), find the value of p.
Απάντηση
(A)
\(\frac{1}{3}\)
22
The probabilities that a husband and wife will be alive in 15 years time are m and n respectively. Find the probability that only one of them will be alive at that time.
Απάντηση
(C)
m + n - 2mn
23
In a class of 50 pupils, 35 like Science and 30 like History. What is the probability of selecting a pupil who likes both Science and History?
Απάντηση
(B)
0.30
24
P, Q, R, S are points in a plane such that PQ = 8i - 5j, QR = 5i + 7j, RS = 7i + 3j and PS = xi + yj. Find (x, y).
Απάντηση
(C)
(20, 5)
25
Find the least value of n for which \(^{3n}C_{2} > 0, n \in R\).
Απάντηση
(C)
\(\frac{2}{3}\)
26
If \(\overrightarrow{OA} = 3i + 4j\) and \(\overrightarrow{OB} = 5i - 6j \) where O is the origin and M is the midpoint of AB, find OM.
Απάντηση
(C)
4i - j
27
Find the direction cosines of the vector \(4i - 3j\).
Απάντηση
(C)
\(\frac{4}{5}, -\frac{3}{5}\)
28
Yomi was asked to label four seats S, R, P, Q. What is the probability he labelled them in alphabetical order?
Απάντηση
(A)
\(\frac{1}{24}\)
29
Two forces (2i - 5j)N and (-3i + 4j)N act on a body of mass 5kg. Find in \(ms^{-2}\), the magnitude of the acceleration of the body.
Απάντηση
(A)
\(\frac{\sqrt{2}}{5}\)
30
Two particles are fired together along a smooth horizontal surface with velocities 4 m/s and 5 m/s. If they move at 60° to each other, find the distance between them in 2 seconds.
Απάντηση
(C)
\(2\sqrt{21}\)
31
Two forces \(F_{1} = (7i + 8j)N\) and \(F_{2} = (3i + 4j)N\) act on a particle. Find the magnitude and direction of \(F_{1} - F_{2}\).
Απάντηση
(B)
\((4\sqrt{2} N, 045°)\)
32
A stone is thrown vertically upwards and its height at any time t seconds is \(h = 45t - 9t^{2}\). Find the maximum height reached.
Απάντηση
(D)
56.25 m
33
Given that \(\frac{\mathrm d y}{\mathrm d x} = 3x^{2} - 4\) and y = 6 when x = 3, find the equation for y.
Απάντηση
(A)
\(x^{3} - 4x - 9\)
34
If \(h(x) = x^{3} - \frac{1}{x^{3}}\), evaluate \(h(a) - h(\frac{1}{a})\).
Απάντηση
(C)
\(2a^{3} - \frac{2}{a^{3}}\)
35
A company took delivery of 12 vehicles made up of 7 buses and 5 saloon cars for two of its departments; Personnel and General Administration. If the Personnel department is to have at least 3 saloon cars, in how many ways can these vehicles be distributed equally between the departments?
