POST UTME ESUT 2018 Mathematics | Objective

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Question 1 View Details
Find the derivative of the function ( f(x) = \(\frac{x^2 + 2x - 3}{x^2 - 4}\)\)\) ) using the quotient rule.
A. \(\frac{2x x^2 - 4 - x^2 + 2x - 3\) (2x)}{ \(x^2 - 4\) ^2}\)\)
B. \(\frac{2x x^2 - 4 + x^2 + 2x - 3\) (2x)}{ \(x^2 - 4\) ^2}\)\)
Correct C. \(\frac{2x x^2 - 4 - x^2 + 2x - 3\) (2x)}{ \(x^2 - 4\) ^2}\)\)
D. \(\frac{2x x^2 - 4 + x^2 + 2x - 3\) (2x)}{ \(x^2 - 4\) ^2}\)\)

Correct Answer: C

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Question 2 View Details
A circle has a radius of 5 cm. Find the area of the circle.
Correct A. \pi \(r^2\)
B. 2\pi r
C. \pi r
D. \pi \(r^2 + 2\)\pi r

Correct Answer: A

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Question 3 View Details
A random experiment has two independent events, A and B, with probabilities 0.4 and 0.6, respectively. 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 4 View Details
Solve the inequality \(2x^2 + 5x - 3 > 0\).
A. \(x < -1\)
Correct B. \(x > -1\)
C. \(x < 1\)
D. \(x > 1\)

Correct Answer: B

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

Correct Answer: A

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Question 6 View Details
Find the equation of the circle with center \(-2, 3\) and radius 4.
Correct A. \(x^2\) + \\((y^2 + 4x - 6y + 13\)\(= 0\)\)
B. \(x^2\) + \\((y^2 - 4x + 6y + 13\)\(= 0\)\)
C. \(x^2\) + \\((y^2 + 2x - 3y + 13\)\(= 0\)\)
D. \(x^2\) + \\((y^2 - 2x + 3y + 13\)\(= 0\)\)

Correct Answer: A

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Question 7 View Details
Solve the system of equations: \begin{align*} x + y &= 4 \ 2x - 3y &= 5 \end{align*}
Correct A. \(x = 3\), \(y = 1\)
B. \(x = 2\), \(y = 2\)
C. \(x = 1\), \(y = 3\)
D. \(x = 4\), \(y = 0\)

Correct Answer: A

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Question 8 View Details
Find the mean and standard deviation of the data set: \{2, 4, 6, 8, 10\}
Correct A. \(Mean = 6\), Standard \(Deviation = 2\)
B. \(Mean = 4\), Standard \(Deviation = 2\)
C. \(Mean = 6\), Standard \(Deviation = 4\)
D. \(Mean = 4\), Standard \(Deviation = 4\)

Correct Answer: A

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Question 9 View Details
Solve the inequality: \(\frac{x + 2}{x - 1}\)\\() > 0\)
Correct A. x < -2 or \(x > 1\)
B. \(x < 1\) or \(x > 2\)
C. x < -1 or \(x > 2\)
D. \(x < 1\) or \(x < 2\)

Correct Answer: A

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Question 10 View Details
Find the equation of the line passing through the points (2, 3) and (4, 5)
Correct A. \(y = x + 1\)
B. \(y = x - 1\)
C. \(y = -x + 1\)
D. \(y = x + 2\)

Correct Answer: A

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Question 11 View Details
Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 4)
Correct A. 12
B. 16
C. 20
D. 24

Correct Answer: A

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Question 12 View Details
Find the equation of the circle with center (1, 2) and radius 3
Correct A. \(x^2\) + \\((y^2 - 2x + 4y + 5\)\(= 0\)\)
B. \(x^2\) + \\((y^2 + 2x - 4y + 5\)\(= 0\)\)
C. \(x^2\) + \\((y^2 - 2x - 4y + 5\)\(= 0\)\)
D. \(x^2\) + \\((y^2 + 2x + 4y + 5\)\(= 0\)\)

Correct Answer: A

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Question 13 View Details
Solve the system of equations: \begin{align*} x + y &= 3 \ x - y &= 1 \end{align*}
A. \(x = 2\), \(y = 1\)
B. \(x = 1\), \(y = 2\)
C. \(x = 2\), \(y = 2\)
D. \(x = 1\), \(y = 1\)

Correct Answer: VIEW ANSWER

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Question 14 View Details
Find the volume of the solid formed by revolving the region bounded by the parabola (y = x\^2\), the x-axis, and the line \\((y = x^2\(x = 2\) about the x-axis.
A. 32\pi
B. 64\pi
Correct C. 128\pi
D. 256\pi

Correct Answer: C

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Question 15 View Details
Solve the inequality |x - 2|\(> 3.\)
Correct A. x < -1 or \(x > 5\)
B. \(x < 1\) or \(x > 5\)
C. x < -1 or \(x > 4\)
D. \(x < 1\) or \(x > 4\)

Correct Answer: A

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Question 16 View Details
Find the area under the curve \(y = x\^3 - 6x^2 + 9x + 2\) from \(x = 0\) to \(x = 4\).
A. 64
B. 128
Correct C. 256
D. 512

Correct Answer: C

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Question 17 View Details
Find the value of x in the equation \(2^x\) + \\((2^x\)\(= 128.\)\)
A. 5
B. 6
Correct C. 7
D. 8

Correct Answer: C

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Question 18 View Details
Find the surface area of the solid formed by revolving the region bounded by the parabola (y = x\^2\), the x-axis, and the line \\((y = x^2\(x = 2\) 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 19 View Details
Solve for x in the equation \(\log_{10} x^2 \\)\(= 4 ).\)
Correct A. 10
B. 100
C. 1000
D. 10000

Correct Answer: A

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Question 20 View Details
Find the area under the curve \(y = x^2 + 2x + 1\) from \(x = 0\) to \(x = 2\).
A. 7
Correct B. 8
C. 9
D. 10

Correct Answer: B

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Question 21 View Details
Solve the inequality \(x^2 - 4x + 3 > 0\).
Correct A. \(-\infty, 1\) \cup \(3, \infty\)
B. \(-\infty, 3\) \cup \(1, \infty\)
C. (1, 3)
D. \(-\infty, 1\) \cup \(3, \infty\)

Correct Answer: A

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Question 22 View Details
A particle moves along the x-axis with the equation of motion ( x(t) = \((t^2 - 2t + 1\)\) ). Find the velocity of the particle at time \(t = 1\\((t^2 - 2t + 1) ). Find the velocity of the particle at time\).
A. 0
Correct B. 1
C. 2
D. 3

Correct Answer: B

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Question 23 View Details
Find the value of ( x ) in the equation \(x^3 - 6x^2 + 11x - 6 = 0\).
A. 1
B. 2
Correct C. 3
D. 4

Correct Answer: C

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Question 24 View Details
Find the area under the curve \(y = \frac{1}{2}x^2 + 3x - 2\) from \(x = 0\) to \(x = 4\).
Correct A. \(12 + 12 \sqrt{2} - 8 \\)
B. \(12 + 12 \sqrt{2} + 8 \\)
C. \(12 - 12 \sqrt{2} - 8 \\)
D. \(12 - 12 \sqrt{2} + 8 \\)

Correct Answer: A

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Question 25 View Details
Solve for ( x ) in the equation \(2^x + 3^x = 5^x\).
A. \(x = 2 \\)
B. \(x = 3 \\)
Correct C. \(x = 4 \\)
D. \(x = 5 \\)

Correct Answer: C

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