POST UTME RSU 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the derivative of the function [ f(x) = 3x^2 - 2x + 1 ].
A. ( f'(x) = 6x - 2 )
B. ( f'(x) = 6x + 2 )
C. ( f'(x) = 3x^2 - 2 )
D. ( f'(x) = 3x^2 + 2 )
Question 2
A right triangle has a hypotenuse of length 10 and one leg of length 6. What is the length of the other leg?
A. 4
B. 6
C. 8
D. 10
Question 3
Find the value of x in the equation \( 2^x + 5^x = 7^x \).
A. x = 2
B. x = 3
C. x = 4
D. x = 5
Question 4
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \) u\sing integration.
A. \( \frac{64}{3} \)
B. \( \frac{32}{3} \)
C. \( \frac{16}{3} \)
D. \( \frac{8}{3} \)
Question 5
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \).
A. 16
B. 32
C. 64
D. 128
Question 6
A histogram of exam scores is shown below. If the mean score is 75, and the s\tandard deviation is 10, what is the area under the curve between 60 and 80?
A. 0.5
B. 1.0
C. 1.5
D. 2.0
Question 7
Solve for x in the equation \( \frac{1}{2}x^2 + 5x - 3 = 0 \) u\sing the quadratic formula.
A. x = -10 \pm \sqrt{109}
B. x = -5 \pm \sqrt{13}
C. x = 3 \pm \sqrt{7}
D. x = -3 \pm \sqrt{11}
Question 8
Solve the inequality [ 2x - 5 > 3x + 2 ].
A. \( x < -\frac{7}{3} \)
B. \( x > -\frac{7}{3} \)
C. \( x < \frac{7}{3} \)
D. \( x > \frac{7}{3} \)
Question 9
Find the derivative of the function [ f(x) = \frac{1}{x^2} \].
A. f'(x) = -\frac{2}{x^3}
B. f'(x) = \frac{2}{x^3}
C. f'(x) = -\frac{1}{x^3}
D. f'(x) = \frac{1}{x^3}
Question 10
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -\infty, -1 \) \cup \( 3, \infty \)
B. \( -\infty, -1 \) \cup \( 1, \infty \)
C. \( -\infty, 1 \) \cup \( 3, \infty \)
D. \( -\infty, 1 \) \cup \( 1, \infty \)
Question 11
Let \( A = \begin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix} \). Find the determinant of ( A ).
A. -1
B. 1
C. 2
D. 3
Question 12
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).
A. -2
B. 0
C. 2
D. 4
Question 13
Find the equation of the circle with center at ((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 14
A random variable X has a probability distribution given by \( P\( X = x \ \) = \frac{1}{2} ) for \( x = 1, 2, 3 \). Find the probability that X is greater than 2.
A. \frac{1}{4}
B. \frac{1}{2}
C. \frac{3}{4}
D. \frac{1}{3}
Question 15
A curve is defined by the equation [ y = \frac{1}{x^2 + 1} \]. Find the derivative of this function 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}

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