POST UTME UNIPORT 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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. \( x < -1 \) or \( x < \frac{3}{2} \)
D. \( x > -1 \) or \( x < \frac{3}{2} \)
Question 2
A fair six-sided die is rolled. What is the probability that the number rolled is a multiple of 3?
A. \( \frac{1}{6} \)
B. \( \frac{1}{3} \)
C. \( \frac{2}{3} \)
D. \( \frac{5}{6} \)
Question 3
A circle passes through the points (0, 2), (2, 0), and \( 0, -2 \). Find the equation of the circle.
A. x^2 + y^2 = 4
B. x^2 + y^2 = 8
C. x^2 + y^2 = 16
D. x^2 + y^2 = 32
Question 4
Solve the equation 2x + 5y = 11, where x and y are vectors.
A. x = 2, y = 1
B. x = 3, y = 2
C. x = 4, y = 3
D. x = 5, y = 4
Question 5
Express the number 456 in base 8.
A. 720
B. 721
C. 722
D. 723
Question 6
Find the equation of the circle with center (2, 3) and radius 4.
A. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 3 \)^2 + \( y - 2 \)^2 = 16
C. \( x - 4 \)^2 + \( y - 3 \)^2 = 16
D. \( x - 3 \)^2 + \( y - 4 \)^2 = 16
Question 7
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 2 \) u\sing integration.
A. \( \frac{8}{3} \)
B. \( \frac{16}{3} \)
C. \( \frac{32}{3} \)
D. \( \frac{64}{3} \)
Question 8
Find the volume of the solid formed by revolving the region bounded by the curve y = x^2, the x-axis, and the line x = 2 about the x-axis.
A. \frac{32\pi}{5}
B. \frac{64\pi}{5}
C. \frac{128\pi}{5}
D. \frac{256\pi}{5}
Question 9
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 10
A box contains 5 red balls and 3 blue balls. If 2 balls are drawn at random, what is the probability that both balls are red?
A. \( \frac{1}{14} \)
B. \( \frac{5}{14} \)
C. \( \frac{9}{14} \)
D. \( \frac{13}{14} \)
Question 11
A histogram of exam scores is shown below. What is the mean score of the exam?
A. 60
B. 70
C. 80
D. 90
Question 12
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( x < -\frac{3}{2} \) or \( x > \frac{1}{2} \)
B. \( x < -\frac{1}{2} \) or \( x > \frac{3}{2} \)
C. \( x < -\frac{3}{2} \) or \( x < \frac{1}{2} \)
D. \( x > -\frac{3}{2} \) or \( x < \frac{1}{2} \)
Question 13
Find the area of the region bounded by the curves $y = x^2$ and $y = 2x$.
A. \frac{4}{3}
B. \frac{2}{3}
C. \frac{1}{3}
D. \frac{1}{2}
Question 14
Solve the equation x^4 - 6x^3 + 11x^2 - 6x - 20 = 0.
A. \( x - 1 \)\( x + 2 \)\( x^2 - 3x + 10 \) = 0
B. \( x - 2 \)\( x + 1 \)\( x^2 - 4x + 5 \) = 0
C. \( x - 3 \)\( x + 4 \)\( x^2 - 2x - 5 \) = 0
D. \( x - 4 \)\( x + 3 \)\( x^2 - x - 6 \) = 0
Question 15
In a triangle $ABC$, if $\tan A = \frac{1}{2}$ and $\tan B = \frac{1}{3}$, find $\tan C$.
A. \frac{11}{7}
B. \frac{7}{11}
C. \frac{5}{3}
D. \frac{3}{5}

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