POST UTME CALEB UNIVERSITY 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the determinant of the matrix [ egin{pmatrix} 2 & 3 & 4 \ 5 & 6 & 7 \ 8 & 9 & 10 \end{pmatrix} ].
A. 0
B. -1
C. 1
D. 2
Question 2
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 3
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 )
Question 4
Find the area under the curve y = x^2 + 2x - 3 from x = 0 to x = 2.
A. \boxed{\frac{11}{3}}
B. \frac{13}{3}
C. \frac{15}{3}
D. \frac{17}{3}
Question 5
Solve the quadratic equation \( x^2 + 5x + 6 = 0 \) u\sing the quadratic formula.
A. -2
B. -3
C. 1
D. 4
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
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 8
A histogram of exam scores is shown below. If the mean score is 60, what is the median?
A. 60
B. 65
C. 70
D. 75
Question 9
Find the mean of the numbers 2, 4, 6, 8, 10.
A. 6
B. 7
C. 8
D. 9
Question 10
Find the value of x in the equation \( \frac{x}{2} + 3 = 7 \).
A. 4
B. 5
C. 6
D. 7
Question 11
A particle moves in a straight line with a velocity of 5 m/s. If the acceleration is 2 m/s^2, find the dis\tance traveled in 4 seconds.
A. 20 m
B. 30 m
C. 40 m
D. 50 m
Question 12
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 13
Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 24\pi
B. 48\pi
C. 96\pi
D. 192\pi
Question 14
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ \) )
B. \( \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ \) + 3 )
C. \( \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ \) - 2 )
D. \( \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ \) + 2 )
Question 15
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

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