Exam Body

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Subject

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POST UTME RSU 2023 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 2023 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

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

Correct A. 10^4

B. 10^8

C. 10^2

D. 10^6

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

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

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

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

Correct Answer: A

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Question 3

A box contains 5 red balls and 3 blue balls. If two balls are drawn at random, what is the probability that both balls are blue?

A. \frac{1}{14}

Correct B. \frac{3}{14}

C. \frac{1}{7}

D. \frac{3}{7}

Correct Answer: B

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Question 4

In the circuit below, find the equivalent resis\tance between points A and B.

A. R1 + R2

Correct B. R1 || R2

C. R1 || R2 || V

D. R1 + R2 + V

Correct Answer: B

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Question 5

Solve the trigonometric equation \( \sin^2 x + \cos^2 x = 1 \) for x.

A. x = \frac{\pi}{2}

Correct B. x = \frac{\pi}{4}

C. x = \frac{3\pi}{4}

D. x = \frac{5\pi}{4}

Correct Answer: B

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Question 6

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

Correct A. \( 22.5 + 24 - 8 = 38.5 \)

B. \( 8 + 24 - 2 = 30 \)

C. \( 8 + 24 - 8 = 24 \)

D. \( 22.5 + 24 - 8 = 38.5 \)

Correct Answer: A

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Question 7

Solve for ( x ) in the equation \( 2x^2 - 5x + 3 = 0 \).

Correct A. \( x = \frac{5 \pm \sqrt{25 - 24}}{4} = \frac{5 \pm 1}{4} \ \)

B. \( x = \frac{5 \pm \sqrt{25 + 24}}{4} = \frac{5 \pm 7}{4} \ \)

C. \( x = \frac{5 \pm \sqrt{25 - 24}}{2} = \frac{5 \pm 1}{2} \ \)

D. \( x = \frac{5 \pm \sqrt{25 + 24}}{2} = \frac{5 \pm 7}{2} \ \)

Correct Answer: A

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Question 8

Find the determinant of the matrix \( \begin{bmatrix} 2 & 3 & 1 \\ 4 & 1 & 2 \\ 3 & 2 & 1 \end{bmatrix} \).

Correct A. \( 2\( 1 - 4 \ \) - 3\( 8 - 6 \) + 1\( 8 - 3 \) = -6 - 6 + 5 = -7 )

B. \( 2\( 1 - 4 \ \) - 3\( 8 - 6 \) + 1\( 8 - 3 \) = -6 - 6 + 5 = -7 )

C. \( 2\( 1 - 4 \ \) - 3\( 8 - 6 \) + 1\( 8 - 3 \) = -6 - 6 + 5 = -7 )

D. \( 2\( 1 - 4 \ \) - 3\( 8 - 6 \) + 1\( 8 - 3 \) = -6 - 6 + 5 = -7 )

Correct Answer: A

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Question 9

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

Correct A. \( x < -\frac{5}{4} \ \) or \( x > \frac{3}{2} \ \)

B. \( x < -\frac{3}{2} \ \) or \( x > \frac{5}{4} \ \)

C. \( x < -\frac{3}{2} \ \) or \( x > \frac{5}{4} \ \)

D. \( x < -\frac{5}{4} \ \) or \( x > \frac{3}{2} \ \)

Correct Answer: A

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Question 10

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

Correct A. \( \frac{1}{2}\( 3 \ \)(4) = 6 \)

B. \( \frac{1}{2}\( 4 \ \)(3) = 6 \)

C. \( \frac{1}{2}\( 3 \ \)(4) = 6 \)

D. \( \frac{1}{2}\( 4 \ \)(3) = 6 \)

Correct Answer: A

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Question 11

A random variable X has a probability distribution given by P(X) = \( 1/2 \)^\( X-1 \) for X = 1, 2, 3, ... . Find the expected value of X.

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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Question 12

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

A. 13/3

Correct B. 14/3

C. 15/3

D. 16/3

Correct Answer: B

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Question 13

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

A. 16\pi/5

B. 32\pi/5

Correct C. 48\pi/5

D. 64\pi/5

Correct Answer: C

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Question 14

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.

A. 32\pi/5

Correct B. 48\pi/5

C. 64\pi/5

D. 80\pi/5

Correct Answer: B

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Question 15

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

A. 32\pi/5

B. 48\pi/5

Correct C. 64\pi/5

D. 80\pi/5

Correct Answer: C

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Question 16

Determine the volume of the frustum of a cone with a height of 10 cm, a lower base radius of 4 cm, and an upper base radius of 2 cm.

A. 50\pi cm^3

Correct B. 75\pi cm^3

C. 100\pi cm^3

D. 125\pi cm^3

Correct Answer: B

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Question 17

Solve the system of equations u\sing matrices: \[\begin{array}{ccc} x+y+z &=& 6 \\ x+2y+3z &=& 11 \\ 2x+3y+4z &=& 14 \end{array}\]

Correct A. x=1, y=2, z=3

B. x=2, y=3, z=1

C. x=3, y=1, z=2

D. x=4, y=2, z=1

Correct Answer: A

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Question 18

A histogram of exam scores is shown below. What is the mean score of the exam?

A. 60

B. 70

Correct C. 80

D. 90

Correct Answer: C

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Question 19

Solve the quadratic equation: \(x^2+4x+4=0\)

Correct A. x=-2

B. x=2

C. x=-1

D. x=1

Correct Answer: A

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Question 20

A right-angled triangle has a hypotenuse of length 10 cm and one leg of length 6 cm. Find the length of the other leg.

Correct A. 8 cm

B. 6 cm

C. 4 cm

D. 2 cm

Correct Answer: A

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Question 21

Solve for x in the equation \( \sin^2 x + \cos^2 x = 1 \) u\sing the identity \( \sin^2 x + \cos^2 x = 1 \).

Correct A. \( x = \frac{pi}{2} \)

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

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

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

Correct Answer: A

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Question 22

A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. What is the probability that a randomly selected score is between 60 and 90?

Correct A. 0.68

B. 0.80

C. 0.90

D. 0.95

Correct Answer: A

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Question 23

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{1}{\( x^2 + 1 \)^2} )

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

Correct Answer: A

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Question 24

Evaluate the definite integral \( int_0^1 x^2 , dx \) u\sing the power rule.

Correct A. \( \frac{1}{3} \)

B. \( \frac{1}{2} \)

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

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

Correct Answer: A

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Question 25

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 = 9 )

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

D. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 36 )

Correct Answer: A

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