Calculate, correct to one decimal place, the angle between 5 i + 12 j and -2 i + 3 j
Answer
(A)
56.3º
2
Find the equation of the normal to the curve y = \(3x^2 + 2\) at point (1, 5).
Answer
(B)
6y + x - 31 = 0
3
The distance S metres moved by a body in t seconds is given by \(S = 5t^3 - \frac{19}{2} t^2 + 6t - 4\). Calculate the acceleration of the body after 2 seconds
Answer
(C)
41 \(ms ^{-2}\)
4
Evaluate \(\int^1_0 x(x^2-2)^2 dx\)
Answer
(B)
\(1\frac{1}{6}\)
5
Given that \(sin x = \frac{4}{5}\) and \(cos y = \frac{12}{13}\), where x is an obtuse angle and y is an acute angle, find the value of sin (x - y).
Answer
(A)
\(\frac{63}{65}\)
6
If\((\frac{1}{9})^{2x-1} = (\frac{1}{81})^{2-3x}\)find the value of x
Answer
(D)
\(-\frac{5}{8}\)
7
The table shows the operation * on the set {x, y, z, w}.
*
X
Y
Z
W
X
Y
Z
X
W
Y
Z
W
Y
X
Z
X
Y
Z
W
W
W
X
W
Z
Find the identity of the element.
Answer
(C)
Z
8
Find the radius of the circle \(2x^2 + 2y^2 - 4x + 5y + 1 = 0\)
Answer
(A)
\(\frac{\sqrt33}{4}\)
9
Given that M is the midpoint of T (2, 4) and Q (-8, 6), find the length of MQ .
Answer
(A)
\(√26 units\)
10
A particle began to move at \(27 ms^{-1}\) along a straight line with constant retardation of \(9 ms^{-2}\). Calculate the time it took the particle to come to a stop.
Answer
(A)
3 sec
11
Find the fifth term in the binomial expansion of \((q + x)^7\).
Answer
(C)
\(35q^3x^4\)
12
Given that P = {x : 2 ≤ x ≤ 8} and Q = {x : 4 < x ≤ 12} are subsets of the universal set μ = {x : x ∈ R}, find (P ⋂ Q\(^1\)).
Answer
(C)
{x : 2 ≤ x ≤ 4}
13
Consider the statements:
x: The school bus arrived late
y: The student walked down to school
Which of the following can be represented by y ⇒ x?
Answer
(B)
Mary walked to school because the school bus arrived late
14
\(Differentiate f (x) = \frac{1}{(1 - x^2)^5}\) with respect to \(x\).
Answer
(D)
\(\frac{10x}{(1-x^2)^6}\)
15
Express \(\frac{3}{3 - √6}\) in the form \(x + m√y\)
Answer
(C)
3 + √6
16
The table shows the mark obtained by students in a test.
Given that r = (10 N , 200º) and n = (16 N , 020º), find (3r - 2n).
Answer
(D)
(62 N , 020º)
19
Solve 6 sin 2θ tan θ = 4, where 0º < θ < 90º
Answer
(C)
35.26º
20
An exponential sequence (G.P.) is given by 8√2, 16√2, 32√2, ... . Find the n\(^{th}\) term of the sequence
Answer
(B)
\(2^{(n+2)}\sqrt2\)
21
If \(f : x → 2 tan x\) and \(g : x → √(x^2 + 8), find ( g o f )(45^o)\)
Answer
(B)
2√3
22
A uniform beam PQ of length 80 cm and weight 60 N rests on a support at X where | PX | = 30 cm. If the body is kept in equilibrium by a mass m kg which is placed at P , calculate the value of m
[Take g = 10 ms\(^{-2}\)]
Answer
(A)
2.0
23
An exponential sequence (G.P.) is given by \(\frac{9}{2},\frac{3}{4},\frac{1}{8},\)....Find its sum to infinity.
Answer
(A)
\(5\frac{2}{5}\)
24
Adu's scores in five subjects in an examination are 85, 84, 83, 86 and 87. Calculate the standard deviation.
Answer
(B)
1.4
25
In how many ways can a committee of 3 women and 2 men be chosen from a group of 7 men and 5 women?
Answer
(D)
210
26
Evaluate: \(\int(2x + 1)^3 dx\)
Answer
(C)
\(\frac{1}{8} (2x + 1)^4 + k\)
27
If α and β are the roots of \(7x2 +12x - 4 = 0\),find the value of \(\frac{αβ}{(α + β)^2}\)
Answer
(D)
-\( \frac{7}{36}\)
28
If \(3x^2 + p x + 12 = 0\) has equal roots, find the values of p .
Answer
(A)
±12
29
Given that \(\frac{3x + 4}{(x - 2)(x + 3)}≡\frac{P}{x + 3}+\frac{Q}{x - 2}\),find the value of Q.
Answer
(A)
2
30
The velocity of a body of mass 4.56 kg increases from \((10 ms^{-1}, 060^o) to (50 ms ^{-1}, 060^o)\) in 16 seconds . Calculate the magnitude of force acting on it.
Answer
(B)
11.4 N
31
A linear transformation on the oxy plane is defined by \(P : (x, y) → (2x + y, -2y)\). Find \(P^2\)
Answer
(C)
\(\begin{bmatrix} 4&0\\0&4\end{bmatrix}\)
32
Given that \(y^2 + xy = 5,find \frac{dy}{dx}\).
Answer
(B)
\(\frac{-y}{2y + x}\)
33
If \(X\) and \(Y\) are two independent events such that \(P (X) = \frac{1}{8}\) and \(P (X ⋃ Y) = \frac{5}{8}\), find \(P (Y)\).
Answer
(B)
\(\frac{4}{7}\)
34
A function \(f\) is defined by \(f :x→\frac{x + 2}{x - 3},x ≠ 3\).Find the inverse of \(f\) .
Answer
(D)
\(\frac{3x + 2}{x - 1},x ≠ 1\)
35
The probabilities that Atta and Tunde will hit a target in a shooting contest are \(\frac{1}{6}\) and \({1}{9}\) respectively. Find the probability that only one of them will hit the target.
