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POST UTME OSUSTECH 2022 Mathematics | Objective

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Question 1 View Details

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

A. 1

Correct B. -1

C. 2

D. 3

Correct Answer: B

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Question 2 View Details

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

Correct A. -2

B. 0

C. 2

D. 4

Correct Answer: A

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Question 3 View Details

Find the volume of the solid formed by revolving the region bounded by the curves \(y = x^2\) and \(y = 4 - x\) about the x-axis.

A. 16\pi

B. 32\pi

Correct C. 64\pi

D. 128\pi

Correct Answer: C

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Question 4 View Details

Find the equation of the circle with center ( (2, 3) ) and radius 4.

Correct A. \(x - 2\)^2 + \(y - 3\)^\(2 = 16\)

B. \(x - 3\)^2 + \(y - 2\)^\(2 = 16\)

C. \(x + 2\)^2 + \(y + 3\)^\(2 = 16\)

D. \(x - 3\)^2 + \(y + 2\)^\(2 = 16\)

Correct Answer: A

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Question 5 View Details

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

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

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

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

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

Correct Answer: A

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Question 6 View Details

Find the equation of the line passing through the points (2,3) and (4,5) in the coordinate plane.

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

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

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

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

Correct Answer: B

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Question 7 View Details

Find the area of the region bounded by the parabola (y = x\^2\), the x-axis, and the line \\((y = x^2\(x = 3\).

A. 9

Correct B. 18

C. 27

D. 36

Correct Answer: B

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Question 8 View Details

Find the value of x in the equation \(egin{bmatrix} 2 & 1 \ 1 & 2 \end{bmatrix} egin{bmatrix} x \ 1 \end{bmatrix} = egin{bmatrix} 4 \ 4 \end{bmatrix}\).

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 9 View Details

Find the value of \(\log_{10} x^2 \\) ) given that \(\log_{10} x \\)\(= 2 ).\)

A. 4

Correct B. 6

C. 8

D. 10

Correct Answer: B

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Question 10 View Details

Find the mean of the data set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and calculate the standard deviation.

Correct A. 5.5, 2.87

B. 6.5, 2.87

C. 7.5, 2.87

D. 8.5, 2.87

Correct Answer: A

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Question 11 View Details

Determine the value of (n\) in the sequence \(a_n = 2n^2 + 3n - 1\\((n) in the sequence\), given that \(a_1 = 0\) and \(a_2 = 5\).

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 12 View Details

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

Correct A. \(y = -x + 5\)

B. \(y = x + 1\)

C. \(y = -2x - 3\)

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

Correct Answer: A

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Question 13 View Details

A binary operation (\star\) is defined as \\((star\(a star b = a^2 + b^2\). Find the value of \(x\\(star b = a^2 + b^2). Find the value of\) such that \(2 \star x = 17\).

A. 3

Correct B. 4

C. 5

D. 6

Correct Answer: B

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Question 14 View Details

Find the mean of the numbers \(2, 4, 6, 8, 10\).

A. 6

B. 7

Correct C. 8

D. 9

Correct Answer: C

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Question 15 View Details

A circle has a radius of 4 cm. Find the area of the circle.

Correct A. 50.24

B. 50.27

C. 50.29

D. 50.31

Correct Answer: A

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Question 16 View Details

Find the volume of the solid formed by rotating the region bounded by the curves \(y = x^2\) and \(y = 4 - x^2\) 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 17 View Details

Solve the inequality \(\log_2 x^2 + 1\)\(> 3\)\).

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

B. \(-\infty, -2\) \cup \(-1, \infty\)

C. \(-\infty, 0\) \cup \(1, \infty\)

D. \(-\infty, -2\) \cup \(0, \infty\)

Correct Answer: A

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Question 18 View Details

Find the surface area of the solid formed by rotating the region bounded by the curves \(y = x^2\) and \(y = 4 - x^2\) 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 the equation \(\frac{1}{x} + \frac{1}{x+1} = \frac{1}{2}\).

A. \(x = -1\)

Correct B. \(x = 1\)

C. \(x = -2\)

D. \(x = 2\)

Correct Answer: B

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Question 20 View Details

Find the area under the curve \(y = x^2\) from \(x = 0\) to \(x = 2\).

Correct A. \(8/3\)

B. \(16/3\)

C. \(32/3\)

D. \(64/3\)

Correct Answer: A

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Question 21 View Details

Determine the value of x in the equation \(\frac{1}{2}x^2 + 3x - 5 = 0\) using the quadratic formula.

Correct A. \(x = -6 \pm \sqrt{6} \\)

B. \(x = 2 \pm \sqrt{3} \\)

C. \(x = -2 \pm \sqrt{3} \\)

D. \(x = 6 \pm \sqrt{6} \\)

Correct Answer: A

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Question 22 View Details

Solve for y in the equation \(y = \frac{1}{2} \log_{10} x^2 \\) ) where \(x = 10\).

Correct A. \(y = 1 \\)

B. \(y = 2 \\)

C. \(y = 3 \\)

D. \(y = 4 \\)

Correct Answer: A

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Question 23 View Details

Find the equation of the circle with center \(-2, 3\) and radius 4.

Correct A. \(x + 2 \\)^2 + \(y - 3\)^\(2 = 16\) \)

B. \(x - 2 \\)^2 + \(y + 3\)^\(2 = 16\) \)

C. \(x + 2 \\)^2 + \(y + 3\)^\(2 = 16\) \)

D. \(x - 2 \\)^2 + \(y - 3\)^\(2 = 16\) \)

Correct Answer: A

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Question 24 View Details

Solve the system of equations using matrices: \(\begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 5 \ 6 \end{bmatrix}\).

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

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

C. \(x = 4, y = 5 \\)

D. \(x = 5, y = 4 \\)

Correct Answer: A

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Question 25 View Details

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

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

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

C. ( f'\((x) = 6x + 5\)\)

D. ( f'\((x) = 6x - 5\)\)

Correct Answer: A

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