If \(\begin{vmatrix} 3 & x \\ 2 & x - 2 \end{vmatrix} = -2\), find the value of x.
отговор
(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.
отговор
(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.
отговор
(A)
2
18
Find the axis of symmetry of the curve \(y = x^{2} - 4x - 12\).
отговор
(C)
x = 2
19
Find the equation of the tangent to the curve \(y = 4x^{2} - 12x + 7\) at point (2, -1).
отговор
(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.
отговор
(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.
отговор
(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.
отговор
(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?
отговор
(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).
отговор
(C)
(20, 5)
25
Find the least value of n for which \(^{3n}C_{2} > 0, n \in R\).
отговор
(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.
отговор
(C)
4i - j
27
Find the direction cosines of the vector \(4i - 3j\).
отговор
(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?
отговор
(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.
отговор
(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.
отговор
(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 \(F_{1} - F_{2}\).
отговор
(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.
отговор
(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.
отговор
(A)
\(x^{3} - 4x - 9\)
34
If \(h(x) = x^{3} - \frac{1}{x^{3}}\), evaluate \(h(a) - h(\frac{1}{a})\).
отговор
(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?
