POST UTME UNIOSUN 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the system of linear equations \begin{align*} x + y &= 4 \ 2x - 3y &= 5 \end{align*} u\sing matrices.
A. \begin{pmatrix} 2 \ 1 \end{pmatrix}
B. \begin{pmatrix} 1 \ 2 \end{pmatrix}
C. \begin{pmatrix} -1 \ 2 \end{pmatrix}
D. \begin{pmatrix} 1 \ -1 \end{pmatrix}
Question 2
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( x < -1 \) or \( x > \frac{3}{2} \)
B. \( x < -\frac{3}{2} \) or \( x > 1 \)
C. \( x < -\frac{1}{2} \) or \( x > 3 \)
D. \( x < 1 \) or \( x > -3 \)
Question 3
Find the vector product of vectors A = (2, 3, 4) and B = (1, 2, 3).
A. \( 3, -7, -5 \)
B. \( 7, -3, 5 \)
C. \( -3, 7, 5 \)
D. \( 5, -7, 3 \)
Question 4
Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 24\pi cm^3
B. 48\pi cm^3
C. 96\pi cm^3
D. 192\pi cm^3
Question 5
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 between 60 and 90?
A. 0.9544
B. 0.9772
C. 0.9987
D. 0.9999
Question 6
A fair six-sided die is rolled. What is the probability that the number obtained is a multiple of 3?
A. 1/6
B. 1/3
C. 2/3
D. 5/6
Question 7
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 8
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{2}{\( x^2 + 1 \)^2}
D. \frac{2}{\( x^2 + 1 \)^2}
Question 9
Find the volume of the solid formed by revolving the region bounded by the parabola y = x^2 and the line y = 4 about the x-axis.
A. \boxed{\frac{32\pi}{3}}
B. \frac{16\pi}{3}
C. \frac{64\pi}{3}
D. \frac{128\pi}{3}
Question 10
Find the sum of the first 5 terms of the geometric sequence ( 2, 6, 18, 54, ... ).
A. 242
B. 242.5
C. 242.8
D. 243
Question 11
Solve the quadratic equation x^2 + 5x + 6 = 0.
A. x = -2
B. x = -3
C. x = 2
D. x = 3
Question 12
Solve for x in the equation 2^x + 3^x = 5^x.
A. x = 2
B. x = 3
C. x = 4
D. x = 5
Question 13
Solve the system of equations u\sing matrices: \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix} \).
A. \( egin{bmatrix} -1 \ 2 \end{bmatrix} \)
B. \( egin{bmatrix} 1 \ -2 \end{bmatrix} \)
C. \( egin{bmatrix} 2 \ -1 \end{bmatrix} \)
D. \( egin{bmatrix} -2 \ 1 \end{bmatrix} \)
Question 14
Find the determinant of the matrix \begin{pmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 3 & 1 & 2 \end{pmatrix} u\sing cofactor expansion.
A. 0
B. 1
C. -1
D. 2
Question 15
Find the sum of the first 10 terms of the geometric series \( 2 + 6 + 18 + \cdots \).
A. 2040
B. 2050
C. 2060
D. 2070

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