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POST UTME ESUT 2024 Mathematics | Objective

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Question 1 View Details

Determine the value of x in the equation \(\frac{1}{2}x^2 + 5x - 3 = 17\).

A. -4

Correct B. 4

C. -2

D. 2

Correct Answer: B

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Question 2 View Details

A histogram of exam scores is shown below. What is the mean score?

A. 60

B. 70

Correct C. 80

D. 90

Correct Answer: C

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Question 3 View Details

Find the derivative of the function ( f(x) = \(\frac{1}{x^2 + 1}\)\)\) ) using the chain rule.

Correct A. \(\frac{-2x}{x^2 + 1\) \ ^2}\)\) )

B. \(\frac{-2}{x^2 + 1\) \ ^2}\)\) )

C. \(\frac{2x}{x^2 + 1\) \ ^2}\)\) )

D. \(\frac{2}{x^2 + 1\) \ ^2}\)\) )

Correct Answer: A

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Question 4 View Details

A sequence is defined by the formula \(a_n = 2n^2 - 5n + 1\). Find the sum of the first 5 terms of the sequence.

A. 120

B. 130

Correct C. 140

D. 150

Correct Answer: C

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Question 5 View Details

A polynomial function is defined by the equation ( f(x) = \(x^3 - 6x^2 + 11x - 6\) ). Find the value of x that makes f(x) = 0.

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 6 View Details

Let A be a 3x3 matrix with determinant 8. If A is multiplied by a scalar k, what is the determinant of kA?

Correct A. 64

B. 8

C. 512

D. -8

Correct Answer: A

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Question 7 View Details

Solve for x in the equation \(\log_2 x^2\)\(= 4\)\)

Correct A. 16

B. 8

C. 4

D. 2

Correct Answer: A

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Question 8 View Details

A histogram of exam scores has a mean of 75 and a standard deviation of 10. What is the probability that a randomly selected score is between 60 and 90?

A. 0.5

Correct B. 0.6

C. 0.7

D. 0.8

Correct Answer: B

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Question 9 View Details

A circle has a radius of 4 cm. What is the area of the circle?

A. 50.24

Correct B. 100.48

C. 200.96

D. 50.24

Correct Answer: B

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Question 10 View Details

A probability experiment has two independent events, A and B. If P(A) = 0.4 and P(B) = 0.6, what is the probability that both events occur?

Correct A. 0.2

B. 0.4

C. 0.6

D. 0.8

Correct Answer: A

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Question 11 View Details

Solve the inequality \(\frac{x}{2} - 3 > 7\) for ( x ).

A. \(x > 20\)

B. \(x < -20\)

Correct C. \(x > 16\)

D. \(x < 16\)

Correct Answer: C

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Question 12 View Details

Find the derivative of the function ( f(x) = \(3x^2 + 2x - 5\) ) using the chain rule.

Correct A. f'\((x) = 6x + 2\)

B. f'\((x) = 6x - 2\)

C. f'\((x) =\)\(6x^2 + 2x\)

D. f'\((x) =\)\(6x^2 - 2x\)

Correct Answer: A

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Question 13 View Details

A set of exam scores has a mean of 75 and a standard deviation of 10. If a new score of 90 is added to the set, what is the new mean?

A. 80

Correct B. 85

C. 90

D. 95

Correct Answer: B

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Question 14 View Details

Solve the quadratic equation \(x^2 + 5x + 6 = 0\) using the quadratic formula.

Correct A. \(x = -2\),\(x = -3\)

B. \(x = 2\), \(x = 3\)

C. \(x = -1\),\(x = -6\)

D. \(x = 1\), \(x = 6\)

Correct Answer: A

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Question 15 View Details

A sequence is defined by the formula \(a_n = 2n + 1\). Find the sum of the first 5 terms of the sequence.

