Exam Body

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Subject

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POST UTME ACHIEVERS UNIVERSITY 2022 Mathematics | Objective

Are you preparing for POST UTME ACHIEVERS UNIVERSITY exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2022 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

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

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 = x + 2

D. y = x - 2

Correct Answer: A

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Question 3

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

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

A. 16π

B. 32π

Correct C. 64π

D. 128π

Correct Answer: C

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Question 5

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

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

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

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

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

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

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

Solve the system of linear equations u\sing 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

Find the equation of the circle pas\sing 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

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

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

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.

A. 16π

B. 32π

Correct C. 64π

D. 128π

Correct Answer: C

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Question 17

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

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

Correct A. ln(2)

B. ln(1)

C. ln(4)

D. ln\( 1/2 \)

Correct Answer: A

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Question 19

Two events, A and B, are indep\endent. 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

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

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

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

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

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

Correct Answer: A

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Question 21

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

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

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

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

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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