POST UTME UNIPORT 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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 2
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 3
Find the mean of the data set [ 2, 4, 6, 8, 10 ].
A. $6$
B. $8$
C. $10$
D. $12$
Question 4
Solve the inequality $\frac{2x-1}{x+2}>0$.
A. \( -\infty,-2)\cup\( \frac{1}{2},\infty \ \)
B. \( -\infty,-2)\cup\( \frac{1}{2},\infty \ \)
C. \( -\infty,-2)\cup\( \frac{1}{2},\infty \ \)
D. \( -\infty,-2)\cup\( \frac{1}{2},\infty \ \)
Question 5
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 6
Solve the equation $\frac{1}{2} \log_{10} \( x^2 \) = 4$ for $x$.
A. 10
B. 100
C. 1000
D. 10000
Question 7
Find the equation of the circle with center $(2,3)$ and radius $4$.
A. $x^2 + y^2 - 4x - 6y + 13 = 0$
B. $x^2 + y^2 - 4x - 6y + 25 = 0$
C. $x^2 + y^2 - 4x - 6y + 9 = 0$
D. $x^2 + y^2 - 4x - 6y + 1 = 0$
Question 8
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 9
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 10
Find the sum of the first 5 terms of the geometric series \( 2 + 6 + 18 + \ldots \).
A. 2 + 6 + 18 + 54 + 162 = 242
B. 2 + 6 + 18 + 54 + 162 = 242
C. 2 + 6 + 18 + 54 + 162 = 242
D. 2 + 6 + 18 + 54 + 162 = 242
Question 11
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 12
Find the value of $x$ in the equation [ \log_{10} \( x^2 \) = 4 ].
A. $10^4$
B. $10^2$
C. $10^{-2}$
D. $10^{-4}$
Question 13
Find the value of x in the equation \( x^2 + 4x + 4 = 0 \).
A. -2
B. -1
C. 0
D. 1
Question 14
Find the area of the triangle with vertices $A(0,0), B(3,0), C(1,2)$.
A. 4
B. 6
C. 8
D. 10
Question 15
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x^2 + 1}} ) u\sing the chain rule.
A. f'(x) = \frac{-x}{\( x^2 + 1 \)^{3/2}}
B. f'(x) = \frac{x}{\( x^2 + 1 \)^{3/2}}
C. f'(x) = \frac{1}{\( x^2 + 1 \)^{3/2}}
D. f'(x) = \frac{-1}{\( x^2 + 1 \)^{3/2}}

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