A. 15

B. 20

Correct C. 25

D. 30

Correct Answer: C

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Question 16 View Details

Find the equation of the circle passing through the points (2, 3), (4, 5), and \(-1, 1\).

Correct A. \boxed{ x - 1 ^2 + y - \(2 ^2 = 10\)}

B. \boxed{ x + 1 ^2 + y - \(3 ^2 = 10\)}

C. \boxed{ x - 2 ^2 + y + \(1 ^2 = 10\)}

D. \boxed{ x + 2 ^2 + y - \(1 ^2 = 10\)}

Correct Answer: A

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Question 17 View Details

Solve the inequality \(\frac{x^2 - 4x + 3}{x^2 - 2x - 3}\)\)\\() > 0.\)

Correct A. \boxed{(2, 3) \cup 5, \infty }

B. \boxed{ -\infty, -1 \cup (1, 3)}

C. \boxed{ -\infty, -3 \cup (1, 5)}

D. \boxed{(2, 5)}

Correct Answer: A

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Question 18 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.

Correct A. \boxed{\(\frac{32\pi}{3}\)\)}

B. \boxed{\(\frac{64\pi}{3}\)\)}

C. \boxed{\(\frac{128\pi}{3}\)\)}

D. \boxed{\(\frac{256\pi}{3}\)\)}

Correct Answer: A

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Question 19 View Details

Solve the equation \log_2 \(x + 1\) + \log_2 \(x - 1 = 2\).

Correct A. \boxed{\(x = 3\)}

B. \boxed{\(x = 5\)}

C. \boxed{\(x = 7\)}

D. \boxed{\(x = 9\)}

Correct Answer: A

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Question 20 View Details

Find the equation of the line passing through the points (1, 2) and (3, 4).

Correct A. \boxed{\(y = 2x - 1\)}

B. \boxed{\(y = 2x + 1\)}

C. \boxed{\(y = x - 1\)}

D. \boxed{\(y = x + 1\)}

Correct Answer: A

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Question 21 View Details

Let \(\mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix}\) and \(\mathbf{b} = egin{pmatrix} -1 \ 4 end{pmatrix}\). Find the vector \(\\(end{pmatrix}). Find the vector \mathbf{a} \times \mathbf{b}\) using the determinant method.

Correct A. \(egin{pmatrix} -11 \ -2 \end{pmatrix}\)

B. \(egin{pmatrix} 11 \ 2 \end{pmatrix}\)

C. \(egin{pmatrix} -2 \ 11 \end{pmatrix}\)

D. \(egin{pmatrix} 2 \ -11 \end{pmatrix}\)

Correct Answer: A

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Question 22 View Details

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

Correct A. ( f'\((x) =\)\(\frac{-2x}{x^2 + 1\) ^2}\)\) )

B. ( f'\((x) =\)\(\frac{2x}{x^2 + 1\) ^2}\)\) )

C. ( f'\((x) =\)\(\frac{2}{x^2 + 1\) ^2}\)\) )

D. ( f'\((x) =\)\(\frac{-2}{x^2 + 1\) ^2}\)\) )

Correct Answer: A

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Question 23 View Details

Solve the inequality \(x^2 - 4x - 5 > 0\).

Correct A. \(x < -1\) or \(x > 5\)

B. \(x < 1\) or \(x > 5\)

C. \(x < -1\) or \(x < 5\)

D. \(x > -1\) or \(x < 5\)

Correct Answer: A

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Question 24 View Details

A fair six-sided die is rolled. What is the probability that the number obtained is a multiple of 3?

A. \(\frac{1}{6}\)

Correct B. \(\frac{1}{3}\)

C. \(\frac{2}{3}\)

D. \(\frac{5}{6}\)

Correct Answer: B

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Question 25 View Details

Solve the quadratic equation \(x^2 + 4x + 4 = 0\).

Correct A. \(x = -2\)

B. \(x = -1\)

C. \(x = 1\)

D. \(x = 2\)

Correct Answer: A

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