POST UTME COVENANT UNIVERSITY 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A set of 5 points is chosen at random from a square with side length 10. What is the probability that the five points form a convex pentagon?
A. 0.5
B. 0.6
C. 0.7
D. 0.8
Question 2
Find the equation of the circle with center \( -2, 3 \) and radius 4.
A. \( x + 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 2 \)^2 + \( y + 3 \)^2 = 16
C. \( x + 3 \)^2 + \( y - 2 \)^2 = 16
D. \( x - 3 \)^2 + \( y + 2 \)^2 = 16
Question 3
Determine the value of \( mathbf{a} cdot \( mathbf{b} \times mathbf{c} \ \) ) given that \( mathbf{a} = egin{pmatrix} 1 \ 2 \ 3 \end{pmatrix} \), \( mathbf{b} = egin{pmatrix} 4 \ 5 \ 6 \end{pmatrix} \), and \( mathbf{c} = egin{pmatrix} 7 \ 8 \ 9 \end{pmatrix} \).
A. -18
B. 18
C. 0
D. 36
Question 4
In a geometric sequence with first term (a) and common ratio (r), the sum of the first three terms is 12. If the sum of the first four terms is 24, what is the value of (r)?
A. 2
B. 3
C. 4
D. 5
Question 5
Solve for x in the equation \[ \begin{array}{c} 2x + 5y = 11 \ 3x - 2y = -7 \end{array} \] u\sing matrices.
A. x = 1, y = 2
B. x = 2, y = 1
C. x = 3, y = 4
D. x = 4, y = 3
Question 6
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
A. \frac{-2x}{\( x^2 + 1 \)^2}
B. \frac{2x}{\( x^2 + 1 \)^2}
C. \frac{-2x}{\( x^2 + 1 \)^2}
D. \frac{2x}{\( x^2 + 1 \)^2}
Question 7
Find the derivative of the function ( f(x) = \frac{x^2 + 2x - 3}{x^2 - 4} ) u\sing the quotient rule.
A. \frac{2x\( x^2 - 4 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}
B. \frac{2x\( x^2 - 4 \) + \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}
C. \frac{2x\( x^2 - 4 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}
D. \frac{2x\( x^2 - 4 \) + \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}
Question 8
Solve the inequality \( \log_{10} \( x^2 \ \) > 4 ).
A. \( x > 10 \)
B. \( x < -10 \)
C. \( x > 100 \)
D. \( x < -100 \)
Question 9
Solve the trigonometric equation \sin^2 x + \cos^2 x = 1 for x.
A. x = \frac{\pi}{4}
B. x = \frac{\pi}{2}
C. x = \frac{3\pi}{4}
D. x = \frac{5\pi}{4}
Question 10
A bag contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?
A. \frac{1}{2}
B. \frac{2}{7}
C. \frac{3}{7}
D. \frac{4}{7}
Question 11
Solve the inequality \( \frac{x-2}{x+1} geq 0 \) for ( x in mathbb{R} ).
A. \( x leq -1 \) or ( x geq 2 )
B. \( x < -1 \) or \( x > 2 \)
C. \( x leq -1 \) or \( x > 2 \)
D. \( x < -1 \) or ( x leq 2 )
Question 12
A polynomial function (f(x)) has a root at \( x = 2 \) and a root at \( x = -3 \). If the leading coefficient of the polynomial is 2, what is the value of (f(0))?
A. 10
B. -10
C. 20
D. -20
Question 13
Solve for (x) in the equation \( x^2 + 5x + 6 = 0 \).
A. 2
B. -2
C. -3
D. 3
Question 14
Find the determinant of the matrix \[ \begin{array}{ccc} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{array} \].
A. 0
B. 1
C. 2
D. 3
Question 15
A solid right circular cone has a height of 12 cm and a base radius of 4 cm. What is the volume of the cone?
A. 150.72
B. 200.72
C. 250.72
D. 300.72

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