POST UTME ESUT 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the area under the curve of the function f(x) = 2x^2 + 3x - 1 from x = 0 to x = 2.
A. 17
B. 19
C. 21
D. 23
Question 2
Find the value of x in the equation \( \sin^2 x + \cos^2 x = 1 \) if \( \sin x = \frac{3}{5} \).
A. 0
B. \frac{\pi}{4}
C. \frac{\pi}{2}
D. \frac{3\pi}{4}
Question 3
Solve the equation \( x^3 - 6x^2 + 11x - 6 = 0 \) u\sing the rational root theorem.
A. 1
B. 2
C. 3
D. 4
Question 4
Find the derivative of the function y = x^4 - 2x^3 + 3x^2 - x + 1.
A. 4x^3 - 6x^2 + 6x - 1
B. 4x^3 - 6x^2 + 6x + 1
C. 4x^3 - 6x^2 - 6x + 1
D. 4x^3 + 6x^2 - 6x + 1
Question 5
A random sample of 25 students from a university had a mean height of 175.5 cm with a s\tandard deviation of 5.2 cm. Calculate the coefficient of variation (CV) of the sample.
A. 12.5%
B. 15%
C. 17.5%
D. 20%
Question 6
Solve the inequality \( \frac{x^2 - 4}{x + 2} geq 0 \) for \( x in \( -infty, -2 \ \) cup \( -2, infty \) ).
A. \( -2, -1 \) ∪ (1, ∞)
B. \( -∞, -2 \) ∪ \( -2, 1 \)
C. \( -∞, -2 \) ∪ (1, ∞)
D. \( -2, 1 \)
Question 7
Find the value of ( x ) that satisfies the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 8
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 9
A circle passes through the points (2,3), (4,5), and (6,7). Find the equation of the circle.
A. \( x - 4 \)^2 + \( y - 3 \)^2 = 5
B. \( x - 3 \)^2 + \( y - 4 \)^2 = 5
C. \( x - 5 \)^2 + \( y - 3 \)^2 = 5
D. \( x - 3 \)^2 + \( y - 5 \)^2 = 5
Question 10
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 11
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).
A. \( -2, 0 \)
B. \( -∞, -2 \) ∪ (0, ∞)
C. \( -∞, 0 \) ∪ (2, ∞)
D. \( -∞, -2 \) ∪ (2, ∞)
Question 12
A histogram shows the distribution of exam scores for a class of 50 students. The histogram has 5 bars, each representing a range of scores. The heights of the bars are 8, 12, 15, 10, and 5, respectively. Find the mean score of the class.
A. 10
B. 12
C. 15
D. 18
Question 13
Solve the inequality \[\frac{x^2 - 4}{x^2 - 9} > 0\].
A. \( -3, -2 \) \cup (2, 3)
B. \( -3, -2 \) \cup (2, 3) \cup \( -\infty, -3 \) \cup \( 3, \infty \)
C. \( -3, -2 \) \cup (2, 3) \cup \( -\infty, -3 \) \cup \( 3, \infty \) \cup (0, 1)
D. \( -3, -2 \) \cup (2, 3) \cup \( -\infty, -3 \) \cup \( 3, \infty \) \cup (0, 1) \cup (4, 5)
Question 14
A binary operation \oplus is defined as a \oplus b = \( a + b \)^2. Find the value of \( 2 \oplus 3 \).
A. 25
B. 27
C. 29
D. 31
Question 15
Solve the equation \( x^3 - 6x^2 + 11x - 6 = 0 \).
A. 1
B. 2
C. 3
D. 4

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