POST UTME ABU 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve for x in the equation \( \frac{1}{x} + \frac{1}{x+1} = \frac{1}{2} \).
A. \( x = -1 \)
B. \( x = 2 \)
C. \( x = -2 \)
D. \( x = 1 \)
Question 2
A number is divisible by 2, 3, and 5. What is the least common multiple (LCM) of these numbers?
A. 30
B. 60
C. 90
D. 120
Question 3
Solve the system of equations \( x + y = 2 \) and \( x - y = 1 \).
A. \( x = 1, y = 1 \)
B. \( x = 1, y = 2 \)
C. \( x = 2, y = 1 \)
D. \( x = 2, y = 2 \)
Question 4
A diagram of a circuit is shown below. If the voltage source is 12V and the resis\tance is 4Ω, what is the current flowing through the circuit?
A. 1A
B. 2A
C. 3A
D. 4A
Question 5
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, -3 \) ∪ (1, ∞)
C. \( -∞, 1 \) ∪ (3, ∞)
D. \( -∞, -3 \) ∪ (1, ∞)
Question 6
In the diagram below, ( ABC ) is a right-angled triangle with \( AB = 3 \) and \( BC = 4 \). Find the length of the hypotenuse ( AC ).
A. 5
B. 7
C. 9
D. 11
Question 7
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 8
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 9
Solve the system of linear equations u\sing matrices:\n\( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix} \).
A. \( egin{bmatrix} 2 \ 1 \end{bmatrix} \)
B. \( egin{bmatrix} 1 \ 2 \end{bmatrix} \)
C. \( egin{bmatrix} 3 \ 4 \end{bmatrix} \)
D. \( egin{bmatrix} 4 \ 3 \end{bmatrix} \)
Question 10
Find the derivative of the function ( f(x) = \frac{1}{2x^2 + 3x - 1} ) u\sing the quotient rule.
A. \( \frac{-2x + 3}{\( 2x^2 + 3x - 1 \ \)^2} )
B. \( \frac{2x + 3}{\( 2x^2 + 3x - 1 \ \)^2} )
C. \( \frac{2x - 3}{\( 2x^2 + 3x - 1 \ \)^2} )
D. \( \frac{3x + 2}{\( 2x^2 + 3x - 1 \ \)^2} )
Question 11
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 12
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 13
Solve the equation \( x^2 + 4x + 4 = 0 \).
A. x = -2
B. x = 2
C. x = -1
D. x = 1
Question 14
A die is rolled twice. Find the probability that the sum of the two numbers is 7.
A. 1/6
B. 1/12
C. 1/36
D. 1/24
Question 15
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

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