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POST UTME ACHIEVERS UNIVERSITY 2022 Mathematics | Objective

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Question 1 View Details

Determine the value of x in the equation \(egin{bmatrix} 2 & 1 \ 3 & 2 \end{bmatrix} egin{bmatrix} x \ 1 \end{bmatrix} = egin{bmatrix} 4 \ 8 \end{bmatrix}\).

A. 1

B. 2

C. 3

Correct D. 4

Correct Answer: D

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Question 2 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. \(y = x + 2\)

D. \(y = x - 2\)

Correct Answer: A

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Question 3 View Details

A histogram of exam scores is shown below. If the mean score is 60, what is the value of the class width?

A. 5

Correct B. 10

C. 15

D. 20

Correct Answer: B

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Question 4 View Details

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

A. 16π

B. 32π

Correct C. 64π

D. 128π

Correct Answer: C

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Question 5 View Details

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

A. 0

Correct B. π/2

C. π

D. 3π/2

Correct Answer: B

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Question 6 View Details

Determine the value of x in the equation \(\frac{x}{2} + 5 = 11\).

Correct A. 4

B. 6

C. 8

D. 10

Correct Answer: A

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Question 7 View Details

Find the sum of the first 10 terms of the geometric series ( 2, 6, 18, 54, ... ).

A. 3120

Correct B. 3240

C. 3360

D. 3480

Correct Answer: B

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Question 8 View Details

Solve for x in the equation \(\log_{10} x^2 \\)\(= 4 ).\)

A. 10

Correct B. 20

C. 40

D. 80

Correct Answer: B

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Question 9 View Details

Find the volume of the frustum of a cone with height 10 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 100π

Correct B. 120π

C. 140π

D. 160π

Correct Answer: B

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Question 10 View Details

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

Correct A. \(-∞, -1\) ∪ (3, ∞)

B. \(-∞, 1\) ∪ (3, ∞)

C. \(-∞, -1\) ∪ (1, ∞)

D. \(-∞, 3\) ∪ (1, ∞)

Correct Answer: A

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Question 11 View Details

Find the volume of the frustum of a cone with height 8 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 64\pi \(cm^3\)

Correct B. 128\pi \(cm^3\)

C. 256\pi \(cm^3\)

D. 512\pi \(cm^3\)

Correct Answer: B

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Question 12 View Details

Solve the system of linear equations using matrices: \begin{align*} x + 2y - z &= 3 \ 2x - 3y + 4z &= 5 \ -x + y - 2z &= -2 \end{align*}

Correct A. \begin{pmatrix} 1 \ 2 \ -1 \end{pmatrix}

B. \begin{pmatrix} 2 \ -1 \ 3 \end{pmatrix}

C. \begin{pmatrix} 3 \ 4 \ 5 \end{pmatrix}

D. \begin{pmatrix} 5 \ 6 \ 7 \end{pmatrix}

Correct Answer: A

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Question 13 View Details

Find the equation of the circle passing through the points (2, 3), (4, 5), and (6, 7).

A. \(x - 4\)^2 + \(y - 5\)^\(2 = 9\)

Correct B. \(x - 3\)^2 + \(y - 4\)^\(2 = 16\)

C. \(x - 5\)^2 + \(y - 6\)^\(2 = 25\)

D. \(x - 6\)^2 + \(y - 7\)^\(2 = 36\)

Correct Answer: B

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Question 14 View Details

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

A. \(x = -2\)

Correct B. \(x = -3\)

C. \(x = 2\)

D. \(x = 3\)

Correct Answer: B

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Question 15 View Details

Find the area of the triangle formed by the points (0, 0), (3, 0), and (0, 4).

Correct A. 6

B. 12

C. 18

D. 24

Correct Answer: A

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Question 16 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.

A. 16π

B. 32π

Correct C. 64π

D. 128π

Correct Answer: C

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Question 17 View Details

A circle with center ( C(2, 3) ) and radius 4 passes through the point ( P(0, 0) ). Find the equation of the circle.

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 18 View Details

Find the area under the curve \(y = \frac{1}{x}\) from \(x = 1\) to \(x = 2\) using integration.

Correct A. ln(2)

B. ln(1)

C. ln(4)

D. ln\(1/2\)

Correct Answer: A

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Question 19 View Details

Two events, A and B, are independent. If ( P(A) = 0.3 ) and ( P(B) = 0.4 ), find ( P(A cap B) ).

Correct A. 0.12

B. 0.24

C. 0.36

D. 0.48

Correct Answer: A

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Question 20 View Details

Find the vector ( mathbf{a} ) such that \(\mathbf{a} \cdot \mathbf{b} = 10\) and \(\mathbf{a} \cdot \mathbf{c} = 5\), where \(\mathbf{b} = 2\mathbf{i} + 3\mathbf{j}\) and \(\mathbf{c} = \mathbf{i} - 2\mathbf{j}\).

Correct A. \(5\mathbf{i} + 3\mathbf{j}\)

B. \(3\mathbf{i} + 5\mathbf{j}\)

C. \(2\mathbf{i} + 4\mathbf{j}\)

D. \(4\mathbf{i} + 2\mathbf{j}\)

Correct Answer: A

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Question 21 View Details

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

Correct A. \(\frac{-x}{x^2 + 1 \\)^{\(3/2\)}} )

B. \(\frac{x}{x^2 + 1 \\)^{\(3/2\)}} )

C. \(\frac{1}{x^2 + 1 \\)^{\(3/2\)}} )

D. \(\frac{-1}{x^2 + 1 \\)^{\(3/2\)}} )

Correct Answer: A

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Question 22 View Details

Solve the equation \(2 \log_{10} x^2 \\) = 4 ) for ( x ).

Correct A. \(x = 10\)

B. \(x = 10^2\)

C. \(x = 10^{-2}\)

D. \(x = 10^{-1}\)

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 + \(y - 3\)^\(2 = 4\) )

C. \(x - 2 \\)^2 + \(y - 3\)^\(2 = 9\) )

D. \(x - 2 \\)^2 + \(y - 3\)^\(2 = 25\) )

Correct Answer: A

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Question 24 View Details

A sequence is defined by the recurrence relation \(a_n = 2a_{n-1} + 1\) with initial term \(a_1 = 3\). Find the value of \(a_5\).

Correct A. ( 73 )

B. ( 71 )

C. ( 69 )

D. ( 67 )

Correct Answer: A

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Question 25 View Details

Solve the inequality \(|x - 2| > 3\).

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

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

C. \(x < -1\) or \(x > 2\)

D. \(x < 1\) or \(x > 2\)

Correct Answer: A

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