Exam Body

Year

Subject

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POST UTME UNILORIN 2022 Mathematics | Objective

Are you preparing for POST UTME UNILORIN exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2022 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

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

A. 5

B. 6

C. 7

Correct D. 8

Correct Answer: D

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Question 2

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

Correct A. ( f'(x) = -\frac{2}{x^3} )

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

C. ( f'(x) = -\frac{1}{x^3} )

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

Correct Answer: A

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Question 3

A random experiment consists of rolling a fair six-sided die. If the number rolled is even, the experimenter wins. If the number rolled is odd, the experimenter loses. What is the probability of winning?

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

B. \( \frac{1}{3} \)

C. \( \frac{2}{3} \)

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

Correct Answer: A

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Question 4

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

A. \( x = 2 \)

B. \( x = 3 \)

C. \( x = 4 \)

Correct D. \( x = 5 \)

Correct Answer: D

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Question 5

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

A. \( \frac{1}{3} pi \)

B. \( \frac{2}{3} pi \)

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

D. \( \frac{5}{3} pi \)

Correct Answer: C

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Question 6

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

Correct A. ( f'(x) = \frac{-x}{\( 1-x^2 \)^{3/2}} )

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

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

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

Correct Answer: A

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Question 7

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

Correct A. \( x < -\frac{5}{4} \) or \( x > \frac{3}{2} \)

B. \( x < -\frac{3}{2} \) or \( x > -\frac{5}{4} \)

C. \( x < -\frac{5}{4} \) or \( x < \frac{3}{2} \)

D. \( x > -\frac{3}{2} \) or \( x > \frac{5}{4} \)

Correct Answer: A

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Question 8

Find the sum of the first 10 terms of the geometric series \( 2 + 6 + 18 + ldots \).

A. \( 2 + 6 + 18 + ldots + 972 \)

B. \( 2 + 6 + 18 + ldots + 1022 \)

Correct C. \( 2 + 6 + 18 + ldots + 1032 \)

D. \( 2 + 6 + 18 + ldots + 1042 \)

Correct Answer: C

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Question 9

Find the area of the triangle formed by the points ( (0, 0) ), ( (3, 0) ), and ( (0, 2) ).

Correct A. ( 6 )

B. ( 8 )

C. ( 10 )

D. ( 12 )

Correct Answer: A

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Question 10

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

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

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

C. \( x = -1, y = 1 \)

D. \( x = -1, y = -1 \)

Correct Answer: A

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Question 11

Determine the mean of the data set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} u\sing the formula \( ar{x} = \frac{1}{n} sum_{i=1}^{n} x_i \).

A. 5

B. 6

C. 7

Correct D. 8

Correct Answer: D

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Question 12

Solve the equation \( x^2 + 4x + 4 = 0 \) u\sing the quadratic formula \( x = \frac{-b pm \sqrt{b^2 - 4ac}}{2a} \).

Correct A. -2

B. -1

C. 0

D. 1

Correct Answer: A

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Question 13

A histogram is a graphical representation of a frequency distribution. What is the primary purpose of a histogram?

A. To show the relationship between two variables

Correct B. To display the distribution of a \single variable

C. To compare the means of two groups

D. To illustrate the concept of probability

Correct Answer: B

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Question 14

A circle with center ( C(2, 3) ) and radius \( r = 4 \) is drawn on a coordinate plane. What is the equation of the circle in s\tandard form?

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

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

C. \( x - 4 \ \)^2 + \( y - 3 \)^2 = 16 )

D. \( x - 2 \ \)^2 + \( y - 4 \)^2 = 16 )

Correct Answer: A

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Question 15

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

Correct A. -3

B. -2

C. -1

D. 0

Correct Answer: A

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Question 16

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

Correct A. \( -∞, 2 \) ∪ (2, ∞)

B. \( -∞, 2 \) ∪ (2, ∞) ∪ {2}

C. \( -∞, 2 \) ∪ (2, ∞) ∪ \( -2, 2 \)

D. \( -∞, 2 \) ∪ (2, ∞) ∪ (2, ∞)

Correct Answer: A

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Question 17

A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If 80% of the scores lie within 2 s\tandard deviations of the mean, what is the minimum score that 80% of the students scored?

A. 50

Correct B. 55

C. 60

D. 65

Correct Answer: B

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Question 18

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

Correct A. 16π/3

B. 32π/3

C. 64π/3

D. 128π/3

Correct Answer: A

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Question 19

A polynomial function has a degree of 4 and has roots at \( x = -2, 0, 1, 3 \). What is the polynomial function?

Correct A. x\( x - 2 \)\( x - 1 \)\( x - 3 \)

B. x\( x + 2 \)\( x + 1 \)\( x + 3 \)

C. x\( x - 2 \)\( x + 1 \)\( x + 3 \)

D. x\( x + 2 \)\( x - 1 \)\( x - 3 \)

Correct Answer: A

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Question 20

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

Correct A. 13/3

B. 26/3

C. 39/3

D. 52/3

Correct Answer: A

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Question 21

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 22

A set A contains 5 elements. If we select 2 elements at random from set A, what is the probability that the selected elements are not equal?

A. 1/3

B. 1/2

Correct C. 2/3

D. 5/6

Correct Answer: C

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Question 23

Find the value of x in the equation \( x^2 + 4x + 4 = 0 \).

Correct A. -2

B. -1

C. 1

D. 2

Correct Answer: A

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Question 24

A histogram represents the distribution of exam scores for a class of 50 students. The histogram shows that 10 students scored between 70-79, 15 students scored between 80-89, and 25 students scored between 90-100. What is the mean score of the class?

A. 85

Correct B. 87

C. 90

D. 92

Correct Answer: B

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Question 25

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

A. x < -3

Correct B. x > -3

C. x < 1

D. x > 1

Correct Answer: B

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