Exam Body

Year

Subject

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POST UTME DELSU 2021 Mathematics | Objective

Are you preparing for POST UTME DELSU exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2021 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

Determine the volume of the frustum of a cone with a height of 10 cm, a lower base radius of 4 cm, and an upper base radius of 6 cm.

A. 200\pi\text{ cm}^3

Correct B. 300\pi\text{ cm}^3

C. 400\pi\text{ cm}^3

D. 500\pi\text{ cm}^3

Correct Answer: B

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Question 2

A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 90?

A. 0.135

B. 0.225

Correct C. 0.315

D. 0.405

Correct Answer: C

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Question 3

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

A. -1

Correct B. 1

C. -3

D. 2

Correct Answer: B

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Question 4

Find the determinant of the matrix \( egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \).

Correct A. 0

B. 1

C. -1

D. 2

Correct Answer: A

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Question 5

A vector ( mathbf{a} ) has a magnitude of 5 and is directed at an angle of 30° to the x-axis. Find the x and y components of ( mathbf{a} ).

Correct A. \( mathbf{a} = 4.33mathbf{i} + 2.5mathbf{j} \)

B. \( mathbf{a} = 2.5mathbf{i} + 4.33mathbf{j} \)

C. \( mathbf{a} = 3.54mathbf{i} + 2.5mathbf{j} \)

D. \( mathbf{a} = 2.5mathbf{i} + 3.54mathbf{j} \)

Correct Answer: A

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Question 6

Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).

Correct A. \( \frac{1}{2} \times 4^2 + 3 \times 4 - 2 \)

B. \( \frac{1}{2} \times 4^2 + 3 \times 4 + 2 \)

C. \( \frac{1}{2} \times 4^2 - 3 \times 4 - 2 \)

D. \( \frac{1}{2} \times 4^2 - 3 \times 4 + 2 \)

Correct Answer: A

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Question 7

A particle moves along the curve \( y = x^2 - 2x + 1 \) with a velocity of \( \frac{dy}{dx} = 2x - 2 \). Find the acceleration at the point where \( x = 2 \).

Correct A. \( 2 \times 2 - 2 \)

B. \( 2 \times 2 + 2 \)

C. \( 2 \times 2 - 4 \)

D. \( 2 \times 2 + 4 \)

Correct Answer: A

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Question 8

Solve for ( x ) in the equation \( 2^x = 32 \).

A. \( x = 5 \)

Correct B. \( x = 6 \)

C. \( x = 7 \)

D. \( x = 8 \)

Correct Answer: B

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Question 9

A bag contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?

A. \( \frac{1}{2} \)

Correct B. \( \frac{3}{8} \)

C. \( \frac{1}{4} \)

D. \( \frac{3}{4} \)

Correct Answer: B

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Question 10

Find the volume of the solid formed by revolving the area under the curve \( y = x^2 - 2x + 1 \) about the x-axis from \( x = 0 \) to \( x = 2 \).

A. \( \frac{1}{3} pi \times 2^3 \)

B. \( \frac{1}{3} pi \times 3^3 \)

Correct C. \( \frac{1}{3} pi \times 4^3 \)

D. \( \frac{1}{3} pi \times 5^3 \)

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 value of \( \frac{d}{dx} \( x^3 - 6x^2 + 11x - 6 \ \) ).

Correct A. 3x^2 - 12x + 11

B. 3x^2 - 12x + 6

C. 3x^2 - 12x - 11

D. 3x^2 - 12x + 5

Correct Answer: A

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Question 13

Solve the system of equations \( egin{cases} x + y = 2 \ x - y = 0 \end{cases} \).

Correct A. x = 1, y = 1

B. x = 1, y = 0

C. x = 0, y = 1

D. x = 0, y = 0

Correct Answer: A

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Question 14

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 = 9

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

Correct Answer: A

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Question 15

Solve the trigonometric equation \( \sin^2 x + \cos^2 x = 1 \).

A. x = 0

Correct B. x = 90

C. x = 180

D. x = 270

Correct Answer: B

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Question 16

Solve for x in the equation \( 2^x + 2^{x+1} = 3 cdot 2^x \).

A. \( x = -1 \)

B. \( x = 0 \)

Correct C. \( x = 1 \)

D. \( x = 2 \)

Correct Answer: C

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Question 17

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

Correct A. ( 4 )

B. ( 6 )

C. ( 8 )

D. ( 10 )

Correct Answer: A

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Question 18

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 \( x < \frac{1}{2} \)

Correct Answer: A

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Question 19

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

Correct A. ( 1 )

B. \( -1 \)

C. ( 0 )

D. ( 2 )

Correct Answer: A

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Question 20

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

Correct A. \( x = -2 \)

B. \( x = 0 \)

C. \( x = 2 \)

D. \( x = -1 \)

Correct Answer: A

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Question 21

Given that ( f(x) = \frac{1}{x^2 + 1} ), find \( lim_{x \to infty} f\( x \ \) ).

Correct A. 0

B. 1

C. ∞

D. undefined

Correct Answer: A

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Question 22

Solve the inequality \( |2x - 1| geq 3 \).

Correct A. \( -∞, -2] ∪ [4, ∞ \)

B. \( -∞, -1] ∪ [2, ∞ \)

C. \( -∞, -3] ∪ [1, ∞ \)

D. \( -∞, -4] ∪ [3, ∞ \)

Correct Answer: A

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Question 23

Find the equation of the \tangent line to the curve \( y = x^2 - 2x + 1 \) at the point ( (1, 0) ).

Correct A. y = x - 1

B. y = x + 1

C. y = 2x - 1

D. y = 2x + 1

Correct Answer: A

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Question 24

A random variable ( X ) has a probability density function ( f(x) = egin{cases} 2x & 0 < x < 1 \ 0 & \text{otherwise} \end{cases} ). Find \( E\( X^2 \ \) ).

Correct A. 1/3

B. 1/2

C. 2/3

D. 1

Correct Answer: A

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Question 25

The polynomial ( P(x) = x^3 - 6x^2 + 11x - 6 ) has a root at \( x = 1 \). Find the other two roots.

Correct A. 2, 3

B. 1, 2

C. 1, 3

D. 2, 4

Correct Answer: A

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