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POST UTME RHEMA UNIVERSITY 2019 Mathematics | Objective

Are you preparing for POST UTME RHEMA UNIVERSITY 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.

Practice these randomly selected questions to test your readiness.

Question 1

Let X be a random variable with probability density function ( f(x) = egin{cases} 2x & 0 leq x leq 1 \ 0 & \text{otherwise} \end{cases} ). Find the probability that X is greater than 0.5.

Correct A. \( P\( X > 0.5 \ \) = \frac{1}{2} )

B. \( P\( X > 0.5 \ \) = \frac{1}{4} )

C. \( P\( X > 0.5 \ \) = \frac{3}{4} )

D. \( P\( X > 0.5 \ \) = \frac{1}{3} )

Correct Answer: A

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Question 2

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

Correct A. ( f'(x) = \frac{-2x}{\( x^2 + 1 \)^2} )

B. ( f'(x) = \frac{2x}{\( x^2 + 1 \)^2} )

C. ( f'(x) = \frac{2}{\( x^2 + 1 \)^2} )

D. ( f'(x) = \frac{-2}{\( x^2 + 1 \)^2} )

Correct Answer: A

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Question 3

A rec\tangular prism has dimensions 3 cm, 4 cm, and 5 cm. Find the volume of the prism.

Correct A. \( V = 60 \text{ cm}^3 \)

B. \( V = 120 \text{ cm}^3 \)

C. \( V = 180 \text{ cm}^3 \)

D. \( V = 240 \text{ cm}^3 \)

Correct Answer: A

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Question 4

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

Correct A. \( A = \frac{8}{3} \)

B. \( A = \frac{16}{3} \)

C. \( A = \frac{24}{3} \)

D. \( A = \frac{32}{3} \)

Correct Answer: A

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Question 5

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

Correct A. \( x = \frac{pi}{4}, \frac{3pi}{4} \)

B. \( x = \frac{pi}{4}, \frac{5pi}{4} \)

C. \( x = \frac{pi}{4}, \frac{7pi}{4} \)

D. \( x = \frac{pi}{4}, \frac{9pi}{4} \)

Correct Answer: A

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Question 6

Find the area under the curve \( y = \frac{1}{x^2} \) from \( x = 1 \) to \( x = 2 \).

Correct A. 0.5

B. 1

C. 1.5

D. 2

Correct Answer: A

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Question 7

A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find its volume.

Correct A. 30

B. 40

C. 50

D. 60

Correct Answer: A

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Question 8

Find the derivative of the function \( y = 3x^2 + 2x - 5 \) u\sing the chain rule.

Correct A. 6x + 2

B. 6x + 2 + 2x

C. 6x + 2 - 5

D. 6x + 2x - 5

Correct Answer: A

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Question 9

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{\pi}{6}

Correct Answer: C

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Question 10

A circle has a radius of 4 cm. Find its circumference.

Correct A. 8\pi

B. 10\pi

C. 12\pi

D. 16\pi

Correct Answer: A

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Question 11

Find the equation of the circle pas\sing through the points (2, 3), (4, 1), and \( -1, 2 \).

Correct A. x^2 + y^2 - 6x - 2y + 12 = 0

B. x^2 + y^2 - 4x + 2y + 8 = 0

C. x^2 + y^2 + 2x - 4y + 4 = 0

D. x^2 + y^2 - 2x + 4y - 8 = 0

Correct Answer: A

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Question 12

Solve the equation \( \sin^2 x + \cos^2 x = \frac{3}{4} \) for x in the interval [0, 2\pi].

Correct A. \( x = \frac{\pi}{6}, \frac{5\pi}{6} \)

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

C. \( x = \frac{\pi}{3}, \frac{2\pi}{3} \)

D. \( x = \frac{\pi}{2}, \frac{3\pi}{2} \)

Correct Answer: A

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Question 13

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

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

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

Correct C. \( \frac{128\pi}{3} \)

D. \( \frac{256\pi}{3} \)

Correct Answer: C

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Question 14

Solve the matrix equation \( \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 7 \end{bmatrix} \) for x and y.

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

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

C. \( x = 3, y = 4 \)

D. \( x = 4, y = 3 \)

Correct Answer: A

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Question 15

Find the equation of the line pas\sing through the points (1, 2) and (3, 4).

Correct A. y = 2x - 1

B. y = 2x + 1

C. y = x + 1

D. y = x - 1

Correct Answer: A

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Question 16

Determine the value of x in the equation \( \frac{x}{2} + \frac{1}{3} = \frac{7}{12} \).

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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Question 17

Find the area under the curve \( y = \frac{1}{x^2} \) from \( x = 1 \) to \( x = 2 \).

Correct A. 0.5

B. 1

C. 1.5

D. 2

Correct Answer: A

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Question 18

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

Correct A. \( -∞, -1 \) ∪ (3, ∞)

B. \( -∞, 1 \) ∪ (3, ∞)

C. \( -∞, -1 \) ∪ (1, ∞)

D. \( -∞, 3 \) ∪ (1, ∞)

Correct Answer: A

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Question 19

A set of 5 numbers has a mean of 10. If 2 is added to each number, what is the new mean?

A. 8

B. 10

Correct C. 12

D. 14

Correct Answer: C

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Question 20

In a geometric sequence, the first term is 2 and the common ratio is 3. Find the 5th term.

Correct A. 243

B. 2430

C. 24300

D. 243000

Correct Answer: A

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Question 21

Find the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 22

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

Correct A. x > 4

B. x < 4

C. x > 2

D. x < 2

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 = 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 24

Solve the system of equations \( x + y = 4 \) and \( x - y = 2 \).

Correct A. x = 3, y = 1

B. x = 1, y = 3

C. x = 2, y = 2

D. x = 4, y = 0

Correct Answer: A

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Question 25

Find the derivative of the function ( f(x) = 3x^2 + 2x - 5 ).

Correct A. f'(x) = 6x + 2

B. f'(x) = 6x - 2

C. f'(x) = 3x^2 + 2

D. f'(x) = 3x^2 - 2

Correct Answer: A

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