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

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Question 1

Solve for x in the equation \( \frac{1}{2}x^2 + 5x - 3 = 0 \).

A. \( x = -10 \)

B. \( x = 3 \)

Correct C. \( x = -3 \)

D. \( x = 10 \)

Correct Answer: C

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Question 2

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

Correct A. \( \frac{14}{3} \)

B. \( \frac{16}{3} \)

C. \( \frac{18}{3} \)

D. \( \frac{20}{3} \)

Correct Answer: A

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Question 3

In the diagram below, find the value of ( vec{a} cdot vec{b} ).

Correct A. ( 0 )

B. ( 1 )

C. ( 2 )

D. ( 3 )

Correct Answer: A

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Question 4

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 = 20 )

C. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 24 )

D. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 28 )

Correct Answer: A

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Question 5

Solve the inequality \( x^2 + 4x - 5 > 0 \).

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

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

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

D. \( x < -5 \) or \( x < 1 \)

Correct Answer: A

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Question 6

Find the derivative of the function ( f(x) = \frac{1}{2x^2 + 5x + 3} ) u\sing the quotient rule.

Correct A. \( \frac{-2x + 5}{\( 2x^2 + 5x + 3 \ \)^2} )

B. \( \frac{2x + 5}{\( 2x^2 + 5x + 3 \ \)^2} )

C. \( \frac{2x - 5}{\( 2x^2 + 5x + 3 \ \)^2} )

D. \( \frac{-2x - 5}{\( 2x^2 + 5x + 3 \ \)^2} )

Correct Answer: A

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Question 7

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 student scored above 90?

A. 0.1587

B. 0.3413

C. 0.4772

Correct D. 0.6745

Correct Answer: D

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Question 8

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

Correct A. \( x = \frac{pi}{4}, \frac{3pi}{4} \)

B. \( x = \frac{pi}{4}, \frac{5pi}{4} \)

C. \( x = \frac{pi}{4}, \frac{7pi}{4} \)

D. \( x = \frac{pi}{4}, \frac{9pi}{4} \)

Correct Answer: A

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Question 9

A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. What is its volume?

Correct A. 30

B. 40

C. 50

D. 60

Correct Answer: A

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Question 10

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

Correct A. 1

B. -1

C. 2

D. 3

Correct Answer: A

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Question 11

Solve for x in the equation \( \sin^2 x + \cos^2 x = 1 \) u\sing the identity \( \sin^2 x + \cos^2 x = 1 \).

Correct A. \( x = \frac{pi}{2} \)

B. \( x = \frac{pi}{4} \)

C. \( x = \frac{3pi}{4} \)

D. \( x = \frac{pi}{4} + \frac{pi}{2} \)

Correct Answer: A

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Question 12

A set A is defined as \( A = { x in mathbb{R} : x^2 - 4x + 3 = 0 } \). Find the number of elements in set A.

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 13

The mean of a data set is 25 and the s\tandard deviation is 3. Find the sum of the squares of the deviations from the mean.

Correct A. 900

B. 1000

C. 1100

D. 1200

Correct Answer: A

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Question 14

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

A. \frac{16}{15}pi

B. \frac{32}{15}pi

Correct C. \frac{64}{15}pi

D. \frac{128}{15}pi

Correct Answer: C

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Question 15

Evaluate the definite integral \( int_{0}^{1} x^2 \sin x , dx \).

Correct A. \frac{1}{2} - \frac{1}{3}

B. \frac{1}{2} + \frac{1}{3}

C. \frac{1}{2} - \frac{1}{4}

D. \frac{1}{2} + \frac{1}{4}

Correct Answer: A

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Question 16

Determine the mean of the following data set: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

A. 5

Correct B. 6

C. 7

D. 8

Correct Answer: B

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Question 17

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

A. \( \sin\( x \ \) = 1 )

B. \( \cos\( x \ \) = 1 )

Correct C. \( \sin\( x \ \) = \cos(x) )

D. \( \sin\( x \ \) = -\cos(x) )

Correct Answer: C

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Question 18

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 19

A rec\tangular box has a length of 6 cm, a width of 4 cm, and a height of 3 cm. Find its volume.

Correct A. 72 cm^3

B. 48 cm^3

C. 36 cm^3

D. 24 cm^3

Correct Answer: A

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Question 20

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

Correct A. ( f'(x) = 6x + 2 )

B. ( f'(x) = 6x - 2 )

C. ( f'(x) = 6x + 4 )

D. ( f'(x) = 6x - 4 )

Correct Answer: A

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Question 21

Find the sum of the infinite geometric series with first term 1/2 and common ratio 1/4.

Correct A. 1

B. 3/4

C. 5/8

D. 7/16

Correct Answer: A

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Question 22

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

Correct A. x < -3/2 or x > 1/2

B. x < -1/2 or x > 3/2

C. x < 1/2 or x > -3/2

D. x < 3/2 or x > -1/2

Correct Answer: A

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Question 23

Find the area of the region bounded by the parabola y = x^2 and the line y = 2x.

Correct A. 4/3

B. 2/3

C. 1/3

D. 4/5

Correct Answer: A

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Question 24

Solve the system of equations \( x + y = 2 \) and \( xy = 1 \).

Correct A. (1, 1)

B. \( 1, -1 \)

C. \( -1, 1 \)

D. \( -1, -1 \)

Correct Answer: A

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Question 25

Find the equation of the circle with center (1, 2) and radius 3.

Correct A. \( x - 1 \)^2 + \( y - 2 \)^2 = 9

B. \( x + 1 \)^2 + \( y - 2 \)^2 = 9

C. \( x - 1 \)^2 + \( y + 2 \)^2 = 9

D. \( x + 1 \)^2 + \( y + 2 \)^2 = 9

Correct Answer: A

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