POST UTME ABU 2023 Mathematics | Objective

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Question 1 View Details
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 View Details
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 View Details
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 View Details
Find the equation of the line passing 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 View Details
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 View Details
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 View Details
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 View Details
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 View Details
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 \(t = 2\\((2t^2 + 5t - 3) ). Find the velocity of the particle at time\).
A. 10
Correct B. 13
C. 16
D. 19

Correct Answer: B

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Question 10 View Details
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 View Details
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 View Details
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 View Details
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 View Details
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 View Details
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 View Details
Find the derivative of the function ( f(x) = \(\frac{1}{2x^2 + 3x - 1}\)\)\) ) using 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 View Details
A histogram of exam scores has a mean of 75 and a standard 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 View Details
Solve the system of linear equations using 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 View Details
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 View Details
Solve the quadratic equation \(x^2 + 5x + 6 = 0\) using 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 View Details
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 View Details
A diagram of a circuit is shown below. If the voltage source is 12V and the resistance 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 View Details
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 View Details
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 View Details
Find the derivative of the function ( f(x) = \(\frac{1}{x^2 + 1}\)\)\) ) using 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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