POST UTME UNILORIN 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the determinant of the matrix \( egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \).
A. 0
B. 1
C. 2
D. 3
Question 2
In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the other sides is 6 cm. Find the length of the third side u\sing the Pythagorean theorem.
A. 8 cm
B. 12 cm
C. 14 cm
D. 16 cm
Question 3
A cylindrical \tank with a radius of 5m and a height of 10m is filled with water. Find the volume of water in the \tank.
A. 785
B. 785.4
C. 785.5
D. 785.6
Question 4
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 is greater than 90?
A. ( 0.1587 )
B. ( 0.3413 )
C. ( 0.5 )
D. ( 0.8413 )
Question 5
Determine the equation of the \tangent line to the curve \( y = \frac{1}{x} \) at the point ( (1, 1) ).
A. \( y = x - 1 \)
B. \( y = x + 1 \)
C. \( y = -x + 1 \)
D. \( y = x - 2 \)
Question 6
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 7
A fair six-sided die is rolled twice. What is the probability that the sum of the two numbers shown is greater than 9?
A. \( \frac{1}{6} \)
B. \( \frac{1}{3} \)
C. \( \frac{5}{36} \)
D. \( \frac{1}{2} \)
Question 8
Solve the inequality \( 2x^2 + 5x - 3 > 0 \) u\sing the quadratic formula.
A. \( x < -\frac{5}{4} \) or \( x > \frac{3}{2} \)
B. \( x < -\frac{3}{2} \) or \( x > -\frac{5}{4} \)
C. \( x < -\frac{5}{4} \) or \( x < \frac{3}{2} \)
D. \( x > -\frac{3}{2} \) or \( x > \frac{5}{4} \)
Question 9
Solve the inequality \( \frac{x^2 - 4}{x + 2} > 0 \) for ( x in mathbb{R} ).
A. \( x < -2 \) or \( x > 2 \)
B. \( x > -2 \) or \( x < 2 \)
C. \( x < -2 \) or \( x = 2 \)
D. \( x > -2 \) or \( x = 2 \)
Question 10
Find the equation of the line pas\sing through the points (2, 3) and (4, 5).
A. y = x + 1
B. y = x - 1
C. y = -x + 1
D. y = x - 2
Question 11
The histogram below shows the distribution of exam scores for a class of 50 students. What is the mean score?
A. 60
B. 70
C. 80
D. 90
Question 12
Find the determinant of the matrix \( egin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 1 & 3 & 2 \end{bmatrix} \).
A. ( 0 )
B. ( 1 )
C. \( -1 \)
D. ( 2 )
Question 13
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, 1 \) ∪ (3, ∞)
C. \( -∞, -1 \) ∪ (1, ∞)
D. \( -∞, 3 \) ∪ (1, ∞)
Question 14
Determine the value of x in the equation \( \sin^2\( x \ \) + \cos^2(x) = 1 ) if \( \sin\( x \ \) = \frac{3}{5} ).
A. \( \frac{4pi}{3} \)
B. \( \frac{5pi}{3} \)
C. \( \frac{2pi}{3} \)
D. \( \frac{pi}{3} \)
Question 15
Solve the system of equations \begin{align*} x + y &= 4 \ x - 2y &= 2 \end{align*}.
A. \begin{pmatrix} 2 \ 2 \end{pmatrix}
B. \begin{pmatrix} 1 \ 3 \end{pmatrix}
C. \begin{pmatrix} 3 \ 1 \end{pmatrix}
D. \begin{pmatrix} 4 \ 0 \end{pmatrix}

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