Exam Body

Year

Subject

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POST UTME AAUA 2020 Mathematics | Objective

Are you preparing for POST UTME AAUA 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.

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Question 1

Find the area under the curve \( y = \frac{1}{2}x^2 \) from \( x = 0 \) to \( x = 4 \).

Correct A. \( \frac{16}{3} \)

B. \( \frac{32}{3} \)

C. \( \frac{64}{3} \)

D. \( \frac{128}{3} \)

Correct Answer: A

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Question 2

Solve for ( x ) in the equation \( 2x^2 + 5x - 3 = 0 \).

A. \( x = -\frac{3}{2} \)

Correct B. \( x = \frac{1}{2} \)

C. \( x = -\frac{1}{2} \)

D. \( x = \frac{3}{2} \)

Correct Answer: B

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Question 3

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

Correct A. \( \frac{32pi}{3} \)

B. \( \frac{64pi}{3} \)

C. \( \frac{128pi}{3} \)

D. \( \frac{256pi}{3} \)

Correct Answer: A

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Question 4

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

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

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

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

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

Correct Answer: A

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Question 5

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

Correct A. \( y = \frac{1}{2}x + \frac{1}{2} \)

B. \( y = \frac{1}{2}x - \frac{1}{2} \)

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

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

Correct Answer: A

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Question 6

Find the value of \( int_{0}^{2} \( 2x^2 + 3x - 1 \ \) dx ).

A. 4

B. 6

Correct C. 8

D. 10

Correct Answer: C

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Question 7

Solve the matrix equation \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix} \).

Correct A. x = 1, y = 2

B. x = 2, y = 3

C. x = 3, y = 4

D. x = 4, y = 5

Correct Answer: A

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Question 8

Find the sum of the first 5 terms of the geometric progression 2, 6, 18, ...

A. 62

B. 64

Correct C. 66

D. 68

Correct Answer: C

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Question 9

A histogram is constructed from the following data: 2, 4, 6, 8, 10. Find the mean of the data.

A. 5

Correct B. 6

C. 7

D. 8

Correct Answer: B

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Question 10

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

Correct A. 3x^2 - 6x + 2

B. 3x^2 - 6x + 1

C. 3x^2 - 6x - 1

D. 3x^2 + 6x - 1

Correct Answer: A

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Question 11

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

Correct A. \text{Equation: } \( x + 2 \)^2 + \( y - 3 \)^2 = 16

B. \text{Equation: } \( x - 2 \)^2 + \( y + 3 \)^2 = 16

C. \text{Equation: } \( x + 2 \)^2 + \( y + 3 \)^2 = 16

D. \text{Equation: } \( x - 2 \)^2 + \( y - 3 \)^2 = 16

Correct Answer: A

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Question 12

Solve the inequality \frac{x}{2} - 3 > 2.

Correct A. x > 10

B. x < 10

C. x > 4

D. x < 4

Correct Answer: A

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Question 13

Find the volume of the cylinder with radius 6 cm and height 8 cm.

Correct A. 768\pi \text{ cm}^3

B. 512\pi \text{ cm}^3

C. 384\pi \text{ cm}^3

D. 256\pi \text{ cm}^3

Correct Answer: A

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Question 14

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

Correct A. y = \frac{2}{3}x + \frac{1}{3}

B. y = \frac{3}{2}x - 1

C. y = \frac{1}{2}x + 2

D. y = \frac{2}{3}x - 2

Correct Answer: A

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Question 15

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

Correct A. 6

B. 8

C. 10

D. 12

Correct Answer: A

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Question 16

Find 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

B. 32\pi

Correct C. 48\pi

D. 64\pi

Correct Answer: C

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Question 17

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 18

A circle has a diameter of 10 cm. Find the area of the circle.

A. 50\pi

Correct B. 100\pi

C. 200\pi

D. 300\pi

Correct Answer: B

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Question 19

A right-angled triangle has a hypotenuse of length 10 cm and one leg of length 6 cm. Find the length of the other leg.

A. 4

B. 6

Correct C. 8

D. 12

Correct Answer: C

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Question 20

A rec\tangular prism has a length of 8 cm, a width of 5 cm, and a height of 3 cm. Find the volume of the prism.

A. 120

B. 150

Correct C. 180

D. 200

Correct Answer: C

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Question 21

Find the area under the curve \( y = \frac{1}{2}x^2 \) from \( x = 0 \) to \( x = 4 \).

Correct A. 16

B. 32

C. 64

D. 128

Correct Answer: A

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Question 22

Solve for ( x ) in the equation \( 2^x + 3^x = 5^x \).

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 23

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

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

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

C. \left\( x - 4 \right \)^2 + \left\( y - 3 \right \)^2 = 16

D. \left\( x - 2 \right \)^2 + \left\( y - 4 \right \)^2 = 16

Correct Answer: A

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Question 24

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

Correct A. 6x + 2

B. 6x - 2

C. 3x^2 + 2

D. 3x^2 - 2

Correct Answer: A

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Question 25

Find the area of the triangle with vertices ( (0, 0) ), ( (3, 0) ), and ( (0, 4) ).

A. 6

Correct B. 12

C. 18

D. 24

Correct Answer: B

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