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POST UTME UNIBEN 2020 Mathematics | Objective

Are you preparing for POST UTME UNIBEN 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 value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).

Correct A. 10

B. 100

C. 1000

D. 10000

Correct Answer: A

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Question 2

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

Correct A. \( -∞, -1 \) ∪ (3, ∞)

B. \( -∞, -3 \) ∪ (1, ∞)

C. \( -∞, 1 \) ∪ (3, ∞)

D. \( -∞, -3 \) ∪ (1, ∞)

Correct Answer: A

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Question 3

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

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

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

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

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

Correct Answer: A

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Question 4

Solve the system of equations \( x + y = 2 \) and \( xy = 3 \).

Correct A. (1, 3)

B. (3, 1)

C. (2, 2)

D. \( -1, -3 \)

Correct Answer: A

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Question 5

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

Correct A. 62

B. 64

C. 66

D. 68

Correct Answer: A

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Question 6

A random variable X has a probability distribution given by P\( X = 1 \) = 0.4, P\( X = 2 \) = 0.3, P\( X = 3 \) = 0.2, and P\( X = 4 \) = 0.1. If two indep\endent random variables X and Y have the same probability distribution as X, find the probability that X + Y is greater than 5.

A. 0.2

B. 0.3

Correct C. 0.4

D. 0.5

Correct Answer: C

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Question 7

Find the volume of the solid formed by revolving the region bounded by the parabola y = x^2, the x-axis, and the line x = 2 about the x-axis.

A. 16\pi

B. 32\pi

Correct C. 64\pi

D. 128\pi

Correct Answer: C

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Question 8

Find the equation of the plane pas\sing through the points (1, 2, 3), (2, 3, 4), and (3, 4, 5).

Correct A. x + y + z = 6

B. x - y + z = 6

C. x + y - z = 6

D. x - y - z = 6

Correct Answer: A

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Question 9

Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.

A. 59048

Correct B. 59049

C. 59050

D. 59051

Correct Answer: B

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Question 10

Find the equation of the circle pas\sing through the points (1, 2), (2, 3), and (3, 4).

A. \( x - 2 \)^2 + \( y - 3 \)^2 = 1

B. \( x - 2 \)^2 + \( y - 3 \)^2 = 4

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

D. \( x - 2 \)^2 + \( y - 3 \)^2 = 16

Correct Answer: C

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Question 11

Determine the value of x in the equation \( 2^x + 5^x = 3^x \).

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 12

A circle has a radius of 4 cm. Find the area of the circle.

A. 16π

B. 32π

Correct C. 64π

D. 128π

Correct Answer: C

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Question 13

In a set of 5 numbers, the mean is 10 and the median is 8. If the largest number is 15, find the sum of the remaining 3 numbers.

A. 25

B. 30

Correct C. 35

D. 40

Correct Answer: C

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Question 14

A binary operation \( * \) on the set of real numbers is defined as \( a * b = a^2 + b^2 \). Find the value of \( 2 * 3 \).

A. 13

B. 17

Correct C. 19

D. 21

Correct Answer: C

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Question 15

A vector ( vec{a} ) has a magnitude of 5 units and makes an angle of 60° with the positive x-axis. Find the x-component of ( vec{a} ).

A. 2.5

B. 3.75

Correct C. 4.33

D. 5.00

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 \( x = 4 \).

A. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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Question 17

Solve the matrix equation \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 3 \ 7 \end{bmatrix} \).

A. x = 1, y = 2

Correct B. x = 2, y = 1

C. x = 3, y = 4

D. x = 4, y = 3

Correct Answer: B

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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. \( x - 3 \ \)^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 19

Find the sum of the first 10 terms of the geometric progression ( 2, 6, 18, ldots ).

Correct A. 59049

B. 59048

C. 59050

D. 59051

Correct Answer: A

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Question 20

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

Correct A. 6

B. 8

C. 10

D. 12

Correct Answer: A

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Question 21

A random variable X has a probability distribution given by P\( X = 1 \) = 0.3, P\( X = 2 \) = 0.4, and P\( X = 3 \) = 0.3. Find the expected value of X.

Correct A. 1.1

B. 1.2

C. 1.3

D. 1.4

Correct Answer: A

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Question 22

A set A contains 5 elements, and a set B contains 3 elements. If the intersection of A and B contains 2 elements, find the number of elements in the union of A and B.

A. 8

B. 9

Correct C. 10

D. 11

Correct Answer: C

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Question 23

A sequence is defined as: \[ a_n = \frac{1}{n} + \frac{1}{n+1} \]. Find the sum of the first 5 terms of the sequence.

A. 2.5

Correct B. 2.6

C. 2.7

D. 2.8

Correct Answer: B

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Question 24

A histogram is shown below: \[ \begin{array}{|c|c|c|c|} \hline \text{Class} & 0-10 & 10-20 & 20-30 \ \hline \text{Frequency} & 5 & 10 & 15 \ \hline \end{array} \]. Find the mean of the data.

A. 20

B. 21

Correct C. 22

D. 23

Correct Answer: C

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Question 25

A quadratic equation is given by: \[ x^2 + 4x + 4 = 0 \]. Find the roots of the equation.

A. 0

Correct B. -2

C. -1

D. 1

Correct Answer: B

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