POST UTME UNIBEN 2023 Mathematics | Objective

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Question 1 View Details
Determine the value of x in the equation \(egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ 1 \end{bmatrix} = egin{bmatrix} 7 \ 11 \end{bmatrix}\).
A. 5
B. 6
Correct C. 7
D. 8

Correct Answer: C

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Question 2 View Details
Solve the inequality \(2^x + 5^x \geq 7^x\) for x.
A. -1
B. 0
Correct C. 1
D. 2

Correct Answer: C

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Question 3 View Details
Find the mean and standard deviation of the data set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
Correct A. {\(mean = 5.5\), \(std_dev = 2.9\)}
B. {\(mean = 6.0\), \(std_dev = 2.8\)}
C. {\(mean = 5.0\), \(std_dev = 2.7\)}
D. {\(mean = 4.5\), \(std_dev = 2.6\)}

Correct Answer: A

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

Correct Answer: A

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Question 5 View Details
Determine the value of the determinant of the matrix \(egin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix}\).
A. 1
Correct B. 2
C. 3
D. 4

Correct Answer: B

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Question 6 View Details
Find the value of \(\int_{0}^{\pi/2} \sin^2 x \cos^2 x \, dx\).
Correct A. \(1/16\)
B. \(1/8\)
C. \(1/4\)
D. \(1/2\)

Correct Answer: A

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Question 7 View Details
Solve the inequality \(|x - 2| > 3\).
Correct A. \(-∞, -1\) ∪ (4, ∞)
B. \(-∞, 1\) ∪ (4, ∞)
C. \(-∞, -1\) ∪ (1, 4)
D. \(-∞, 1\) ∪ (1, 4)

Correct Answer: A

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Question 8 View Details
Find the area of the region bounded by the curves \(y = x^2\) and \(y = 4 - x^2\).
A. 8\\(\pi/3\)
Correct B. 16\\(\pi/3\)
C. 32\\(\pi/3\)
D. 64\\(\pi/3\)

Correct Answer: B

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Question 9 View Details
A sequence is defined by \(a_n = 2n^2 + 3n - 1\). Find the sum of the first 5 terms of the sequence.
A. 65
B. 70
Correct C. 75
D. 80

Correct Answer: C

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Question 10 View Details
A circle has a radius of 4 cm. Find the area of the circle.
Correct A. 50.24
B. 50.26
C. 50.28
D. 50.30

Correct Answer: A

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Question 11 View Details
Solve the inequality \(\frac{x^2 - 4}{x + 2} > 0\) for ( x in mathbb{R} ).
Correct A. \(x < -2\) or \(x > 2\)
B. \(x < -2\) or \(x = 2\)
C. \(x > -2\) or \(x = 2\)
D. \(x < -2\) or \(x < 2\)

Correct Answer: A

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Question 12 View Details
If ( f(x) = \(\frac{x^2 - 4}{x + 2}\)\)) ), find \(f -3 \\\() ), find (f -3\) ).
Correct A. -1
B. 1
C. 2
D. -2

Correct Answer: A

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Question 13 View Details
Solve the equation \(\sin^2 x + \cos^2 x = 1\) for ( x in [0, 2pi] ).
Correct A. \(x = \frac{\pi}{2}\) or \(x = \frac{3\pi}{2}\)
B. \(x = \frac{\pi}{4}\) or \(x = \frac{5\pi}{4}\)
C. \(x = \frac{\pi}{6}\) or \(x = \frac{11\pi}{6}\)
D. \(x = \frac{\pi}{3}\) or \(x = \frac{2\pi}{3}\)

Correct Answer: A

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Question 14 View Details
A random variable ( X ) has a probability distribution given by \(P X = x \\) = \(frac{1}{2}\)\) ) for \\(frac{1}{2})\(x = 1, 2, 3\). Find the expected value of ( X ).
A. 1
Correct B. 2
C. 3
D. 4

Correct Answer: B

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Question 15 View Details
Find the derivative of ( f(x) = \(\frac{1}{x^2 + 1}\)\)\) ) using the chain rule.
Correct 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}\)\) )

Correct Answer: A

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Question 16 View Details
Solve the inequality (\(\frac{x-2}{x+1}\(> 0\)\) for x in \\((frac{x-2}{x+1} > 0\(-\infty, -1 \ cup -1, 2\) cup (2\), infty) ).
Correct A. \(x < -1\) or \(x > 2\)
B. \(x < -1\) or \(x = 2\)
C. \(x > -1\) and \(x < 2\)
D. \(x < -1\) or \(x > 2\)

Correct Answer: A

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Question 17 View Details
A histogram of exam scores is shown below. If the mean score is 60, find the value of ( k ).
A. 40
B. 50
Correct C. 60
D. 70

Correct Answer: C

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Question 18 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-2 \\)^2 + \(y-3\)^\(2 = 4\) )
C. \(x-2 \\)^2 + \(y-3\)^\(2 = 9\) )
D. \(x-2 \\)^2 + \(y-3\)^\(2 = 25\) )

Correct Answer: A

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Question 19 View Details
Solve the equation \(x^2 + 4x - 5 = 0\) using the quadratic formula.
Correct A. \(x = -2 \pm \sqrt{6}\)
B. \(x = -2 \pm \sqrt{3}\)
C. \(x = -2 \pm \sqrt{2}\)
D. \(x = -2 \pm \sqrt{1}\)

Correct Answer: A

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Question 20 View Details
A polynomial function has zeros at \(x = -2\) and \(x = 3\). If the leading coefficient is ( 2 ), find the polynomial function.
Correct A. \(( f(x) = 2\)\(x+2\), x-3\) )
B. \(( f(x) = 2\)\(x-2\), x-3\) )
C. \(( f(x) = 2\)\(x+2\), x+3\) )
D. \(( f(x) = 2\)\(x-2\), x+3\) )

Correct Answer: A

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Question 21 View Details
Solve the inequality (\(\frac{x}{x-2}\(> 1\)\) for \\((frac{x}{x-2} > 1\(x > 2\)\).
A. \(2 < x\)\(< 3\)
Correct B. \(x > 3\)
C. \(x < 2\)
D. \(x = 3\)

Correct Answer: B

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Question 22 View Details
A circle with center ( C(2, 3) ) and radius (r = 4\) has an equation of the form \(x - h \\((r = 4) has an equation of the form \\)^2 + \(y - k\)^\(2 = r\^2\) ). Find the equation of the circle.
Correct A. \(x - 2\)^2 + \(y - 3\)^\(2 = 16\)
B. \(x + 2\)^2 + \(y + 3\)^\(2 = 16\)
C. \(x - 3\)^2 + \(y - 2\)^\(2 = 16\)
D. \(x + 3\)^2 + \(y + 2\)^\(2 = 16\)

Correct Answer: A

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Question 23 View Details
A random experiment consists of two independent events, ( A ) and ( B ). If ( P(A) = 0.4 ) and ( P(B) = 0.6 ), find the probability that both events occur.
Correct A. 0.24
B. 0.48
C. 0.64
D. 0.76

Correct Answer: A

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Question 24 View Details
Find the equation of the line passing through the points ( (2, 3) ) and ( (4, 5) ).
Correct A. \(y = 1x + 1\)
B. \(y = 1x - 1\)
C. \(y = -1x + 1\)
D. \(y = -1x - 1\)

Correct Answer: A

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Question 25 View Details
Solve the quadratic 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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