Exam Body

Year

Subject

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POST UTME RSU 2019 Mathematics | Objective

Are you preparing for POST UTME RSU 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

Find the area under the curve \( y = \frac{1}{2}x^2 - 3x + 2 \) from \( x = 0 \) to \( x = 4 \).

Correct A. 40

B. 42

C. 44

D. 46

Correct Answer: A

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Question 2

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 3

Find the value of ( x ) in the equation \( x^3 - 6x^2 + 11x - 6 = 0 \).

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 4

A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?

A. 1/6

B. 1/3

C. 1/2

Correct D. 2/3

Correct Answer: D

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Question 5

In the circuit below, what is the equivalent resis\tance between points A and B?

A. 2Ω

B. 4Ω

Correct C. 6Ω

D. 8Ω

Correct Answer: C

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Question 6

Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 24π cm³

Correct B. 48π cm³

C. 96π cm³

D. 192π cm³

Correct Answer: B

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Question 7

A die is rolled twice. What is the probability that the sum of the two numbers is 7?

A. 1/6

B. 1/3

Correct C. 1/2

D. 2/3

Correct Answer: C

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Question 8

Find the derivative of the function f(x) = \( 2x^2 + 3x - 1 \) / \( x^2 - 4x + 3 \) u\sing the quotient rule.

Correct A. \( 4x + 3 \) / \( x^2 - 4x + 3 \)²

B. \( 4x + 3 \) / \( x^2 - 4x + 3 \)

C. \( 2x^2 + 3x - 1 \) / \( x^2 - 4x + 3 \)²

D. \( 2x^2 + 3x - 1 \) / \( x^2 - 4x + 3 \)

Correct Answer: A

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Question 9

A set A contains 5 elements, and a set B contains 3 elements. What is the number of elements in the union of sets A and B?

A. 8

Correct B. 10

C. 12

D. 15

Correct Answer: B

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Question 10

Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 1/2.

A. 1.9375

B. 1.96875

Correct C. 1.984375

D. 2.000000

Correct Answer: C

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Question 11

Find the area under the curve \( y = \frac{1}{2}x^2 + 2x - 3 \) from \( x = 0 \) to \( x = 4 \).

A. 40

B. 60

Correct C. 80

D. 100

Correct Answer: C

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Question 12

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

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

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

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

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

Correct Answer: A

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Question 13

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

Correct A. y = x + 1

B. y = x - 1

C. y = 2x - 1

D. y = 2x + 1

Correct Answer: A

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Question 14

Find the area of the circle \( x^2 + y^2 = 4 \).

Correct A. 4\pi

B. 8\pi

C. 16\pi

D. 32\pi

Correct Answer: A

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Question 15

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

Correct A. \begin{bmatrix} 3 \ 1 \end{bmatrix}

B. \begin{bmatrix} 1 \ 3 \end{bmatrix}

C. \begin{bmatrix} 2 \ 2 \end{bmatrix}

D. \begin{bmatrix} 4 \ 0 \end{bmatrix}

Correct Answer: A

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Question 16

Solve the inequality \( \frac{x^2 - 4x - 5}{x + 1} > 0 \) for \( x in \( -infty, infty \ \) ).

Correct A. \( -infty, -1 \) \cup (5, infty)

B. \( -infty, -1 \) \cup \( -1, 5 \)

C. \( -infty, 5 \)

D. (5, infty)

Correct Answer: A

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Question 17

Find the area under the curve \( y = \sin^2 x \) from \( x = 0 \) to \( x = \frac{pi}{2} \).

Correct A. \frac{\pi}{4}

B. \frac{\pi}{2}

C. \frac{\pi}{3}

D. \frac{\pi}{6}

Correct Answer: A

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Question 18

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

A. (0, 2)

Correct B. (1, 1)

C. (2, 0)

D. (1, 2)

Correct Answer: B

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Question 19

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 = 9

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

Correct Answer: A

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Question 20

Solve the equation \( x^3 - 6x^2 + 11x - 6 = 0 \).

Correct A. (1, 2, 3)

B. (1, 2, 6)

C. (1, 3, 6)

D. (2, 3, 6)

Correct Answer: A

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Question 21

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

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

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

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

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

Correct Answer: A

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Question 22

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

Correct A. \( x < -1 \) or \( x > 5 \)

B. \( x > -1 \) or \( x < 5 \)

C. \( x < 1 \) or \( x > 5 \)

D. \( x > 1 \) or \( x < 5 \)

Correct Answer: A

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Question 23

A set ( A ) contains 5 elements. If 3 elements are randomly selected from set ( A ), find the probability that the selected elements are distinct.

Correct A. \( \frac{3}{10} \)

B. \( \frac{3}{20} \)

C. \( \frac{3}{5} \)

D. \( \frac{3}{15} \)

Correct Answer: A

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Question 24

Find the sum of the first 10 terms of the geometric series \( 2x + 3x^2 + 4x^3 + ldots \).

Correct A. \( \frac{2x\( 1 - x^{10} \)\( 1 + x \ \)}{\( 1 - x \)^2} )

B. \( \frac{2x\( 1 - x^{10} \ \)}{\( 1 - x \)^2} )

C. \( \frac{2x\( 1 - x^{10} \)\( 1 + x \ \)^2}{\( 1 - x \)^2} )

D. \( \frac{2x\( 1 - x^{10} \ \)}{\( 1 - x \)^3} )

Correct Answer: A

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Question 25

A box contains 5 red balls and 3 blue balls. If 2 balls are randomly selected, find the probability that both balls are red.

Correct A. \( \frac{5}{8} \)

B. \( \frac{5}{14} \)

C. \( \frac{3}{14} \)

D. \( \frac{1}{4} \)

Correct Answer: A

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