If \(\frac{5}{\sqrt{2}}\) - \(\frac{\sqrt{8}}{8}\) = m\(\sqrt{2}\), find the value of m
Answer
(B)
\(\frac{9}{4}\)
2
Given that f: x → \(\sqrt{x}\) and g : x → 25 - x\(^2\), find the value of f o g(3)
Answer
(A)
4
3
\(\sqrt{x}\) - \(\frac{6}{\sqrt{x}}\) = 1, find the value of x
Answer
(C)
9
4
A binary operation * is defined on the set of real numbers, R by x * y = \(\frac{y^2 - x^2}{2xy}\), x, y ≠ 0, where x and y are real numbers. Evaluate -3 * 2
Answer
(A)
\(\frac{5}{12}\)
5
If the n\(^{th}\) term of a linear sequence (A.P) is (5n - 2), find the sum of the first 12 terms of the sequence.
Answer
(C)
366
6
If h(x) = x\(^2\) + px + 2 is divided by (x + 3), the remainder is 5, find p
Answer
(C)
2
7
If 5x + 7 \(\equiv\) P(x + 3) + Q(x - 1), find the value of p
If f(x) = \(\frac{2 - x}{x}\), x ≠ 0, find the inverse of f.
Answer
(B)
\(\frac{2}{x+1}\), x ≠ -1
11
Solve 2\(^{2x}\) - 5(2\(^x\)) + 4 = 0
Answer
(A)
x = 0 and 2
12
If p = \(\begin{pmatrix}2 \\ 4 \end{pmatrix}\) and q = \(\begin{pmatrix} 10 \\ -1 \end{pmatrix}\), find a vector, r such that 2p - 3r = q
Answer
(A)
\(\begin{pmatrix} -2 \\ 3 \end{pmatrix}\)
13
Given that p = \(\begin{pmatrix} m + 1 & m - 1 \\ m + 4 & m - 8 \end{pmatrix}\) and |p| = - 34, find the value of m.
Answer
(C)
3
14
If r = i + 2j and n = -i + 3j, find |2n - r|.
Answer
(C)
5.0
15
The gradient of the curve y = mx\(^2\) + 3x - 1 at the point (-1, 1) is 9. Find the value of m
Answer
(A)
- 3
16
If kx\(^2\) is a term in the binomial expansion of (1 - 2x)\(^4\), find the value of k.
Answer
(D)
24
17
A fair dice is thrown twice. Find the probability that the sum obtained will be a factor of 12.
Answer
(A)
\(\frac{1}{3}\)
18
A body of mass 42 kg increases its speed from 15 ms\(^{-1}\) to 43 ms\(^{-1}\) in 12 seconds. Find the force acting on the body.
Answer
(C)
98N
19
Given that M and N are two sets. Which of the following is the same as (M ∩ N)'?
Answer
(D)
M' U N'
20
A particle starts from rest accelerates at 4ms\(^{-2}\). Find the distance covered after 4 seconds.
Answer
(D)
32 m
21
Find the range of values of x for which 9x - 1 > 14x\(^2\)
Answer
(A)
\(\frac{1}{7}\) < x < \(\frac{1}{2}\)
22
A particle of mass 40 kg is kept on a smooth plane inclined at an angle of 30º to the horizontal by a force up the plane. find, correct to one decimal place, the magnitude of the normal reaction of the plane of the particle.[Take g = 10 ms\(^{-2}\)]
Answer
(C)
346.4N
23
The point P(-3, 5) lies on a line which is perpendicular to 2x - 4y + 3 = 0. Find the equation of the line.
Answer
(C)
y + 2x + 1 = 0
24
Find the coefficient of y\(^2\) in the binomial expansion of (y - 2x)\(^5\).
Answer
(D)
- 80x\(^3\)
25
Given that f(x) = x\(^2\) + 3x + 1, find the value of x at the turning point.
Answer
(C)
-1\(\frac{1}{2}\)
26
How many three-digit numbers can be formed from the digits 2, 3, 4, 5, 6, 7, and 8 if repetition is not allowed?
Answer
(B)
210
27
If \(\begin{pmatrix} 6 & 4 \\ 7 & 5 \end{pmatrix}\) \(\begin{pmatrix} 2 \\ m \end{pmatrix}\) = 2\(\begin{pmatrix} 12 \\ 14.5 \end{pmatrix}\), find the value of m.
Answer
(C)
3
28
A body of mass 80 kg moving with a velocity of 25 ) ms\(^{-1}\) collides with another moving in the opposite direction at 10 ms\(^{-1}\). After collision, both bodies moved with a common velocity of 12.8 ms\(^{-1}\). Calculate, correct to the nearest whole number, the mass of the second body.
Answer
(C)
43 kg
29
In how many ways can 12 people be seated on a bench if only 5 spaces are available?
Answer
(A)
95040
30
In triangle XYZ, |XY| = 10cm, |YZ| = 9 cm and |XZ| = 7 cm. If XZY = \(\alpha\), find the value of cos \(\alpha\).
Answer
(C)
\(\frac{5}{21}\)
31
If y\(^2\) + 2xy - 8 = 0, find \(\frac{dy}{dx}\)
Answer
(A)
\(\frac{- y}{y + x}\)
32
The mean of four numbers is 5 and the mean of another three numbers is 12. Find the mean of the seven numbers.
Answer
(C)
8
33
Find, correct to the nearest degree, the acute angle between 3x - y - 5 = 0, and 7x - y - 3 = 0
Answer
(A)
10\(^0\)
34
The gradient of a curve is given by 3x\(^2\) - 8x + 2. If the curve passes through P(0, 4), find the equation of the curve.
