POST UTME UNIPORT 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the equation $\frac{1}{2} \log_{10} \( x^2 \) = 4$ for $x$.
A. 10
B. 100
C. 1000
D. 10000
Question 2
A set of numbers has a mean of 10 and a s\tandard deviation of 2. Find the probability that a randomly selected number from the set is greater than 12.
A. 0.5
B. 0.6
C. 0.7
D. 0.8
Question 3
Solve the inequality [ 2x^2 - 5x - 3 > 0 ].
A. $x in \( -\infty, -1 \) \cup \( 3, \infty \)$
B. $x in \( -\infty, 1 \) \cup \( 3, \infty \)$
C. $x in \( -\infty, -3 \) \cup \( 1, \infty \)$
D. $x in \( -\infty, 3 \) \cup \( 1, \infty \)$
Question 4
Find the volume of the solid formed by rotating the region bounded by $y = x^2$ and $y = 4x$ about the x-axis.
A. \frac{256}{15}\pi
B. \frac{64}{3}\pi
C. \frac{32}{3}\pi
D. \frac{16}{3}\pi
Question 5
Find the determinant of the matrix $\begin{bmatrix}1&2&3\4&5&6\7&8&9\end{bmatrix}$.
A. 0
B. 1
C. -1
D. 2
Question 6
Find the area under the curve $y = \frac{1}{x^2 + 1}$ from $x = 0$ to $x = 1$.
A. \frac{\pi}{2}
B. \frac{\pi}{4}
C. \frac{\pi}{6}
D. \frac{\pi}{8}
Question 7
Find the value of x in the equation \( x^2 + 4x + 4 = 0 \).
A. -2
B. -1
C. 0
D. 1
Question 8
Determine the value of $\int_{0}^{\frac{\pi}{2}} \frac{\sin^2 x}{\cos^2 x + \sin^2 x} dx$.
A. \frac{\pi}{4}
B. \frac{\pi}{2}
C. \frac{\pi}{3}
D. \frac{\pi}{6}
Question 9
A circle has a radius of 4 cm. Find the area of the circle.
A. 50.24
B. 100.48
C. 150.72
D. 201.06
Question 10
Find the mean of the data set [ 2, 4, 6, 8, 10 ].
A. $6$
B. $8$
C. $10$
D. $12$
Question 11
Find the derivative of the function $f(x)=\frac{1}{x^2+1}$.
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 12
A particle moves in a straight line with a velocity given by $v(t) = 2t^2 - 5t + 3$. Find the acceleration at time $t = 2$ seconds.
A. 4
B. -3
C. 2
D. -2
Question 13
Find the area of the triangle with vertices ( A(1, 2) ), ( B(3, 4) ), and ( C(2, 1) ).
A. 5
B. 10
C. 15
D. 20
Question 14
Solve for y in the equation \( y = \frac{1}{2} \( 3x + 5 \ \) ) when x = 2.
A. 4
B. 6
C. 8
D. 10
Question 15
Find the value of $x$ in the equation [ \log_{10} \( x^2 \) = 4 ].
A. $10^4$
B. $10^2$
C. $10^{-2}$
D. $10^{-4}$

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