POST UTME CALEB UNIVERSITY 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A die is rolled twice. What is the probability that the sum of the two numbers is 7?
A. 1/6
B. 1/12
C. 1/2
D. 2/3
Question 2
A fair six-sided die is rolled. What is the probability that the number obtained is greater than 4?
A. 1/2
B. 1/3
C. 2/3
D. 1/6
Question 3
Solve the equation \sin(x) = \cos(x) for 0 ≤ x ≤ 2π.
A. π/4
B. 3π/4
C. π/2
D. 5π/4
Question 4
Find the derivative of the function f(x) = x^3 - 2x^2 + 5x - 1.
A. \boxed{3x^2 - 4x + 5}
B. x^2 - 2x + 5
C. x^3 - 2x^2 + 5
D. x^2 - 4x + 5
Question 5
Solve the inequality \( x^2 - 4x - 5 > 0 \).
A. \( x < -1 \) or \( x > 5 \)
B. \( x < 1 \) or \( x > 5 \)
C. \( x < -1 \) or \( x < 5 \)
D. \( x > 1 \) or \( x > 5 \)
Question 6
Find the derivative of the function f(x) = 3x^2 + 2x - 5 u\sing the chain rule.
A. 6x + 2
B. 6x - 2
C. 6x^2 + 2x
D. 6x^2 - 2x
Question 7
Solve the equation \( \sin^2 x + \cos^2 x = 1 \) for x.
A. \frac{\pi}{4}
B. \frac{\pi}{2}
C. \frac{3\pi}{4}
D. \pi
Question 8
If \( vec{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( vec{b} = egin{pmatrix} 1 \ -2 \end{pmatrix} \), find the magnitude of the vector \( vec{a} + vec{b} \).
A. 3.6
B. 4.2
C. 5.1
D. 6.3
Question 9
Find the equation of the circle pas\sing through the points (2, 3), (4, 1), and \( -1, 5 \).
A. x^2 + y^2 - 6x - 2y + 12 = 0
B. x^2 + y^2 + 6x - 2y + 12 = 0
C. x^2 + y^2 - 6x + 2y + 12 = 0
D. x^2 + y^2 + 6x + 2y + 12 = 0
Question 10
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 11
A circle has a radius of 5 cm. Find the area of the circle.
A. 25\pi
B. 50\pi
C. 75\pi
D. 100\pi
Question 12
Find the equation of the line pas\sing through the points (2, 3) and (4, 5).
A. y = 2x - 1
B. y = 2x + 1
C. y = x - 1
D. y = x + 1
Question 13
Find the equation of the circle pas\sing through the points (2, 3), (4, 1), and \( -1, 2 \).
A. \boxed{\( x - 1 \)^2 + \( y - 2 \)^2 = 5}
B. \( x - 2 \)^2 + \( y - 3 \)^2 = 5
C. \( x + 1 \)^2 + \( y - 2 \)^2 = 5
D. \( x - 1 \)^2 + \( y + 2 \)^2 = 5
Question 14
Solve for x in the equation \( 2^x + 5^x = 10^x \).
A. 2
B. 3
C. 4
D. 5
Question 15
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. \( x - 2 \ \)^2 + \( y + 3 \)^2 = 16 )
D. \( x + 2 \ \)^2 + \( y + 3 \)^2 = 16 )

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