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POST UTME ACHIEVERS UNIVERSITY 2020 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 2020 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

Determine the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 24\pi cm^3

Correct B. 48\pi cm^3

C. 96\pi cm^3

D. 192\pi cm^3

Correct Answer: B

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Question 2

Find the mean deviation about the median of the data set: 2, 4, 6, 8, 10.

A. 2

B. 4

Correct C. 6

D. 8

Correct Answer: C

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Question 3

Solve for x in the equation: \( x^2 + 4x + 4 = 0 \).

Correct A. -2

B. -1

C. 1

D. 2

Correct Answer: A

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Question 4

A binary operation \( * \) on the set of integers is defined as: \( a * b = a^2 + b^2 \). Find the value of \( 2 * 3 \).

Correct A. 13

B. 17

C. 19

D. 25

Correct Answer: A

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Question 5

Find the surface area of the sphere with radius 5 cm.

A. 100\pi cm^2

B. 200\pi cm^2

Correct C. 300\pi cm^2

D. 400\pi cm^2

Correct Answer: C

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Question 6

Find the value of ( k ) in the equation \( 2x^2 + 7x + k = 0 \) if the sum of the roots is \( -\frac{7}{2} \) and the product of the roots is \( -\frac{3}{4} \).

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 7

A histogram of exam scores is shown below. If the mean score is ( 60 ) and the s\tandard deviation is ( 10 ), what is the value of ( x ) in the interval ( [40, 80] ) where the frequency is maximum?

A. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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Question 8

Solve the 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. pi

Correct Answer: B

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Question 9

Find the value of ( x ) in the equation \( x^3 - 6x^2 + 11x - 6 = 0 \) if the sum of the roots is ( 6 ) and the product of the roots is \( -6 \).

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 10

A matrix ( A ) is given by \( A = egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \). Find the value of ( x ) in the equation \( A^2 = xA \).

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 11

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

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 12

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 13

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

Correct A. \( x < -1 \) or \( x > \frac{3}{2} \)

B. \( x > -1 \) or \( x < \frac{3}{2} \)

C. \( x < -1 \) or \( x < \frac{3}{2} \)

D. \( x > -1 \) or \( x > \frac{3}{2} \)

Correct Answer: A

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Question 14

Find the value of \( \frac{d}{dx} \( x^3 - 2x^2 + x - 1 \ \) ).

Correct A. \( 3x^2 - 4x + 1 \)

B. \( x^2 - 2x - 1 \)

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

D. \( x^2 - 2x + 1 \)

Correct Answer: A

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Question 15

Solve the system of equations \( x + y = 4 \) and \( x - y = 2 \).

Correct A. \( x = 3, y = 1 \)

B. \( x = 1, y = 3 \)

C. \( x = 2, y = 2 \)

D. \( x = 4, y = 0 \)

Correct Answer: A

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Question 16

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

Correct A. \( y = x + 1 \)

B. \( y = x - 1 \)

C. \( y = x + 2 \)

D. \( y = x - 2 \)

Correct Answer: A

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Question 17

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

Correct A. \( x = -2 \)

B. \( x = -1 \)

C. \( x = 0 \)

D. \( x = 1 \)

Correct Answer: A

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Question 18

Find the value of \( \frac{d^2}{dx^2} \( x^3 - 2x^2 + x - 1 \ \) ).

Correct A. ( 6x )

B. ( 2x )

C. \( x^2 \)

D. ( x )

Correct Answer: A

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Question 19

Find the volume of the solid generated by revolving the region bounded by the curves y = x^2, y = 0, and x = 2 about the x-axis.

A. 32\pi

B. 64\pi

Correct C. 128\pi

D. 256\pi

Correct Answer: C

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Question 20

Solve the inequality |x^2 - 4| > 5.

Correct A. x < -3 or x > 4

B. x < -2 or x > 5

C. x < -1 or x > 6

D. x < 0 or x > 7

Correct Answer: A

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Question 21

Find the area of the region bounded by the curves y = x^2 + 1, y = 0, and x = 2.

A. 9

Correct B. 18

C. 27

D. 36

Correct Answer: B

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Question 22

Solve the equation x^3 - 6x^2 + 11x - 6 = 0.

A. x = 1

B. x = 2

Correct C. x = 3

D. x = 4

Correct Answer: C

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Question 23

Find the volume of the solid generated by revolving the region bounded by the curves y = x^2, y = 0, and x = 2 about the y-axis.

A. 32\pi

B. 64\pi

Correct C. 128\pi

D. 256\pi

Correct Answer: C

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Question 24

Solve the inequality |x^2 - 4| < 5.

A. x < -1 or x > 4

Correct B. x < 0 or x > 5

C. x < 1 or x > 6

D. x < 2 or x > 7

Correct Answer: B

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Question 25

Find the area of the region bounded by the curves y = x^2 + 1, y = 0, and x = 2.

A. 9

Correct B. 18

C. 27

D. 36

Correct Answer: B

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