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POST UTME UNILORIN 2022 Mathematics | Objective

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Question 1 View Details

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 View Details

Find the derivative of the function ( f(x) = \(\frac{1}{x^2}\)\)\) ) using 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 View Details

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 View Details

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 View Details

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 View Details

Find the derivative of the function ( f(x) = \(\frac{1}\){\sqrt{1-\(x^2}}\)\) ) using 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 View Details

Solve the inequality \(2x^2 + 5x - 3 > 0\) using 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 View Details

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 View Details

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 View Details

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 View Details

Determine the mean of the data set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} using 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 View Details

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

Correct A. -2

B. -1

C. 0

D. 1

Correct Answer: A

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Question 13 View Details

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 View Details

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 standard 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 View Details

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

Correct A. -3

B. -2

C. -1

D. 0

Correct Answer: A

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Question 16 View Details

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 View Details

A histogram of exam scores has a mean of 75 and a standard deviation of 10. If 80% of the scores lie within 2 standard 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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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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