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

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Question 1

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

Correct A. \( x < -2 \) or \( x > 2 \)

B. \( x > -2 \) and \( x < 2 \)

C. \( x < -2 \) or \( x = 2 \)

D. \( x > -2 \) or \( x = 2 \)

Correct Answer: A

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Question 2

A histogram of exam scores is shown below. What is the mean score?

A. 50

B. 60

Correct C. 70

D. 80

Correct Answer: C

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Question 3

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{2}{\( x^2 + 1 \)^2} )

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

Correct Answer: A

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Question 4

A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. If a marble is drawn at random, what is the probability that it is blue?

A. \( \frac{1}{10} \)

B. \( \frac{1}{5} \)

Correct C. \( \frac{3}{10} \)

D. \( \frac{2}{5} \)

Correct Answer: C

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Question 5

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?

A. 30

B. 40

Correct C. 50

D. 60

Correct Answer: C

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Question 6

A cylindrical \tank with a radius of 4m and a height of 6m is filled with water. If the density of water is 1000kg/m^3, calculate the volume of water in the \tank.

A. 120\pi m^3

B. 240\pi m^3

Correct C. 360\pi m^3

D. 480\pi m^3

Correct Answer: C

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Question 7

Solve for x: \log_{10} \( x^2 \) = 4

A. 10^4

B. 10^8

Correct C. 10^12

D. 10^16

Correct Answer: C

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Question 8

A set of 10 numbers has a mean of 20. If 5 new numbers are added to the set, the mean increases to 25. What is the sum of the original 10 numbers?

Correct A. 150

B. 200

C. 250

D. 300

Correct Answer: A

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Question 9

A geometric sequence has a first term of 2 and a common ratio of 3. What is the sum of the first 5 terms?

A. 242

Correct B. 243

C. 244

D. 245

Correct Answer: B

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Question 10

A histogram shows the distribution of exam scores for a class of 20 students. The histogram has 5 bars, each representing a range of scores. The heights of the bars are 2, 3, 4, 5, and 6. What is the mean score of the class?

A. 4

B. 5

Correct C. 6

D. 7

Correct Answer: C

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Question 11

Let \( mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} 1 \ -2 \end{pmatrix} \). Find the projection of ( mathbf{b} ) onto ( mathbf{a} ).

A. \( egin{pmatrix} 0 \ 0 \end{pmatrix} \)

Correct B. \( egin{pmatrix} 1 \ 2 \end{pmatrix} \)

C. \( egin{pmatrix} 2 \ -4 \end{pmatrix} \)

D. \( egin{pmatrix} 4 \ -8 \end{pmatrix} \)

Correct Answer: B

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Question 12

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 13

A binary operation ( ast ) is defined as \( a ast b = a^2 + b^2 \). Find the value of ( 2 ast 3 ).

A. 5

B. 7

Correct C. 9

D. 11

Correct Answer: C

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Question 14

A fair six-sided die is rolled. What is the probability that the number obtained is a multiple of 3?

A. \frac{1}{2}

B. \frac{1}{3}

Correct C. \frac{2}{3}

D. \frac{4}{5}

Correct Answer: C

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Question 15

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

Correct A. \( x = -2 \)

B. \( x = 2 \)

C. \( x = -1 \) or \( x = 4 \)

D. \( x = -4 \) or \( x = 1 \)

Correct Answer: A

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Question 16

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

A. 64

B. 80

Correct C. 96

D. 112

Correct Answer: C

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Question 17

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 18

Find the value of \( \log_{10} \left\( \frac{1}{2} \right \ \) + \log_{10} \left\( \frac{1}{3} \right \) ).

A. -1

Correct B. -2

C. -3

D. -4

Correct Answer: B

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Question 19

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

A. 242

B. 242.5

Correct C. 243

D. 243.5

Correct Answer: C

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Question 20

Find the determinant of the matrix \( \begin{bmatrix} 2 & 3 & 4 \ 5 & 6 & 7 \ 8 & 9 & 10 \end{bmatrix} \).

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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