POST UTME LEAD CITY UNIVERSITY 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the volume of the solid formed by rotating the region bounded by the curves y = x^2 and y = 4 - x^2 about the x-axis.
A. 16\pi
B. 32\pi
C. 64\pi
D. 128\pi
Question 2
Solve the system of equations \( x + y = 4 \) and \( xy = 5 \).
A. x = 1, y = 3
B. x = 2, y = 2
C. x = 3, y = 1
D. x = 4, y = 0
Question 3
A set of 5 numbers has a mean of 10. If 5 is added to each number, what is the new mean?
A. 12
B. 15
C. 10
D. 8
Question 4
A histogram of exam scores has a mean of 75 and a s\tandard deviation of 5. If the scores are normally distributed, find the probability that a randomly selected score is between 70 and 80.
A. 0.1587
B. 0.3413
C. 0.6915
D. 0.9772
Question 5
Find the volume of the frustum of a cone with height 6cm, lower base radius 4cm, and upper base radius 2cm.
A. 24π cm³
B. 48π cm³
C. 96π cm³
D. 192π cm³
Question 6
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
A. -2x/\( x^2 + 1 \)²
B. 2x/\( x^2 + 1 \)²
C. -2/\( x^2 + 1 \)²
D. 2/\( x^2 + 1 \)²
Question 7
Find the area under the curve y = 2x^2 + 3x - 1 from x = 0 to x = 2.
A. 10
B. 12
C. 15
D. 20
Question 8
In a right triangle, the length of the hypotenuse is 10 and one of the legs is 6. Find the length of the other leg.
A. 8
B. 6
C. 4
D. 2
Question 9
Find the equation of the line pas\sing through the points (1, 2) and (3, 4).
A. y = x + 1
B. y = x - 1
C. y = -x + 3
D. y = x - 3
Question 10
In a geometric sequence with first term (a) and common ratio (r), find the sum of the first 5 terms if \( a = 2 \) and \( r = 3 \).
A. 2 + 6 + 18 + 54 + 162
B. 2 + 6 + 18 + 54 + 162 + 486
C. 2 + 6 + 18 + 54 + 162 + 486 + 1458
D. 2 + 6 + 18 + 54 + 162 + 486 + 1458 + 4374
Question 11
Find the equation of the circle with center (2, 3) and radius 4.
A. \left\( x-2\right \)^2 + \left\( y-3\right \)^2 = 16
B. \left\( x-3\right \)^2 + \left\( y-2\right \)^2 = 16
C. \left\( x-4\right \)^2 + \left\( y-5\right \)^2 = 16
D. \left\( x-5\right \)^2 + \left\( y-4\right \)^2 = 16
Question 12
Solve the equation \frac{1}{x+1} + \frac{1}{x-1} = \frac{1}{2}
A. x = 2
B. x = -2
C. x = 1
D. x = -1
Question 13
Find the area under the curve \( y = \frac{1}{x^2 + 1} \) from \( x = 0 \) to \( x = 1 \).
A. \frac{1}{2} \arc\tan(x) \Big|_0^1
B. \frac{1}{2} \arc\tan(x) \Big|_0^1 + \frac{1}{2}
C. \frac{1}{2} \arc\tan(x) \Big|_0^1 - \frac{1}{2}
D. \frac{1}{2} \arc\tan(x) \Big|_0^1
Question 14
Solve the quadratic equation \( x^2 + 5x + 6 = 0 \) u\sing the quadratic formula.
A. \frac{-5 \pm \sqrt{5^2 - 4(1)(6)}}{2(1)}
B. \frac{-5 \pm \sqrt{5^2 - 4(1)(6)}}{2(1)}
C. \frac{-5 \pm \sqrt{5^2 - 4(1)(6)}}{2(1)}
D. \frac{-5 \pm \sqrt{5^2 - 4(1)(6)}}{2(1)}
Question 15
Find the equation of the circle with center (C(2, 3)) and radius 4.
A. \left\( x - 2 \right \)^2 + \left\( y - 3 \right \)^2 = 16
B. \left\( x - 3 \right \)^2 + \left\( y - 2 \right \)^2 = 16
C. \left\( x - 4 \right \)^2 + \left\( y - 5 \right \)^2 = 16
D. \left\( x - 5 \right \)^2 + \left\( y - 4 \right \)^2 = 16

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