POST UTME UNILORIN 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the system of equations: \( \begin{cases} x + y = 4 \ 2x - 3y = -3 \end{cases} \).
A. x = 1, y = 3
B. x = 2, y = 2
C. x = 3, y = 1
D. x = 4, y = 0
Question 2
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).
A. 0
B. -2
C. 2
D. -4
Question 3
Find the determinant of the matrix [ egin{pmatrix} 2 & 3 & 1 \ 4 & 1 & 2 \ 3 & 2 & 1 \end{pmatrix} ].
A. 13
B. -13
C. 0
D. 1
Question 4
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 5
A car travels from city A to city B at an average speed of 60 km/h and returns at an average speed of 40 km/h. What is the average speed for the round trip?
A. 48
B. 50
C. 52
D. 54
Question 6
A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. If the scores are normally distributed, find the probability that a randomly selected score is greater than 70.
A. \frac{1}{4}
B. \frac{1}{2}
C. \frac{3}{4}
D. \frac{2}{3}
Question 7
Solve the inequality 2x^2 - 5x - 3 > 0.
A. x < -1 or x > 3/2
B. x < -3/2 or x > 1
C. x < -1 or x < 3/2
D. x > -3/2 or x > 1
Question 8
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 = 4 )
C. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 9 )
D. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 25 )
Question 9
A histogram of exam scores has a mean of 75 and a s\tandard deviation of 5. If the scores are normally distributed, what is the probability that a randomly selected score is between 70 and 80?
A. 0.9772
B. 0.6827
C. 0.3413
D. 0.1587
Question 10
Find the volume of the frustum of a cone with height 10 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. \( \frac{1}{3} pi \( 4^2 + 2^2 + 4 cdot 2 cdot 4 \ \) )
B. \( \frac{1}{3} pi \( 4^2 + 2^2 - 4 cdot 2 cdot 4 \ \) )
C. \( \frac{1}{3} pi \( 4^2 + 2^2 + 2 cdot 4 cdot 2 \ \) )
D. \( \frac{1}{3} pi \( 4^2 + 2^2 - 2 cdot 4 cdot 2 \ \) )
Question 11
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 12
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x}} ) u\sing the chain rule.
A. \( \frac{-1}{2x^{3/2}} \)
B. \( \frac{-1}{2x^{5/2}} \)
C. \( \frac{1}{2x^{3/2}} \)
D. \( \frac{1}{2x^{5/2}} \)
Question 13
Solve the inequality \( \frac{x-2}{x+1} > 0 \).
A. \( x < -1 \) or \( x > 2 \)
B. \( x < -1 \) or \( x < 2 \)
C. \( x > -1 \) or \( x < 2 \)
D. \( x > -1 \) or \( x > 2 \)
Question 14
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. 24π cm^3
B. 48π cm^3
C. 96π cm^3
D. 192π cm^3
Question 15
Find the volume of the solid formed by revolving the region bounded by the parabola \( y = x^2 \), the x-axis, and the line \( x = 2 \) about the x-axis.
A. 64\pi
B. 128\pi
C. 256\pi
D. 512\pi

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