Exam Body

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POST UTME ESUT 2024 Mathematics | Objective

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Question 1

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

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

Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing 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

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

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

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

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

A histogram of exam scores has a mean of 75 and a s\tandard 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

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

A probability experiment has two indep\endent 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

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

Find the derivative of the function ( f(x) = 3x^2 + 2x - 5 ) u\sing 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

A set of exam scores has a mean of 75 and a s\tandard 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

Solve the quadratic equation \( x^2 + 5x + 6 = 0 \) u\sing 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

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

Find the equation of the circle pas\sing 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

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

Find the volume of the solid formed by revolving the region bounded by the parabola y = x^2, the x-axis, and the line 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

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

Find the equation of the line pas\sing 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

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

Find the derivative of ( f(x) = \frac{1}{x^2 + 1} ) u\sing 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

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

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

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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