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POST UTME UNIOSUN 2024 Mathematics | Objective

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Question 1

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

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

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

Correct A. \( x^2 \cos x + 2x \sin x \)

B. \( x^2 \sin x - 2x \cos x \)

C. \( x^2 \cos x - 2x \sin x \)

D. \( x^2 \sin x + 2x \cos x \)

Correct Answer: A

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Question 4

Solve the system of equations u\sing 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

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

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

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

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

Find the volume of the solid formed by revolving the region bounded by the parabola y = x^2 and the line 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

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

Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x}} ) u\sing 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

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?

A. 0.9544

Correct B. 0.9772

C. 0.9987

D. 0.9999

Correct Answer: B

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Question 13

Solve the system of linear equations u\sing 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

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

Correct A. 64

B. 32

C. 16

D. 8

Correct Answer: A

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Question 15

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

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

Correct A. 0.25

B. 0.5

C. 0.75

D. 1

Correct Answer: A

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Question 17

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

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?

A. 0.25

Correct B. 0.5

C. 0.75

D. 1

Correct Answer: B

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Question 19

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

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

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

A. 12

Correct B. 14

C. 16

D. 18

Correct Answer: B

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Question 22

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

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

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

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

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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