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POST UTME UNILORIN 2019 Mathematics | Objective

Are you preparing for POST UTME UNILORIN exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2019 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

Determine the volume of the solid formed by revolving the region bounded by the curves y = x^2 and y = 4 - x^2 about the x-axis.

Correct A. \frac{16\pi}{3}

B. \frac{32\pi}{3}

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

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

Correct Answer: A

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Question 2

Find the mean deviation about the median for the data set: 2, 4, 6, 8, 10.

A. 2

Correct B. 4

C. 6

D. 8

Correct Answer: B

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Question 3

Solve the inequality: \frac{x}{x-1} > 0.

Correct A. \( -\infty, 0 \) \cup \( 1, \infty \)

B. \( -\infty, 1 \) \cup \( 1, \infty \)

C. \( -\infty, 0 \) \cup (0, 1)

D. (0, 1)

Correct Answer: A

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Question 4

Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 4).

Correct A. 12

B. 16

C. 20

D. 24

Correct Answer: A

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Question 5

A solid is formed by revolving the region bounded by the curves y = x^2 and y = 4 - x^2 about the x-axis. Find the volume of the solid.

Correct A. \frac{16\pi}{3}

B. \frac{32\pi}{3}

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

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

Correct Answer: A

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Question 6

Find the area under the curve y = 2x^2 + 3x - 1 from x = 0 to x = 2.

Correct A. 13

B. 14

C. 15

D. 16

Correct Answer: A

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Question 7

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

Correct A. \\begin{bmatrix} 1 \\\\ 2 \\end{bmatrix}

B. \\begin{bmatrix} 2 \\\\ 3 \\end{bmatrix}

C. \\begin{bmatrix} 3 \\\\ 4 \\end{bmatrix}

D. \\begin{bmatrix} 4 \\\\ 5 \\end{bmatrix}

Correct Answer: A

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Question 8

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

Correct A. \frac{32\pi}{5}

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

C. \frac{32\pi}{3}

D. \frac{64\pi}{5}

Correct Answer: A

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Question 9

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

Correct A. \( -\\infty, -1 \) \\cup \( 3, \\infty \)

B. \( -\\infty, -3 \) \\cup \( 1, \\infty \)

C. \( -\\infty, -2 \) \\cup \( 2, \\infty \)

D. \( -\\infty, -4 \) \\cup \( 4, \\infty \)

Correct Answer: A

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Question 10

Find the surface area of the solid formed by revolving the region bounded by y = x^2, y = 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 11

Solve the system of equations u\sing matrices: \begin{bmatrix} 2 & 1 \\ 1 & 2 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 3 \\ 4 \end{bmatrix}.

Correct A. \\begin{bmatrix} 1 \\\\ 2 \\end{bmatrix}

B. \\begin{bmatrix} 2 \\\\ 1 \\end{bmatrix}

C. \\begin{bmatrix} 3 \\\\ 4 \\end{bmatrix}

D. \\begin{bmatrix} 4 \\\\ 3 \\end{bmatrix}

Correct Answer: A

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Question 12

Find the volume of the solid formed by revolving the region bounded by y = x^3, y = 0, and x = 2 about the x-axis.

Correct A. \frac{64\pi}{7}

B. \frac{32\pi}{3}

C. \frac{64\pi}{5}

D. \frac{128\pi}{7}

Correct Answer: A

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Question 13

Solve the inequality x^2 - 4x + 3 > 0.

A. (1, 3)

B. \( -\\infty, 1 \) \\cup \( 3, \\infty \)

C. \( -\\infty, -1 \) \\cup \( 1, \\infty \)

D. \( -\\infty, -3 \) \\cup \( 3, \\infty \)

Correct Answer: VIEW ANSWER

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Question 14

In a random sample of 100 students, the mean height is 175 cm with a s\tandard deviation of 5 cm. If the distribution of heights is approximately normal, what is the probability that a randomly selected student will be taller than 180 cm?

Correct A. 0.1587

B. 0.3413

C. 0.4772

D. 0.6179

Correct Answer: A

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Question 15

A circle has a radius of 4 cm. If a chord of the circle subt\ends an angle of 60° at the center, what is the length of the chord?

A. 4 cm

Correct B. 6 cm

C. 8 cm

D. 10 cm

Correct Answer: B

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Question 16

Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).

A. 2

B. 4

Correct C. 8

D. 16

Correct Answer: C

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Question 17

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 will be between 60 and 90?

A. 0.8413

Correct B. 0.9772

C. 0.9986

D. 0.9999

Correct Answer: B

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Question 18

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

A. 32

B. 64

Correct C. 128

D. 256

Correct Answer: C

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Question 19

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

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

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

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

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

Correct Answer: A

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Question 20

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. 0.6915

C. 0.8413

D. 0.6915

Correct Answer: A

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Question 21

Find the equation of the line pas\sing through the points ( (2, 3) ) and ( (4, 5) ).

Correct A. \( y = \frac{1}{2}x + \frac{1}{2} \)

B. \( y = \frac{1}{2}x - \frac{1}{2} \)

C. \( y = 2x - 1 \)

D. \( y = 2x + 1 \)

Correct Answer: A

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Question 22

Solve the system of linear equations \( egin{cases} 2x + 3y = 7 \ x - 2y = -3 \end{cases} \).

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 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 = 4 )

C. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 9 )

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

Correct Answer: A

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Question 24

A binary operation ( ast ) is defined as \( a ast b = a^2 + b^2 \). Find the value of ( 2 ast 3 ).

A. 13

Correct B. 25

C. 5

D. 9

Correct Answer: B

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Question 25

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

Correct A. \( x = -2, x = -3 \)

B. \( x = 2, x = 3 \)

C. \( x = -1, x = -6 \)

D. \( x = 1, x = 6 \)

Correct Answer: A

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