POST UTME UNIBEN 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the derivative of the function ( f(x) = x^3 - 6x^2 + 11x - 6 ).
A. 3x^2 - 12x + 11
B. 3x^2 - 12x + 6
C. 3x^2 - 12x - 6
D. 3x^2 - 12x + 11
Question 2
A circle has a radius of 4 cm. Find the area of the circle.
A. 50.24
B. 50.26
C. 50.28
D. 50.30
Question 3
A sequence is defined by $a_n = 2n^2 + 3n - 1$. Find the sum of the first 5 terms of the sequence.
A. 65
B. 70
C. 75
D. 80
Question 4
Solve the equation \( \sin^2 x + \cos^2 x = 1 \) for ( x in [0, 2pi] ).
A. \( x = \frac{pi}{2} \) or \( x = \frac{3pi}{2} \)
B. \( x = \frac{pi}{4} \) or \( x = \frac{5pi}{4} \)
C. \( x = \frac{pi}{6} \) or \( x = \frac{11pi}{6} \)
D. \( x = \frac{pi}{3} \) or \( x = \frac{2pi}{3} \)
Question 5
If ( f(x) = \frac{x^2 - 4}{x + 2} ), find \( f\( -3 \ \) ).
A. -1
B. 1
C. 2
D. -2
Question 6
Let ( S ) be the set of all positive integers that can be expressed in the form \( 3x + 2y \), where ( x ) and ( y ) are non-negative integers. Find the smallest positive integer in ( S ) that is divisible by 5.
A. 10
B. 15
C. 20
D. 25
Question 7
Solve the equation \( x^2 + 5x + 6 = 0 \).
A. \( -∞, -3 \) ∪ (2, ∞)
B. \( -∞, -2 \) ∪ (3, ∞)
C. \( -∞, -3 \) ∪ (2, ∞)
D. \( -∞, -2 \) ∪ (3, ∞)
Question 8
A binary operation ( ast ) is defined as \( a ast b = a^2 + b^2 \). Find the value of ( 2 ast 3 ).
A. 13
B. 14
C. 15
D. 16
Question 9
Find the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 10
Solve the inequality $|x - 2| > 3$.
A. \( -∞, -1 \) ∪ (4, ∞)
B. \( -∞, 1 \) ∪ (4, ∞)
C. \( -∞, -1 \) ∪ (1, 4)
D. \( -∞, 1 \) ∪ (1, 4)
Question 11
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, -3 \) ∪ (1, ∞)
C. \( -∞, 1 \) ∪ (3, ∞)
D. \( -∞, -3 \) ∪ (1, ∞)
Question 12
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).
A. -2
B. -1
C. 0
D. 1
Question 13
Find the value of $\int_{0}^{\pi/2} \sin^2 x \cos^2 x \, dx$.
A. 1/16
B. 1/8
C. 1/4
D. 1/2
Question 14
A circle with center ( C(2, 3) ) and radius \( r = 4 \) has an equation of the form \( x - h \ \)^2 + \( y - k \)^2 = r^2 ). Find the equation of the circle.
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 15
Solve the inequality \( \frac{x^2 - 4}{x + 2} > 0 \) for ( x in mathbb{R} ).
A. \( x < -2 \) or \( x > 2 \)
B. \( x < -2 \) or \( x = 2 \)
C. \( x > -2 \) or \( x = 2 \)
D. \( x < -2 \) or \( x < 2 \)

Master the Exam!

You've seen a preview, but there are thousands more questions plus AI tutor to break down complex solutions.

Unlock Full Access Available for Android & Windows
Help others prepare! Share this practice hub: