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POST UTME UNILORIN 2023 Mathematics | Objective

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Question 1 View Details

Determine the volume of the solid formed by revolving the region bounded by the parabola (y = \(x^2\)\) and the line \(y = 2x\\((y = x^2) and the line\) 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 View Details

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 View Details

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 View Details

A vector ( mathbf{a} ) is defined as \(\mathbf{a} = 2\mathbf{i} + 3\mathbf{j}\). 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 View Details

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 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 \(x = 2\\((y = x^2), the x-axis, and the line\) about the x-axis.

Correct A. 16π

B. 32π

C. 64π

D. 128π

Correct Answer: A

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Question 7 View Details

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 View Details

Find the equation of the circle passing 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 View Details

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

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

Correct Answer: A

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Question 11 View Details

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 View Details

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 View Details

Find the derivative of the function ( f(x) = \(x^3 - 2x^2 + 5x - 1\) ) using 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 View Details

Solve the system of linear equations \(egin{cases} x + y = 2 \ 2x - 3y = - 1 \end{cases}\) using 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 View Details

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 View Details

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 View Details

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 View Details

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

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

Correct Answer: A

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Question 19 View Details

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 View Details

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 View Details

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 View Details

Solve the system of linear equations using 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 View Details

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 View Details

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 View Details

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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