POST UTME VERITAS UNIVERSITY 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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{1}{\( x^2 + 1 \)^2}
D. \frac{1}{\( x^2 + 1 \)^2}
Question 2
Find the area under the curve y = x^3 from x = 0 to x = 2 u\sing integration by parts.
A. 8
B. 16
C. 32
D. 64
Question 3
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 40
B. 50
C. 60
D. 70
Question 4
A sequence is given by the formula: \[ a_n = 2n^2 + 3n - 1 \]. Find the value of the 6th term.
A. 109
B. 119
C. 129
D. 139
Question 5
A circle has a radius of 5 and a center at ( (0, 0) ). Find the equation of the circle in s\tandard form.
Question 6
The sum of the first n terms of an arithmetic progression is given by the formula: \[ S_n = \frac{n}{2} \( 2a + \( n-1 \ \)d) \]. If the sum of the first 5 terms is 25, and the first term is 3, find the common difference d.
A. 2
B. 3
C. 4
D. 5
Question 7
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, -3 \) ∪ (1, ∞)
C. \( -∞, 1 \) ∪ (3, ∞)
D. \( -∞, -3 \) ∪ (1, ∞)
Question 8
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 9
A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 50 and 70?
A. 0.135
B. 0.341
C. 0.691
D. 0.841
Question 10
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\( y - 3 \right \)^2 = 16
D. \left\( x - 2 \right \)^2 + \left\( y - 4 \right \)^2 = 16
Question 11
A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score will be between 60 and 90?
A. 0.6827
B. 0.3413
C. 0.8413
D. 0.1587
Question 12
A water \tank has a capacity of 1000 liters. Water is flowing into the \tank at a rate of 5 liters per minute. Find the time taken to fill the \tank.
A. 200 minutes
B. 100 minutes
C. 50 minutes
D. 20 minutes
Question 13
A right-angled triangle has a hypotenuse of length 10 cm and one leg of length 6 cm. Find the length of the other leg.
A. 8 cm
B. 6 cm
C. 10 cm
D. 12 cm
Question 14
A random sample of 25 students from a university had a mean height of 175 cm with a s\tandard deviation of 5 cm. Calculate the s\tandard error of the mean.
A. 1
B. 1.25
C. 1.5
D. 2
Question 15
A circle has a radius of 4 cm. Find the area of the circle u\sing the formula A = πr^2.
A. 16\pi
B. 32\pi
C. 64\pi
D. 128\pi

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