Exam Body

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POST UTME UNIOSUN 2021 Mathematics | Objective

Are you preparing for POST UTME UNIOSUN 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.

Practice these randomly selected questions to test your readiness.

Question 1

Solve the inequality \( \frac{x^2 - 4}{x + 2} > 0 \) for ( x in mathbb{R} ).

Correct A. \( -infty, -2 \ \) cup (2, infty) )

B. \( -infty, -2 \ \) cup (2, infty) cup { 0 } )

C. \( -infty, -2 \ \) cup (2, infty) cup { 4 } )

D. \( -infty, -2 \ \) cup (2, infty) cup { -4 } )

Correct Answer: A

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Question 2

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

Correct A. ( f'(x) = \frac{-2x}{\( x^2 + 1 \)^2} )

B. ( f'(x) = \frac{-2x}{\( x^2 + 1 \)^3} )

C. ( f'(x) = \frac{2x}{\( x^2 + 1 \)^2} )

D. ( f'(x) = \frac{2x}{\( x^2 + 1 \)^3} )

Correct Answer: A

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Question 3

Solve the system of linear equations u\sing matrices:

Correct A. \( egin{bmatrix} 1 \ 2 \end{bmatrix} \)

B. \( egin{bmatrix} 2 \ 1 \end{bmatrix} \)

C. \( egin{bmatrix} 1 \ -2 \end{bmatrix} \)

D. \( egin{bmatrix} -2 \ 1 \end{bmatrix} \)

Correct Answer: A

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Question 4

Find the area under the curve \( y = \sin\( x \ \) ) from \( x = 0 \) to \( x = \frac{pi}{2} \).

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

B. \( \frac{pi}{2} \)

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

D. \( \frac{pi}{8} \)

Correct Answer: A

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Question 5

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

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

B. \( x = \frac{pi}{2} \)

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

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

Correct Answer: A

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Question 6

Determine the value of 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 7

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

A. 64\pi

B. 128\pi

Correct C. 256\pi

D. 512\pi

Correct Answer: C

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Question 8

Solve the inequality \( 2x^3 - 5x^2 + 3x - 1 > 0 \).

Correct A. \( -\infty, -1 \) \cup \( 1, \infty \)

B. \( -\infty, 0 \) \cup \( 1, \infty \)

C. \( -\infty, -1 \) \cup (0, 1)

D. \( -\infty, 1 \)

Correct Answer: A

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Question 9

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

A. -\frac{2x}{\( x^2 + 1 \)^2}

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

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

D. \frac{2}{\( x^2 + 1 \)^2}

Correct Answer: B

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Question 10

A rec\tangular box has a length of 6 cm, a width of 4 cm, and a height of 3 cm. Find the surface area of the box.

A. 88

B. 96

Correct C. 104

D. 112

Correct Answer: C

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Question 11

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

A. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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Question 12

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

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 13

Find the derivative of the function \( y = \sin^2\( x \ \) ) u\sing the chain rule.

Correct A. \( 2 \sin\( x \ \) \cos(x) )

B. \( \cos^2\( x \ \) )

C. \( \sin^2\( x \ \) )

D. \( \sin\( x \ \) )

Correct Answer: A

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Question 14

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 15

Find the area of the triangle with vertices ( A(0, 0) ), ( B(3, 0) ), and ( C(0, 2) ).

A. 6

B. 8

Correct C. 10

D. 12

Correct Answer: C

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Question 16

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

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

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

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

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

Correct Answer: A

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Question 17

Solve the system of equations: \( egin{cases} 2x + 3y = 7 \ 4x - 2y = - 3 \end{cases} \).

Correct A. \( x = 1, y = 2 \)

B. \( x = 2, y = 1 \)

C. \( x = 3, y = 4 \)

D. \( x = 4, y = 3 \)

Correct Answer: A

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Question 18

Find the determinant of the matrix \( egin{pmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 3 & 1 & 2 \end{pmatrix} \).

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

B. \( 2 \times \( 2 \times 2 - 1 \times 1 \ \) - 1 \times \( 4 \times 2 - 3 \times 1 \) - 3 \times \( 4 \times 1 - 3 \times 2 \) )

C. \( 2 \times \( 2 \times 2 - 1 \times 1 \ \) + 1 \times \( 4 \times 2 - 3 \times 1 \) + 3 \times \( 4 \times 1 - 3 \times 2 \) )

D. \( 2 \times \( 2 \times 2 - 1 \times 1 \ \) - 1 \times \( 4 \times 2 - 3 \times 1 \) - 3 \times \( 4 \times 1 - 3 \times 2 \) )

Correct Answer: A

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Question 19

A sequence is defined by the recurrence relation \( a_n = 2a_{n-1} + 3 \) with initial term \( a_1 = 2 \). Find the sum of the first 5 terms of the sequence.

Correct A. \( 2 + 7 + 17 + 37 + 79 \)

B. \( 2 + 5 + 13 + 29 + 61 \)

C. \( 2 + 7 + 17 + 37 + 79 \)

D. \( 2 + 5 + 13 + 29 + 61 \)

Correct Answer: A

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Question 20

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

Correct A. \( y = \frac{5 - 3}{4 - 2}x + \frac{3 \times 4 - 5 \times 2}{4 - 2} \)

B. \( y = \frac{5 - 3}{4 - 2}x + \frac{3 \times 4 - 5 \times 2}{4 - 2} \)

C. \( y = \frac{5 - 3}{4 - 2}x + \frac{3 \times 2 - 5 \times 4}{4 - 2} \)

D. \( y = \frac{5 - 3}{4 - 2}x + \frac{3 \times 2 - 5 \times 4}{4 - 2} \)

Correct Answer: A

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Question 21

Let X be a random variable with probability density function (pdf) given by f(x) = \( \frac{1}{2} e^{-|x|} \) for -∞ < x < ∞. Find the probability that X lies between -2 and 2.

Correct A. 0.5

B. 0.6

C. 0.7

D. 0.8

Correct Answer: A

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Question 22

A histogram of exam scores is given below. If the mean score is 60, what is the median score?

A. 55

Correct B. 60

C. 65

D. 70

Correct Answer: B

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Question 23

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

Correct A. ( f'(x) = \frac{-2x}{\( x^2 + 1 \)^2} )

B. ( f'(x) = \frac{2x}{\( x^2 + 1 \)^2} )

C. ( f'(x) = \frac{-x}{\( x^2 + 1 \)^2} )

D. ( f'(x) = \frac{x}{\( x^2 + 1 \)^2} )

Correct Answer: A

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Question 24

Simplify the expression \( \sqrt[3]{64x^3y^3} \).

A. \( 4x^1y^1 \)

B. \( 4x^3y^3 \)

Correct C. \( 8x^3y^3 \)

D. \( 16x^3y^3 \)

Correct Answer: C

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Question 25

A polynomial function is defined as ( f(x) = 2x^3 - 5x^2 + 7x - 1 ). Find the value of \( f\( -1 \ \) ).

A. 3

Correct B. 5

C. 7

D. 9

Correct Answer: B

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