POST UTME ABU 2023 Mathematics | Objective

Are you preparing for POST UTME ABU exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2023 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1
Solve for x in the equation \( \frac{1}{x} + \frac{1}{x+1} = \frac{1}{2} \).
A. \( x = -1 \)
Correct B. \( x = 2 \)
C. \( x = -2 \)
D. \( x = 1 \)

Correct Answer: B

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Question 2
Find the value of \( \sin^2 30^circ + \cos^2 30^circ \).
Correct A. \( \frac{1}{2} \)
B. \( \frac{3}{4} \)
C. \( \frac{1}{4} \)
D. ( 1 )

Correct Answer: A

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Question 3
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
Correct 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 \( x < \frac{3}{2} \)

Correct Answer: A

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Question 4
Find the equation of the line pas\sing through the points ( (1, 2) ) and ( (3, 4) ).
Correct A. \( y = 2x - 1 \)
B. \( y = 2x + 1 \)
C. \( y = 2x - 2 \)
D. \( y = 2x + 2 \)

Correct Answer: A

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Question 5
Solve the system of equations \( x + y = 2 \) and \( x - y = 1 \).
Correct A. \( x = 1, y = 1 \)
B. \( x = 1, y = 2 \)
C. \( x = 2, y = 1 \)
D. \( x = 2, y = 2 \)

Correct Answer: A

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Question 6
Solve for x in the equation \( \frac{1}{x+2} + \frac{1}{x-3} = \frac{1}{2} \).
A. x = -5
Correct B. x = 1
C. x = 2
D. x = 3

Correct Answer: B

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Question 7
Find the volume of the solid formed by rotating the region bounded by the curves \( y = x^2 \) and \( y = 4x \) about the x-axis.
A. 64\pi
B. 128\pi
Correct C. 256\pi
D. 512\pi

Correct Answer: C

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Question 8
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
Correct C. 9
D. 11

Correct Answer: C

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Question 9
A particle moves along the x-axis with its position given by the equation ( x(t) = 2t^2 + 5t - 3 ). Find the velocity of the particle at time \( t = 2 \).
A. 10
Correct B. 13
C. 16
D. 19

Correct Answer: B

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Question 10
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. x < -1
B. x > -1
Correct C. x < 1
D. x > 1

Correct Answer: C

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Question 11
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10^4
Correct B. 10^8
C. 10^2
D. 10^6

Correct Answer: B

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Question 12
Find the equation of the circle with center (2, 3) and radius 4.
Correct 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

Correct Answer: A

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Question 13
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
Correct A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, -3 \) ∪ (1, ∞)
C. \( -∞, 1 \) ∪ (3, ∞)
D. \( -∞, -3 \) ∪ (1, ∞)

Correct Answer: A

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Question 14
Find the value of \( \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} \).
A. 1
B. 2
C. 3
Correct D. 4

Correct Answer: D

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Question 15
Solve the equation \( x^2 + 4x + 4 = 0 \).
Correct A. x = -2
B. x = 2
C. x = -1
D. x = 1

Correct Answer: A

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Question 16
Find the derivative of the function ( f(x) = \frac{1}{2x^2 + 3x - 1} ) u\sing the quotient rule.
Correct 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} )

Correct Answer: A

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Question 17
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?
Correct A. 0.8413
B. 0.8413
C. 0.8413
D. 0.8413

Correct Answer: A

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Question 18
Solve the system of linear equations u\sing matrices:\n\( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix} \).
Correct A. \( egin{bmatrix} 2 \ 1 \end{bmatrix} \)
B. \( egin{bmatrix} 1 \ 2 \end{bmatrix} \)
C. \( egin{bmatrix} 3 \ 4 \end{bmatrix} \)
D. \( egin{bmatrix} 4 \ 3 \end{bmatrix} \)

Correct Answer: A

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Question 19
Find the equation of the circle with center ( (2, 3) ) and radius 4.
Correct 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 )

Correct Answer: A

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Question 20
Solve the quadratic equation \( x^2 + 5x + 6 = 0 \) u\sing the quadratic formula.
Correct A. \( x = -2 \) or \( x = -3 \)
B. \( x = -3 \) or \( x = -2 \)
C. \( x = 2 \) or \( x = 3 \)
D. \( x = 3 \) or \( x = 2 \)

Correct Answer: A

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Question 21
Determine the value of x in the equation \( \frac{1}{x} + \frac{1}{x+1} = \frac{1}{2} \).
A. 1
Correct B. 2
C. 3
D. 4

Correct Answer: B

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Question 22
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
Correct B. 2A
C. 3A
D. 4A

Correct Answer: B

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Question 23
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
Correct A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, -3 \) ∪ (1, ∞)
C. \( -∞, 1 \) ∪ (3, ∞)
D. \( -∞, -3 \) ∪ (1, ∞)

Correct Answer: A

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Question 24
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
Correct B. 1/3
C. 1/2
D. 2/3

Correct Answer: B

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Question 25
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
A. -2x/\( x^2 + 1 \)^2
Correct B. 2x/\( x^2 + 1 \)^2
C. -2/\( x^2 + 1 \)^2
D. 2/\( x^2 + 1 \)^2

Correct Answer: B

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