POST UTME COVENANT UNIVERSITY 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A vector \( \vec{a} \) has a magnitude of 6 units and makes an angle of 30\circ with the positive x-axis. Find the x and y components of \( \vec{a} \).
A. 3\hat{i} + 3\hat{j}
B. 6\hat{i} + 3\hat{j}
C. 3\hat{i} + 6\hat{j}
D. 6\hat{i} + 6\hat{j}
Question 2
Find the determinant of the matrix $\begin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix}$.
A. 0
B. 1
C. -1
D. 2
Question 3
Solve the equation \( \sin^2 x + \cos^2 x = 1 \) for ( x in [0, 2pi] ).
A. x = 0, \pi/2, \pi, 3\pi/2
B. x = 0, \pi/2, \pi, 3\pi/2, 2\pi
C. x = 0, \pi/2, \pi, 3\pi/2, 5\pi/2
D. x = 0, \pi/2, \pi, 3\pi/2, 2\pi, 5\pi/2
Question 4
Solve for ( x ) in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 2
B. 4
C. 8
D. 16
Question 5
In the diagram below, ( ABC ) is a right-angled triangle with \( angle B = 90^\circ \). If \( AB = 3 \) cm and \( BC = 4 \) cm, find the length of ( AC ).
A. 5
B. 6
C. 7
D. 8
Question 6
Find the area under the curve \( y = x^2 - 4x + 3 \) from \( x = 1 \) to \( x = 3 \).
A. 10
B. 12
C. 14
D. 16
Question 7
Solve for x in the equation \( \log_{10} \( x^2 \) = 4 \).
A. 10
B. 100
C. 1000
D. 10000
Question 8
A particle moves in a straight line with an initial velocity of \( 5 , \text{m/s} \) and an acceleration of \( 2 , \text{m/s}^2 \). Find its velocity after ( 3 ) seconds.
A. 13
B. 15
C. 17
D. 19
Question 9
Solve the equation \( x^2 - 4x + 3 = 0 \) u\sing the quadratic formula.
A. x = 1, 3
B. x = 2, 4
C. x = 3, 5
D. x = 4, 6
Question 10
Let X and Y be indep\endent random variables with probability density functions f_X(x) = 2x, 0 < x < 1 and f_Y(y) = 3y^2, 0 < y < 1. Find the probability that X + Y < 1.
A. 1/4
B. 1/2
C. 3/4
D. 1
Question 11
Find the sum of the first 5 terms of the geometric series \( 2x^2 - 3x + 1 \).
A. 2x^2 - 3x + 1 + 2x^2 - 3x + 1 + 2x^2 - 3x + 1 + 2x^2 - 3x + 1 + 2x^2 - 3x + 1
B. 2x^2 - 3x + 1 + 2x^2 - 3x + 1 + 2x^2 - 3x + 1 + 2x^2 - 3x + 1 + 2x^2
C. 2x^2 - 3x + 1 + 2x^2 - 3x + 1 + 2x^2 - 3x + 1 + 2x^2 - 3x + 1 + 3x^2
D. 2x^2 - 3x + 1 + 2x^2 - 3x + 1 + 2x^2 - 3x + 1 + 2x^2 - 3x + 1 + 4x^2
Question 12
Solve the inequality $\frac{x^2 - 4}{x + 2} > 0$.
A. \( -\infty, -2 \) \cup \( 2, \infty \)
B. \( -\infty, -2 \) \cup \( -2, 2 \) \cup \( 2, \infty \)
C. \( -\infty, -2 \) \cup \( 2, \infty \)
D. \( -\infty, 2 \) \cup \( 2, \infty \)
Question 13
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 14
Solve the equation x^2 + 4x - 5 = 0 u\sing the quadratic formula.
A. x = -5, x = 1
B. x = -1, x = 5
C. x = 1, x = -5
D. x = -5, x = -1
Question 15
Solve the inequality \( \frac{x}{x-2} > 0 \) for \( x in \( -infty, infty \ \) ).
A. \( -infty, 2 \) cup (2, infty)
B. \( -infty, 2 \) cup (2, 4)
C. \( -infty, 4 \) cup (4, infty)
D. \( -infty, 2 \) cup (4, infty)

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