POST UTME COVENANT UNIVERSITY 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the equation \( \log_2 \( x + 1 \ \) = 3 ) for ( x ).
A. \( x = 7 \)
B. \( x = 6 \)
C. \( x = 5 \)
D. \( x = 4 \)
Question 2
A set of numbers is defined as \( S = { x in mathbb{R} : x^2 - 4x + 3 = 0 } \). Find the elements of the set.
A. {1, 3}
B. {2, 3}
C. {1, 2}
D. {3, 4}
Question 3
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{1 - x^2}} ) u\sing the chain rule.
A. \( \frac{1}{\( 1 - x^2 \ \)^{\frac{3}{2}}} )
B. \( \frac{x}{\( 1 - x^2 \ \)^{\frac{3}{2}}} )
C. \( \frac{-x}{\( 1 - x^2 \ \)^{\frac{3}{2}}} )
D. \( \frac{1}{\( 1 - x^2 \ \)^{\frac{1}{2}}} )
Question 4
A sequence is defined by the recurrence relation \( a_n = 2a_{n-1} + 1 \), with initial term \( a_1 = 3 \). Find the 5th term of the sequence.
A. 31
B. 33
C. 35
D. 37
Question 5
Find the value of \( \log_{10} \( 1000 \ \) ).
A. 3
B. 2
C. 4
D. 5
Question 6
Solve the inequality \( 2x^2 + 5x - 3 > 0 \) u\sing the concept of variation.
A. \( x < -1 \) or \( x > \frac{3}{2} \)
B. \( x < -\frac{3}{2} \) or \( x > 1 \)
C. \( x < -1 \) or \( x < \frac{3}{2} \)
D. \( x < -\frac{3}{2} \) or \( x > -1 \)
Question 7
Solve the inequality \( \frac{x}{x-2} > 2 \) for \( x > 2 \).
A. x > 4
B. x > 6
C. x < 4
D. x < 6
Question 8
Find the area under the curve \( y = x^2 - 2x + 1 \) from \( x = 0 \) to \( x = 2 \).
A. \( \frac{3}{2} \)
B. \( \frac{5}{2} \)
C. \( \frac{7}{2} \)
D. \( \frac{9}{2} \)
Question 9
Find the value of \( \sin 2x \) given that \( \sin x = \frac{3}{5} \) and \( \cos x = \frac{4}{5} \).
A. \frac{24}{25}
B. \frac{16}{25}
C. \frac{12}{25}
D. \frac{20}{25}
Question 10
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, -3 \) ∪ (1, ∞)
C. \( -∞, 1 \) ∪ (3, ∞)
D. \( -∞, -3 \) ∪ (1, ∞)
Question 11
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -\infty, -1 \) \cup \( 3, \infty \)
B. \( -\infty, 1 \) \cup \( 3, \infty \)
C. \( -\infty, -1 \) \cup \( 1, \infty \)
D. \( -\infty, 1 \) \cup \( 1, \infty \)
Question 12
Find the value of \( \sin \( 2pi/3 \ \) ).
A. 1/2
B. 1/3
C. 2/3
D. 3/4
Question 13
Solve the system of equations \( x + y = 4 \) and \( xy = 5 \).
A. x = 1, y = 3
B. x = 3, y = 1
C. x = 2, y = 2
D. x = 4, y = 0
Question 14
Determine the mean of the following dataset: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
A. 5
B. 6
C. 7
D. 8
Question 15
Find the equation of the \tangent line to the curve \( y = \frac{1}{x} \) at the point where \( x = 2 \).
A. y = -1/2x + 1
B. y = 1/2x + 1
C. y = -1/2x - 1
D. y = 1/2x - 1

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