POST UTME AAUA 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A random variable $X$ has a probability distribution given by $P\( X = x \) = \frac{1}{x^2}$ for $x = 1, 2, 3, \dots$. Find the probability that $X$ is greater than 2.
A. 0.25
B. 0.5
C. 0.75
D. 1
Question 2
A vector →A = 3→i + 4→j has a magnitude of 5 units. What is the value of the vector →B = 2→i + k→k?
A. 2→i + 3→k
B. 3→i + 4→k
C. 4→i + 5→k
D. 5→i + 6→k
Question 3
Solve the system of equations \( x + y = 4 \) and \( 2x - 3y = 5 \).
A. \( x = 2, y = 2 \)
B. \( x = 3, y = 1 \)
C. \( x = 4, y = 0 \)
D. \( x = 1, y = 3 \)
Question 4
A solid is formed by revolving the region bounded by \( y = x^2 \) and \( y = 2x \) about the x-axis. Find the volume of the solid.
A. 16π
B. 32π
C. 64π
D. 128π
Question 5
Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.
A. \( 2\( 1 - 3^{10} \ \)/\( 1 - 3 \) )
B. \( 2\( 3^{10} - 1 \ \)/\( 3 - 1 \) )
C. \( 2\( 3^{11} - 1 \ \)/\( 3 - 1 \) )
D. \( 2\( 3^{10} + 1 \ \)/\( 3 - 1 \) )
Question 6
Find the derivative of ( f(x) = \frac{x^2}{x^2 + 1} ) u\sing the quotient rule.
A. ( f'(x) = \frac{2x}{\( x^2 + 1 \)^2} )
B. ( f'(x) = \frac{2x^3 + 2x}{\( x^2 + 1 \)^2} )
C. ( f'(x) = \frac{2x^3 - 2x}{\( x^2 + 1 \)^2} )
D. ( f'(x) = \frac{2x^3 + 2}{\( x^2 + 1 \)^2} )
Question 7
A random variable X has a probability distribution given by ( P(X) = \frac{1}{2} \) for \( X = 0 \ \) and ( P(X) = \frac{1}{2} \) for \( X = 1 \ \). Find the probability that X is greater than 0.5.
A. 0.25
B. 0.5
C. 0.75
D. 1
Question 8
In a 3x3 matrix, if the determinant is 24, and one of the elements is 4, what is the sum of the other two elements in the same row?
A. 6
B. 8
C. 10
D. 12
Question 9
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 10
Find the area under the curve $y = \frac{1}{x^2 + 1}$ from $x = 0$ to $x = 1$.
A. 0.5
B. 1
C. 1.5
D. 2
Question 11
A 3x3 matrix has a determinant of 24. If one of the elements is 4, what is the sum of the other two elements in the same row?
A. 6
B. 8
C. 10
D. 12
Question 12
In a random experiment, two events A and B are indep\endent. If P(A) = 0.4 and P(B) = 0.3, what is the probability that both events occur?
A. 0.12
B. 0.24
C. 0.36
D. 0.48
Question 13
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 greater than 70?
A. 0.1587
B. 0.3413
C. 0.5
D. 0.8413
Question 14
Solve the equation \( x^2 + 2x + 1 = 0 \) u\sing the quadratic formula.
A. 0
B. -1
C. 1
D. -2
Question 15
A quadratic equation has roots \( x = 1 \) and \( x = 2 \). Find the equation of the axis of symmetry.
A. \( x = 0.5 \)
B. \( x = 1.5 \)
C. \( x = 2.5 \)
D. \( x = 3.5 \)

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