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POST UTME UNILORIN 2023 Mathematics | Objective

Are you preparing for POST UTME UNILORIN exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2023 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

Determine the volume of the solid formed by revolving the region bounded by the parabola \( y = x^2 \) and the line \( y = 2x \) about the x-axis.

A. \( \frac{8}{15} pi \)

Correct B. \( \frac{16}{15} pi \)

C. \( \frac{32}{15} pi \)

D. \( \frac{64}{15} pi \)

Correct Answer: B

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Question 2

A binary operation ( ast ) is defined as \( a ast b = a^2 + b^2 \). Find the value of ( 2 ast 3 ).

Correct A. ( 4 )

B. ( 5 )

C. ( 6 )

D. ( 7 )

Correct Answer: A

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Question 3

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

A. ( 15 )

B. ( 25 )

C. ( 35 )

Correct D. ( 45 )

Correct Answer: D

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Question 4

A vector ( mathbf{a} ) is defined as \( mathbf{a} = 2mathbf{i} + 3mathbf{j} \). Find the magnitude of the vector.

Correct A. \( \sqrt{13} \)

B. \( \sqrt{17} \)

C. \( \sqrt{21} \)

D. \( \sqrt{25} \)

Correct Answer: A

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Question 5

A geometric sequence is defined as \( a_n = 2^n \). Find the sum of the first five terms of the sequence.

A. ( 63 )

B. ( 127 )

C. ( 255 )

Correct D. ( 511 )

Correct Answer: D

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Question 6

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. 16π

B. 32π

C. 64π

D. 128π

Correct Answer: A

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Question 7

Solve the inequality \( \frac{x^2 - 4}{x^2 - 9} > 0 \).

Correct A. \( -∞, -3 \) ∪ (2, ∞)

B. \( -∞, -3 \) ∪ (2, 3)

C. \( -∞, -3 \) ∪ (3, ∞)

D. \( -∞, 3 \) ∪ (3, ∞)

Correct Answer: A

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Question 8

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

Correct A. \( x^2 + y^2 - 4x + 4y - 3 = 0 \)

B. \( x^2 + y^2 - 4x - 4y - 3 = 0 \)

C. \( x^2 + y^2 + 4x - 4y - 3 = 0 \)

D. \( x^2 + y^2 - 4x + 4y + 3 = 0 \)

Correct Answer: A

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Question 9

A die is rolled twice. Find the probability that the sum of the two numbers obtained is 7.

Correct A. 1/6

B. 1/12

C. 1/18

D. 1/24

Correct Answer: A

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Question 10

Find the equation of the line pas\sing through the points (2, 3) and (4, 5).

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

B. \( y = 2x + 1 \)

C. \( y = -2x + 1 \)

D. \( y = -2x - 1 \)

Correct Answer: A

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Question 11

Find the value of x in the equation \( \frac{x}{2} + \frac{3}{4} = \frac{5}{6} \).

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 12

Solve the trigonometric equation \( \sin^2 x + \cos^2 x = 1 \) for x in the interval ( [0, 2pi] ).

A. 0

Correct B. \frac{\pi}{4}

C. \frac{\pi}{2}

D. \frac{3\pi}{4}

Correct Answer: B

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Question 13

Find the derivative of the function ( f(x) = x^3 - 2x^2 + 5x - 1 ) u\sing the power rule.

Correct A. 3x^2 - 4x + 5

B. 3x^2 - 4x + 5

C. 3x^2 - 4x + 6

D. 3x^2 - 4x + 7

Correct Answer: A

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Question 14

Solve the system of linear equations \( egin{cases} x + y = 2 \ 2x - 3y = - 1 \end{cases} \) u\sing substitution.

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 15

Find the sum of the infinite geometric series \( sum_{n=1}^\infty \frac{1}{2^n} \).

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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Question 16

Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).

A. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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Question 17

A random variable ( X ) has a probability distribution given by \( P\( X = x \ \) = \frac{1}{2} \) for \( x = 1, 2, 3 \). Find the expected value of ( X ).

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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Question 18

Find the derivative of \( y = \frac{1}{x^2 + 1} \ \) u\sing the chain rule.

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

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

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

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

Correct Answer: A

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Question 19

A sequence is defined by \( a_n = \frac{1}{n^2} \ \) for \( n = 1, 2, 3, \ldots \ \). Find the sum of the first 5 terms of the sequence.

Correct A. \frac{1}{1^2} + \frac{1}{2^2} + \frac{1}{3^2} + \frac{1}{4^2} + \frac{1}{5^2}

B. \frac{1}{1^2} + \frac{1}{2^2} + \frac{1}{3^2} + \frac{1}{4^2} + \frac{1}{5^2} + \frac{1}{6^2}

C. \frac{1}{1^2} + \frac{1}{2^2} + \frac{1}{3^2} + \frac{1}{4^2} + \frac{1}{5^2} + \frac{1}{6^2} + \frac{1}{7^2}

D. \frac{1}{1^2} + \frac{1}{2^2} + \frac{1}{3^2} + \frac{1}{4^2} + \frac{1}{5^2} + \frac{1}{6^2} + \frac{1}{7^2} + \frac{1}{8^2}

Correct Answer: A

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Question 20

A histogram has the following frequency distribution: \( egin{array}{|c|c|c|c|c|} hline x & 0-10 & 10-20 & 20-30 & 30-40 \ hline f\( x \ \) & 5 & 10 & 15 & 20 \ hline \end{array} ). Find the mean of the distribution.

A. 20

Correct B. 25

C. 30

D. 35

Correct Answer: B

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Question 21

Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).

A. 64

B. 80

Correct C. 96

D. 112

Correct Answer: C

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Question 22

Solve the system of linear equations u\sing matrices: \( \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 7 \end{bmatrix} \).

A. \begin{bmatrix} 1 \ 2 \end{bmatrix}

B. \begin{bmatrix} 2 \ 1 \end{bmatrix}

Correct C. \begin{bmatrix} -1 \ 3 \end{bmatrix}

D. \begin{bmatrix} 3 \ -1 \end{bmatrix}

Correct Answer: C

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Question 23

Find the sum of the first 5 terms of the geometric series \( 2x^2, 4x^3, 8x^4, \ldots \).

Correct A. 2x^2 + 4x^3 + 8x^4 + 16x^5 + 32x^6

B. 2x^2 + 4x^3 + 8x^4 + 16x^5 + 32x^6 + 64x^7

C. 2x^2 + 4x^3 + 8x^4 + 16x^5 + 32x^6 + 64x^7 + 128x^8

D. 2x^2 + 4x^3 + 8x^4 + 16x^5 + 32x^6 + 64x^7 + 128x^8 + 256x^9

Correct Answer: A

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Question 24

Solve the inequality \( 2x^2 + 5x - 3 \geq 0 \).

Correct A. \( -\infty, -1 \) \cup [3, \infty)

B. \( -\infty, -3 \) \cup [1, \infty)

C. \( -\infty, -3 \) \cup \( -1, \infty \)

D. \( -\infty, -1 \) \cup \( -3, \infty \)

Correct Answer: A

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Question 25

Find the determinant of the matrix \( \begin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix} \).

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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