POST UTME ABU 2023 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 will be between 60 and 90?
A. 0.8413
B. 0.8413
C. 0.8413
D. 0.8413
Question 2
A random experiment consists of rolling a fair six-sided die. What is the probability that the sum of the numbers on the two dice is 7?
A. 1/6
B. 1/3
C. 1/2
D. 2/3
Question 3
A binary operation \( \ast \) is defined as: \( a \ast b = ab + 2 \). Find \( 2 \ast 3 \).
A. 8
B. 10
C. 12
D. 14
Question 4
Solve the equation \( x^2 + 4x + 4 = 0 \).
A. x = -2
B. x = 2
C. x = -1
D. x = 1
Question 5
Find the surface area of the solid formed by rotating the region bounded by the curves y = x^2 and y = 2x about the x-axis.
A. \frac{\pi}{3}
B. \frac{\pi}{2}
C. \frac{\pi}{4}
D. \frac{\pi}{6}
Question 6
A circle has a radius of 4 cm. Find the area of the circle.
A. 50.24 cm^2
B. 100.48 cm^2
C. 50.24 cm^2
D. 25.12 cm^2
Question 7
A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 50 and 70?
A. 0.68
B. 0.84
C. 0.95
D. 0.99
Question 8
A fair six-sided die is rolled. If the outcome is an even number, the die is rolled again. If the outcome is an odd number, the die is rolled three more times. What is the probability that the sum of the outcomes is 10?
A. \frac{1}{36}
B. \frac{1}{18}
C. \frac{1}{12}
D. \frac{1}{6}
Question 9
Find the equation of the circle with center (2, 3) and radius 4.
A. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 3 \)^2 + \( y - 2 \)^2 = 16
C. \( x - 4 \)^2 + \( y - 3 \)^2 = 16
D. \( x - 3 \)^2 + \( y - 4 \)^2 = 16
Question 10
A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find the volume of the prism.
A. 30 cm^3
B. 50 cm^3
C. 60 cm^3
D. 70 cm^3
Question 11
Determine the value of x in the equation \( \frac{1}{x} + \frac{1}{x+1} = \frac{1}{2} \).
A. 1
B. 2
C. 3
D. 4
Question 12
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
A. -2x/\( x^2 + 1 \)^2
B. 2x/\( x^2 + 1 \)^2
C. -2/\( x^2 + 1 \)^2
D. 2/\( x^2 + 1 \)^2
Question 13
Find the equation of the line pas\sing through the points ( (1, 2) ) and ( (3, 4) ).
A. \( y = 2x - 1 \)
B. \( y = 2x + 1 \)
C. \( y = 2x - 2 \)
D. \( y = 2x + 2 \)
Question 14
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 15
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. x < -1
B. x > -1
C. x < 1
D. x > 1

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