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POST UTME BSU 2022 Mathematics | Objective

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Question 1 View Details

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 View Details

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

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

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

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

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

Correct Answer: A

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Question 3 View Details

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

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 View Details

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 View Details

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 View Details

A histogram of exam scores has a mean of 75 and a standard 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 View Details

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 View Details

Solve the system of linear equations using 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 View Details

Two events A and B are independent. 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 View Details

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

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 View Details

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 View Details

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 View Details

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 View Details

In the diagram below, the graph of (y = \(\frac{1}{2}\) \(12x\) is shown. If the graph passes through the point \\((y = frac{1}{2}\)12x\(\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 View Details

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 View Details

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 View Details

Find the value of \(\frac{d}{dx} \left \frac{1}{x^2 + 1} \right \\) ) using 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 View Details

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

A. 4

B. 5

Correct C. 6

D. 7

Correct Answer: C

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Question 21 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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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