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POST UTME BSU 2019 Mathematics | Objective

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Question 1 View Details

Determine the value of \(\frac{d}{dx} \left \frac{1}{x^2} \right\)\) using the quotient rule.

Correct A. \(\frac{2}{x^3}\)\)\)

B. -\(\frac{2}{x^3}\)\)\)

C. \(\frac{1}{x^3}\)\)\)

D. -\(\frac{1}{x^3}\)\)\)

Correct Answer: A

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Question 2 View Details

Solve the equation \(\log_2 x^2\)\(= 4\)\) for \(x\).

A. 2

B. 4

Correct C. 8

D. 16

Correct Answer: C

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Question 3 View Details

A histogram of exam scores is shown below. If the mean score is 75, what is the value of \(k\)?

A. 5

Correct B. 10

C. 15

D. 20

Correct Answer: B

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Question 4 View Details

Solve the equation \(\sin^2 x + \cos^2 x = 1\) for \(x\).

A. 0

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

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

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

Correct Answer: C

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Question 5 View Details

A circle with center \(C\) and radius \(r\) is shown below. If the area of the circle is \(\pi r^2\), what is the value of \(r\)?

A. 2

Correct B. 4

C. 6

D. 8

Correct Answer: B

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Question 6 View Details

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

Correct A. 27

B. 30

C. 33

D. 36

Correct Answer: A

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Question 7 View Details

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 8 View Details

Find the volume of the solid formed by revolving the region bounded by \(y = x\^2\), \(x = 0\), and \(x = 2\) about the x-axis.

Correct A. 16\pi

B. 32\pi

C. 64\pi

D. 128\pi

Correct Answer: A

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Question 9 View Details

Solve the system of equations \(x + y = 4\) and \(xy = 6\).

Correct A. (1, 3)

B. (2, 2)

C. (3, 1)

D. (4, 0)

Correct Answer: A

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Question 10 View Details

Find the surface area of the solid formed by revolving the region bounded by \(y = x\^2\), \(x = 0\), and \(x = 2\) about the x-axis.

Correct A. 32\pi

B. 64\pi

C. 128\pi

D. 256\pi

Correct Answer: A

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Question 11 View Details

Solve for 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 12 View Details

Find the area under the curve \(y = x^2\) from \(x = 0\) to \(x = 4\).

A. 64

B. 128

Correct C. 256

D. 512

Correct Answer: C

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Question 13 View Details

Solve the quadratic equation \(x^2 + 4x + 4 = 0\).

Correct A. -2

B. -1

C. 1

D. 2

Correct Answer: A

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Question 14 View Details

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 + \(y + 3\)^\(2 = 16\)

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

Correct Answer: A

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Question 15 View Details

Find the mean of the data set: ( 2, 4, 6, 8, 10 ).

A. 4

B. 6

Correct C. 8

D. 10

Correct Answer: C

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Question 16 View Details

Solve the inequality (\(\frac{x-2}{x+1}\(> 0\)\) for x in \\((frac{x-2}{x+1} > 0\(-\infty, -1 \ cup -1, 2\) cup (2\), infty) ).

Correct A. \(x < -1\) or \(x > 2\)

B. \(x > -1\) and \(x < 2\)

C. \(x < -1\) and \(x > 2\)

D. \(x > -1\) or \(x < 2\)

Correct Answer: A

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Question 17 View Details

Find the equation of the circle with center ( (3, 4) ) and radius ( 5 ).

Correct A. \(x-3 \\)^2 + \(y-4\)^\(2 = 25\) )

B. \(x-4 \\)^2 + \(y-3\)^\(2 = 25\) )

C. \(x-5 \\)^2 + \(y-3\)^\(2 = 25\) )

D. \(x-3 \\)^2 + \(y-5\)^\(2 = 25\) )

Correct Answer: A

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Question 18 View Details

Solve the system of equations \(egin{cases} x + y = 3 \ x - y = 1 \end{cases}\).

Correct A. \(x = 2, y = 1\)

B. \(x = 1, y = 2\)

C. \(x = 2, y = 2\)

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

Correct Answer: A

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Question 19 View Details

Find the vector ( mathbf{a} ) such that \(\mathbf{a} \cdot \mathbf{b} = 10\) and \(\mathbf{a} \cdot \mathbf{c} = 5\), where \(\mathbf{b} = egin{pmatrix} 2 \ 3 \end{pmatrix}\) and \(\mathbf{c} = egin{pmatrix} 1 \ 4 \end{pmatrix}\).

Correct A. \(egin{pmatrix} 5 \ 2 \end{pmatrix}\)

B. \(egin{pmatrix} 2 \ 5 \end{pmatrix}\)

C. \(egin{pmatrix} 3 \ 4 \end{pmatrix}\)

D. \(egin{pmatrix} 4 \ 3 \end{pmatrix}\)

Correct Answer: A

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Question 20 View Details

Solve the logarithmic equation \(\log_2 x^2 + 1 \\(logarithmic equation (\\)\(= 3 ).\)

Correct A. \(x = 7\)

B. \(x = -7\)

C. \(x = 3\)

D. \(x = -3\)

Correct Answer: A

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Question 21 View Details

Solve the system of linear equations using matrices: [ egin{array}{ccc|c} 2 & 1 & -1 & 3 \ 1 & -1 & 2 & 0 \ 3 & -2 & 1 & 5 \end{array} ]. Find the value of x.

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 22 View Details

A binary operation (*\) on the set of integers is defined as: [ \(a * b = a\\((*) on the set of integers is defined as: [ \^2 + b^2\) ]. Find the value of \(5 * 6\).

Correct A. 37

B. 40

C. 41

D. 42

Correct Answer: A

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Question 23 View Details

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

Correct A. -2

B. -1

C. 1

D. 2

Correct Answer: A

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Question 24 View Details

A probability experiment consists of two independent events A and B. The probability of event A occurring is 0.4 and the probability of event B occurring is 0.6. Find the probability of both events occurring.

Correct A. 0.24

B. 0.26

C. 0.28

D. 0.30

Correct Answer: A

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Question 25 View Details

A matrix is given by: [ \begin{bmatrix} 2 & 1 \ 3 & 4 \end{bmatrix} \]. Find the determinant of the matrix.

A. -1

Correct B. 1

C. 2

D. 3

Correct Answer: B

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