POST UTME OSUSTECH 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve for y in the equation \( y = \frac{1}{2}x^2 + 3x - 2 \).
A. x^2 + 6x - 4
B. x^2 + 2x - 1
C. x^2 + 4x - 3
D. x^2 + 8x - 6
Question 2
Find the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 3
A vector $\mathbf{a}$ has magnitude 5 and direction $\theta=30^\circ$. Find the $x$-component of $\mathbf{a}$.
A. 2.5
B. -2.5
C. 5
D. -5
Question 4
Solve for x in the equation \( 2^x = 32 \).
A. 5
B. 6
C. 7
D. 8
Question 5
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. \( \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 \( 4^2 + 2^2 + 4 cdot 2 cdot 2 \ \) )
D. \( \frac{1}{3} pi \( 4^2 + 2^2 - 4 cdot 2 cdot 2 \ \) )
Question 6
Solve the inequality \( 2x^3 - 5x^2 - 3x + 2 > 0 \).
A. \( x < -1 \) or \( x > 2 \)
B. \( x < -2 \) or \( x > 1 \)
C. \( x < 1 \) or \( x > 2 \)
D. \( x < -1 \) or \( x < 2 \)
Question 7
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. x < -1 or x > \frac{3}{2}
B. x > -1 or x < \frac{3}{2}
C. x < -1 or x < \frac{3}{2}
D. x > -1 or x > \frac{3}{2}
Question 8
Find the value of x in the quadratic equation \( x^2 + 5x - 6 = 0 \).
A. 2
B. -3
C. 1
D. -2
Question 9
Solve the quadratic equation: x^2 + 5x + 6 = 0
A. -2
B. -3
C. 1
D. 2
Question 10
A histogram is shown below. If the area under the curve is 20, what is the value of ( x )?
A. 5
B. 10
C. 15
D. 20
Question 11
Find the sum of the first 10 terms of the geometric series 2x^2 + 4x^3 + 8x^4 + ...
A. 2048x^{10}
B. 4096x^{10}
C. 8192x^{10}
D. 16384x^{10}
Question 12
Determine the value of $\int_0^\pi\frac{1}{1+\sin^2x}dx$.
A. \frac{\pi}{2}
B. \frac{\pi}{4}
C. \frac{\pi}{3}
D. \frac{\pi}{1}
Question 13
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. \frac{32\pi}{5}
B. \frac{64\pi}{5}
C. \frac{128\pi}{5}
D. \frac{256\pi}{5}
Question 14
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. \( \frac{1}{4} \)
B. \( \frac{1}{2} \)
C. \( \frac{2}{3} \)
D. \( \frac{3}{4} \)
Question 15
Let A = {1, 2, 3, 4, 5} and B = {2, 3, 4, 5, 6}. Find the number of elements in the set A \cup B.
A. 5
B. 6
C. 7
D. 8

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