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POST UTME UNIOSUN 2024 Mathematics | Objective

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Question 1 View Details

In the number base 8, what is the value of the expression \(5 \times 7 + 3\)?

Correct A. 37

B. 43

C. 53

D. 63

Correct Answer: A

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Question 2 View Details

A fair six-sided die is rolled. What is the probability that the number obtained is a multiple of 3?

A. \(1/6\)

B. \(1/3\)

C. \(2/3\)

Correct D. \(5/6\)

Correct Answer: D

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Question 3 View Details

Find the derivative of the function ( f(x) = \(x^2\) \sin x ) using the chain rule.

Correct A. \(x^2 \(1x + 2x\)1x\)

B. \(x^2 \(1x - 2x\)1x\)

C. \(x^2 \(1x - 2x\)1x\)

D. \(x^2 \(1x + 2x\)1x\)

Correct Answer: A

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Question 4 View Details

Solve the system of equations using matrices: \(\begin{array}{cc|c} 2x + 3y & = & 7 \ 4x - 2y & = & -3 \ \end{array}\)

Correct A. \(\begin{array}{c} x = 1 \ y = 2 \ \end{array}\)

B. \(\begin{array}{c} x = 2 \ y = 1 \ \end{array}\)

C. \(\begin{array}{c} x = 3 \ y = 4 \ \end{array}\)

D. \(\begin{array}{c} x = 4 \ y = 3 \ \end{array}\)

Correct Answer: A

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Question 5 View Details

Simplify the expression \(\sqrt{48} \\)

A. 4\sqrt{3}

Correct B. 6\sqrt{2}

C. 8\sqrt{3}

D. 12\sqrt{2}

Correct Answer: B

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Question 6 View Details

Find the equation of the circle with center at \(-2, 3\) and radius 4.

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

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

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

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

Correct Answer: A

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Question 7 View Details

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

A. \(x = 2\)

B. \(x = 3\)

Correct C. \(x = 4\)

D. \(x = 5\)

Correct Answer: C

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Question 8 View Details

A circle with center at (0, 0) and radius 5 passes through the point (3, 4). Find the equation of the circle.

Correct A. \boxed{\(x^2\) + \\((y^2\)\(= 25\)\)}

B. \(x^2\) + \\((y^2\)\(= 20\)\)

C. \(x^2\) + \\((y^2\)\(= 30\)\)

D. \(x^2\) + \\((y^2\)\(= 35\)\)

Correct Answer: A

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Question 9 View Details

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

Correct A. \boxed{\(\frac{32\pi}{3}\)\)}

B. \(\frac{16\pi}{3}\)\)

C. \(\frac{64\pi}{3}\)\)

D. \(\frac{128\pi}{3}\)\)

Correct Answer: A

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Question 10 View Details

A fair six-sided die is rolled. What is the probability that the number obtained is a multiple of 3?

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

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

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

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

Correct Answer: A

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Question 11 View Details

Find the derivative of the function ( f(x) = \(\frac{1}\){\(\sqrt{x}\)}\) ) using the chain rule.

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

B. \(\frac{1}\){\(2x^{\)\(3/2\)}}\)

C. \(\frac{1}\){\(x^{\)\(3/2\)}}\)

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

Correct Answer: A

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Question 12 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?

A. 0.9544

Correct B. 0.9772

C. 0.9987

D. 0.9999

Correct Answer: B

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Question 13 View Details

Solve the system of linear equations using matrices: \begin{align*} 2x + 3y &= 7 \ 4x - 2y &= -2 \end{align*}

Correct A. \begin{pmatrix} \(x = 1\) \ \(y = 2\) \end{pmatrix}

B. \begin{pmatrix} \(x = 2\) \ \(y = 1\) \end{pmatrix}

C. \begin{pmatrix} \(x = 3\) \ \(y = 4\) \end{pmatrix}

D. \begin{pmatrix} \(x = 4\) \ \(y = 3\) \end{pmatrix}

Correct Answer: A

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Question 14 View Details

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

Correct A. 64

B. 32

C. 16

D. 8

Correct Answer: A

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Question 15 View Details

Convert the decimal number 0.75 to a \fraction in its simplest form.

Correct A. \(3/4\)

B. \(1/2\)

C. \(3/8\)

D. \(1/4\)

Correct Answer: A

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Question 16 View Details

Let X and Y be independent random variables with probability density functions f_\(X(x) = 2x\), \(0 \le x\)\(\le 1\), and f_\(Y(y) =\)\(3y^2\), \(0 \le y\) ≤ 1. Find the probability P\(X + Y \le 1\).

Correct A. 0.25

B. 0.5

C. 0.75

D. 1

Correct Answer: A

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Question 17 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. \(x - 2\)^2 + \(y + 3\)^\(2 = 16\)

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

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

Correct Answer: A

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Question 18 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?

A. 0.25

Correct B. 0.5

C. 0.75

D. 1

Correct Answer: B

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Question 19 View Details

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

Correct A. \(x = -2\)

B. \(x = -3\)

C. \(x = 2\)

D. \(x = 3\)

Correct Answer: A

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Question 20 View Details

Find the vector product of vectors \(A = (2\), 3, 4) and \(B = (1\), 2, 3).

Correct A. \(3, -7, -5\)

B. \(7, -3, 5\)

C. \(-3, 7, 5\)

D. \(5, -7, 3\)

Correct Answer: A

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Question 21 View Details

Determine the mean of the following data set: 2, 4, 6, 8, 10. If the mean is 6, what is the value of the missing data point?

A. 12

Correct B. 14

C. 16

D. 18

Correct Answer: B

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Question 22 View Details

Solve the system of 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. \(egin{bmatrix} -1 \ 2 \end{bmatrix}\)

B. \(egin{bmatrix} 1 \ -2 \end{bmatrix}\)

C. \(egin{bmatrix} 2 \ -1 \end{bmatrix}\)

D. \(egin{bmatrix} -2 \ 1 \end{bmatrix}\)

Correct Answer: A

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Question 23 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 - 2 \\)^2 + \(y - 3\)^\(2 = 20\) )

C. \(x - 2 \\)^2 + \(y - 3\)^\(2 = 24\) )

D. \(x - 2 \\)^2 + \(y - 3\)^\(2 = 28\) )

Correct Answer: A

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Question 24 View Details

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

Correct A. \(x < -1\) or \(x > \frac{3}{2}\)

B. \(x < -\frac{3}{2}\) or \(x > 1\)

C. \(x < -\frac{1}{2}\) or \(x > 3\)

D. \(x < 1\) or \(x > -3\)

Correct Answer: A

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Question 25 View Details

Find the vector ( mathbf{a} ) such that \(\mathbf{a} \cdot \mathbf{b} = 12\) and \(\mathbf{a} \cdot \mathbf{c} = 20\), where \(\mathbf{b} = egin{bmatrix} 2 \ 3 \end{bmatrix}\) and \(\mathbf{c} = egin{bmatrix} 4 \ 5 \end{bmatrix}\).

Correct A. \(egin{bmatrix} 6 \ 4 \end{bmatrix}\)

B. \(egin{bmatrix} 4 \ 6 \end{bmatrix}\)

C. \(egin{bmatrix} 8 \ 6 \end{bmatrix}\)

D. \(egin{bmatrix} 6 \ 8 \end{bmatrix}\)

Correct Answer: A

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