POST UTME IGBINEDION UNIVERSITY 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 90?
A. 0.135
B. 0.25
C. 0.5
D. 0.75
Question 2
Find the volume of the solid formed by revolving the region bounded by the curves y = x^2 and y = 4 - x^2 about the x-axis.
A. \boxed{128\pi/3}
B. 64\pi/3
C. 256\pi/3
D. 512\pi/3
Question 3
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -infty, -1 \) cup (3, infty)
B. \( -infty, -3 \) cup (1, infty)
C. \( -infty, -1 \) cup (1, infty)
D. \( -infty, -3 \) cup (3, infty)
Question 4
Solve the inequality \( \frac{x}{x+1} > \frac{1}{x+1} \) for \( x in mathbb{R} setminus {-1} \).
A. x > 0
B. x < -1
C. x > -1
D. x < 0
Question 5
Find the equation of the line pas\sing through the points (1, 2) and (3, 4).
A. \boxed{y = x + 1}
B. y = x - 1
C. y = x + 2
D. y = x - 2
Question 6
Determine the value of $\frac{d}{dx} \left\( \frac{1}{x^2 + 1} \right \)$ u\sing the quotient rule.
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 7
A 3x3 matrix is given by \begin{pmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{pmatrix}. What is the determinant of the matrix?
A. 0
B. 3
C. 6
D. 9
Question 8
Find the determinant of the matrix \( egin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 1 & 3 & 2 \end{bmatrix} \).
A. 2
B. -2
C. 4
D. -4
Question 9
Solve the quadratic equation \( x^2 + 5x + 6 = 0 \) u\sing the quadratic formula. What is the value of x?
A. -2
B. -3
C. -1
D. 1
Question 10
A histogram of the scores of 10 students on a test is shown below. What is the mean score of the students?
A. 40
B. 42.5
C. 45
D. 50
Question 11
Solve the inequality $|x - 2| > 3$.
A. \( -∞, -1 \) ∪ (4, ∞)
B. \( -∞, 1 \) ∪ (4, ∞)
C. \( -∞, -1 \) ∪ (2, 4)
D. \( -∞, 1 \) ∪ (2, 4)
Question 12
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. \frac{1}{2}\( 4^2 \)(4) + 3(4)(4) - 2(4) = 32
B. \frac{1}{2}\( 4^2 \)(4) + 3(4)(4) - 2(4) = 40
C. \frac{1}{2}\( 4^2 \)(4) + 3(4)(4) - 2(4) = 48
D. \frac{1}{2}\( 4^2 \)(4) + 3(4)(4) - 2(4) = 56
Question 13
Solve the equation $\frac{2x}{x^2-4} = \frac{1}{x-2}$.
A. x = 2
B. x = -2
C. x = 4
D. x = -4
Question 14
Let X be a random variable with probability density function f(x) = \( \frac{1}{2}e^{-|x|} \) for -∞ < x < ∞. Find the probability that X is greater than 1.
A. 0.5
B. 0.6
C. 0.7
D. 0.8
Question 15
Solve the system of equations \( egin{cases} x + y = 4 \ x - 2y = -3 \end{cases} \).
A. (1, 3)
B. (3, 1)
C. (1, 1)
D. (3, 3)

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