Solve; \(\frac{P}{2} + \frac{k}{3}\) = 5 and 2p = k = 6 simultaneously
Answer
(C)
p = 6, k = 6
3
Evaluate tan 75\(^o\); leaving the answer in surd form (radicals)
Answer
(D)
\(\sqrt{3 - 2}\)
4
Rationalize; \(\frac{1}{\sqrt{2 + 1}}\)
Answer
(A)
\(\sqrt{2}\) - 1
5
If \(^nC_2\) = 15, find the value of n
Answer
(C)
6
6
An operation (*) is defined on the set T = {-1, 0, ...., 5} by x * y = x + y - xy. Which of the following operation(s) will give an image which is an element of T?
I. 2(*)5 II. 3(*)5 III. 3(*)4
Answer
(B)
II only
7
Given that g ; x \(\to\) 3x and f ; x \(\to\) cos x. Find the value of g\(^o\) f(20\(^o\))
Answer
(D)
2.82
8
A linear transformation is defined by T: (x, y) \(\to\) (-x + y, -4y). Find the image, Q`, of Q(-3, 2) under T
Answer
(A)
Q`(5, -8)
9
If g : r \(\to\) 5 - 2r, r is a real number, find the image of -3
Answer
(B)
11
10
Consider the following statements:
p: Birds fly
q: The sky is blue
r: The grass is green
What is the symbolic representation of "If the grass is green and the sky is not blue, then the birds do not fly"?
Answer
(C)
(r ^~ q) \(\to\) ~p
11
Given that \(\frac{1}{x^2 - 4} = \frac{p}{(x + 2)} + \frac{Q}{(x - 2})\)
x \(\neq \pm 2\)
Find the value of (P + Q)
Answer
(D)
0
12
Find the sum of the first 20 terms of the sequence -7-3, 1, ......
Answer
(A)
620
13
Find the value of x for which 6\(\sqrt{4x^2 + 1}\) = 13x, where x > 0
Answer
(A)
\(\frac{6}{5}\)
14
Calculate the distance between points (-2, -5) and (-1, 3)
Answer
(C)
\(\sqrt{65}\) units
15
If P = \(\begin {pmatrix} 2 & 3\\ -4 & 1 \end {pmatrix}\), Q = \(\begin{pmatrix} 6 \\ 8 \end {pmatrix}\) and PQ = k \(\begin {pmatrix} 45\\ -20 \end {pmatrix}\). Find the value of k.
Answer
(C)
\(\frac{4}{5}\)
16
The second and fourth terms of an exponential sequence (G.P) are \(\frac{2}{9}\) and \(\frac{8}{81}\) respectively. Find the sixth term of the sequence
Answer
(D)
\(\frac{32}{729}\)
17
Point X and Y are on the same horizontal base as the foot of a building such that X is 96m due east of the building and Y is due west. If the angle of elevation of the top of that building from X is 30\(^o\) and that of Y is 50\(^o\), calculate the distance of Y from the base of the building.
Answer
(B)
32m
18
Find the coordinates of the point in the curve y = 3x\(^2\) - 2x - 5 where the tangent is parallel to the line y = - 5 = 8x
If the mean of 2, 5, (x + 1), (x + 2), 7 and 9 is 6, find the median.
Answer
(A)
6.5
20
Calculate the mean deviation of 5, 8, 2, 9 and 6
Answer
(D)
2
21
A particle starts from rest and moves in a straight line such that its velocity, V ms\(^{-1}\), at time t second is given by V = 3t\(^2\) - 6t. Calculate the acceleration in the 3rd second.
Answer
(B)
16m
22
A particle starts from rest and moves in a straight line such that its velocity, V ms\(^{-1}\), at time t second is given by V = 3t\(^2\) - 6t. Calculate the acceleration in the 3rd second.
Answer
(C)
6 ms\(^{-2}\)
23
Find the constant term in the binomial expansion of (2x\(^2\) + \(\frac{1}{x^2}\))\(^4\)
Answer
(B)
12
24
Which of these inequalities is represented by the shaded portion of the graph?
Answer
(B)
2y - x - 3 < 0
25
A 35 N force acts on a body of mass 5 kg for 2 seconds. Calculate the change in momentum of the body.
Answer
(A)
70 kg ms\(^{-1}\)
26
Solve, correct to three significant figures, (0.3)\(^x\) = (0,5)\(^8\)
Answer
(A)
4.61
27
Given that P and Q are non-empty subsets of the universal set, U. Find P \(\cap\) (Q U Q`).
Answer
(A)
p
28
Find the coefficient of the third term in the binomial expansion of [2x + \(\frac{3y}{4}\)]\(^3\) in descending powers of x.
Answer
(B)
\(\frac{27}{8}\)y\(^2\)
29
Find the coordinates of the centre of the circle 3x\(^2\) + 3y\(^2\) - 6x + 9y - 5 = 0
Answer
(C)
(1, - \(\frac{3}{2}\))
30
Evaluate \(\int^9_0 \sqrt{x} dx\)
Answer
(C)
18
31
The function f : x \(\to\) x\(^2\) + px + q has turning point when x = -3 and remainder of -6 when divided by (x + 2). Find the value of q.
Answer
(B)
2
32
If y = (5 - x)\(^{-3}\), and \(\frac{dy}{dx}\)
Answer
(C)
\(\frac{3}{(5 - x)^4}\)
33
Which of the following vectors is perpendicular to \(\begin{pmatrix} -1 & 3 \end{pmatrix}\)?
Answer
(A)
\(\begin{pmatrix} -3 & 1 \end{pmatrix}\)
34
Find correct to the nearest degree,5 the angle between p = 12i - 5j and q = 4i +3j
Answer
(A)
59\(^o\)
35
Find the area between line y = x + 1 and the x-axis from x = -2 to x = 0.
