POST UTME UNIBEN 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the equation $\begin{vmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{vmatrix} = 0$.
A. 1
B. 2
C. 3
D. 4
Question 2
Solve the equation $\frac{x^2-4x+3}{x^2-4x+4} = \frac{x-1}{x-2}$.
A. x = 1
B. x = 2
C. x = 3
D. x = 4
Question 3
Let ( f(x) = \frac{1}{x^2 + 1} ). Find the value of \( int_{0}^{1} f\( x \ \) , dx ).
A. \( \frac{\pi}{4} \)
B. \( \frac{\pi}{2} \)
C. \( \frac{\pi}{6} \)
D. \( \frac{\pi}{3} \)
Question 4
Find the sum of the infinite geometric series \( \sum_{n=1}^\infty \frac{1}{2^n} \ \).
A. 1
B. \( \frac{1}{2} \)
C. \( \frac{1}{4} \)
D. \( \frac{1}{8} \)
Question 5
Find the value of x in the set {1, 2, 3, 4, 5} such that x is the median of the set.
A. 2
B. 3
C. 4
D. 5
Question 6
Find the sum of the first 5 terms of the geometric series 2, 6, 18, 54, ...
A. 242
B. 242.5
C. 243
D. 243.5
Question 7
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 8
Solve the inequality $\log_2 \( x^2 + 1 \) > 3$.
A. \( -\infty, -\sqrt{7}] \cup [\sqrt{7}, \infty \)
B. \( -\infty, -\sqrt{7} \) \cup [\sqrt{7}, \infty)
C. \( -\infty, -\sqrt{7}] \cup \( -\sqrt{7}, \sqrt{7} \ \) \cup [\sqrt{7}, \infty)
D. \( -\infty, -\sqrt{7} \) \cup \( -\sqrt{7}, \sqrt{7} \) \cup [\sqrt{7}, \infty)
Question 9
Solve for x in the equation 2^x + 2^x = 2^x + 2^x + 2^x.
A. 0
B. 1
C. 2
D. 3
Question 10
Find the area under the curve y = x^2 + 2x - 3 from x = 0 to x = 3.
A. 27
B. 30
C. 33
D. 36
Question 11
Find the value of x in the equation \( \sin^2\( x \ \) + \cos^2(x) = 1 ), given that \( \sin\( x \ \) = \frac{3}{5} ).
A. 0
B. π/2
C. π
D. 3π/2
Question 12
Let \( \mathbf{a} = \begin{pmatrix} 1 \ 2 \ 3 \end{pmatrix} \) and \( \mathbf{b} = \begin{pmatrix} 4 \ 5 \ 6 \end{pmatrix} \). Find the value of \( \mathbf{a} \cdot \mathbf{b} \).
A. 32
B. 40
C. 48
D. 56
Question 13
A vector \overrightarrow{a} has a magnitude of 5 units and makes an angle of 30° with the positive x-axis. Find the x-component of the vector.
A. 4.33
B. 4.58
C. 4.83
D. 5.00
Question 14
Solve the system of equations x + y = 4 and x - y = 2 u\sing the method of substitution.
A. x = 3, y = 1
B. x = 1, y = 3
C. x = 2, y = 2
D. x = 4, y = 0
Question 15
Find the derivative of the function f(x) = 3x^2 + 2x - 5 u\sing the chain rule.
A. 6x + 2
B. 6x + 2 - 5
C. 6x + 2x - 5
D. 6x^2 + 2x - 5

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