Exam Body

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POST UTME BSU 2022 Mathematics | Objective

Are you preparing for POST UTME BSU 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.

Practice these randomly selected questions to test your readiness.

Question 1

Let X be a random variable with probability density function f(x) = \( \frac{1}{2}e^{-|x|} \) for -∞ < x < ∞. Find the probability that X is greater than 1.

Correct A. 0.5

B. 0.6

C. 0.7

D. 0.8

Correct Answer: A

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Question 2

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

Correct A. 0, \( \frac{pi}{2} \), (pi), \( \frac{3pi}{2} \)

B. 0, \( \frac{pi}{4} \), \( \frac{3pi}{4} \), (pi)

C. 0, \( \frac{pi}{6} \), \( \frac{pi}{3} \), \( \frac{2pi}{3} \)

D. 0, \( \frac{pi}{8} \), \( \frac{3pi}{8} \), \( \frac{5pi}{8} \)

Correct Answer: A

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

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

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

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

Correct Answer: A

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Question 4

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

Correct A. [3, 7, 15, 31, 63]

B. [3, 5, 7, 9, 11]

C. [3, 6, 12, 24, 48]

D. [3, 8, 16, 32, 64]

Correct Answer: A

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Question 5

A set of numbers is defined as \( S = {x in mathbb{R} : x^2 - 4x + 3 = 0} \). Find the elements of the set.

Correct A. {1, 3}

B. {2, 3}

C. {1, 2}

D. {3, 4}

Correct Answer: A

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Question 6

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} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ \) )

B. \( \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ \) + 12 )

C. \( \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ \) - 12 )

D. \( \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ \) + 24 )

Correct Answer: A

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Question 7

A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 90?

Correct A. 0.8413

B. 0.8413 + 0.1587

C. 0.8413 - 0.1587

D. 0.5

Correct Answer: A

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Question 8

Find the sum of the first 10 terms of the geometric series \( 2x^2 + 3x + 1 \) with first term \( a = 2 \) and common ratio \( r = 3 \).

Correct A. \( 2 cdot \frac{3^{10} - 1}{3 - 1} \)

B. \( 2 cdot \frac{3^{10} - 1}{3 - 1} + 1 \)

C. \( 2 cdot \frac{3^{10} - 1}{3 - 1} - 1 \)

D. \( 2 cdot \frac{3^{10} - 1}{3 - 1} + 2 \)

Correct Answer: A

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Question 9

Solve the system of linear equations u\sing matrices: \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix} \).

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

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

C. \( egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 3 \ 4 \end{bmatrix} \)

D. \( egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 4 \ 3 \end{bmatrix} \)

Correct Answer: A

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Question 10

Two events A and B are indep\endent. If ( P(A) = 0.4 ) and ( P(B) = 0.6 ), find ( P(A cap B) ).

Correct A. 0.24

B. 0.24 + 0.36

C. 0.24 - 0.36

D. 0.5

Correct Answer: A

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Question 11

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

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

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

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

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

Correct Answer: B

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Question 12

A sequence is defined as \( a_n = 2n^2 + 3n - 1 \). Find the sum of the first 5 terms of the sequence.

Correct A. a_1 + a_2 + a_3 + a_4 + a_5 = 55

B. a_1 + a_2 + a_3 + a_4 + a_5 = 65

C. a_1 + a_2 + a_3 + a_4 + a_5 = 75

D. a_1 + a_2 + a_3 + a_4 + a_5 = 85

Correct Answer: A

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Question 13

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

Correct A. x < -1 or x > 3/2

B. x < 1 or x > 3/2

C. x < -1 or x < 3/2

D. x > 1 or x > 3/2

Correct Answer: A

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Question 14

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

Correct A. \frac{4}{3}

B. \frac{2}{3}

C. \frac{1}{3}

D. \frac{1}{2}

Correct Answer: A

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Question 15

A set of numbers is defined as \( A = \{ x : x^2 - 4x + 3 = 0 \} \). Find the elements of set A.

Correct A. A = \{1, 3\}

B. A = \{2, 3\}

C. A = \{1, 2\}

D. A = \{3, 4\}

Correct Answer: A

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Question 16

In the diagram below, the graph of \( y = \frac{1}{2} \sin 2x \) is shown. If the graph passes through the point \( \frac{pi}{4}, 1 \ \) ), find the value of ( x ) when \( y = 0.5 \).

Correct A. 0.5

B. 1.2

C. 1.5

D. 2.0

Correct Answer: A

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Question 17

A fair six-sided die is rolled. If the number obtained is even, the die is rolled again. If the number obtained is odd, the die is rolled once more. What is the probability that the number obtained is greater than 4?

A. 1/4

B. 1/3

Correct C. 1/2

D. 2/3

Correct Answer: C

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Question 18

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 19

Find the value of \( \frac{d}{dx} left\( \frac{1}{x^2 + 1} \right \ \) ) u\sing the chain rule.

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

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

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

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

Correct Answer: A

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Question 20

A vector ( mathbf{a} ) has magnitude 5 and direction \( 30^circ \) north of east. Find the magnitude of the vector \( mathbf{a} + mathbf{b} \), where ( mathbf{b} ) is a vector with magnitude 3 and direction \( 60^circ \) south of west.

A. 4

B. 5

Correct C. 6

D. 7

Correct Answer: C

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Question 21

Determine the mean of the following dataset: 2, 4, 6, 8, 10. If the mean is increased by 2, what is the new mean?

A. 12

Correct B. 14

C. 16

D. 18

Correct Answer: B

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Question 22

Solve for x in the equation \( \sqrt{x^2 - 4} = 2 \).

Correct A. 2

B. -2

C. 4

D. -4

Correct Answer: A

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Question 23

A histogram is shown below. What is the range of the data?

Correct A. 10-20

B. 20-30

C. 30-40

D. 40-50

Correct Answer: A

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Question 24

Solve the quadratic equation \( x^2 + 5x + 6 = 0 \).

Correct A. -2

B. -3

C. 2

D. 3

Correct Answer: A

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Question 25

A vector ( mathbf{a} ) has a magnitude of 5 and points in the direction of the positive x-axis. A vector ( mathbf{b} ) has a magnitude of 3 and points in the direction of the positive y-axis. What is the magnitude of the sum of vectors ( mathbf{a} ) and ( mathbf{b} )?

A. 5

B. 6

Correct C. 7

D. 8

Correct Answer: C

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