Exam Body

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Subject

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POST UTME RSU 2022 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 2022 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

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 2

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

A. 60

Correct B. 70

C. 80

D. 90

Correct Answer: B

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Question 3

Solve the equation \( 2x^2 + 5x - 3 = 0 \) u\sing the quadratic formula.

A. \frac{-5 \pm \sqrt{109}}{4}

B. \frac{-5 \pm \sqrt{121}}{4}

Correct C. \frac{-5 \pm \sqrt{169}}{4}

D. \frac{-5 \pm \sqrt{225}}{4}

Correct Answer: C

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Question 4

Find the determinant of the matrix \( \begin{bmatrix} 2 & 3 & 4 \ 5 & 6 & 7 \ 8 & 9 & 10 \end{bmatrix} \).

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 5

A vector \( \mathbf{a} = \begin{bmatrix} 2 \ 3 \ 4 \end{bmatrix} \) is given. Find the magnitude of the vector.

Correct A. \sqrt{29}

B. \sqrt{31}

C. \sqrt{33}

D. \sqrt{35}

Correct Answer: A

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Question 6

Find the derivative of ( 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 7

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

Correct A. \( x = 10^4 \)

B. \( x = 10^2 \)

C. \( x = 10^{-2} \)

D. \( x = 10^{-4} \)

Correct Answer: A

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Question 8

Find the value of \( \sin \( 2 \theta \ \) ) given that \( \sin \( \theta \ \) = \frac{3}{5} ) and \( \cos \( \theta \ \) = \frac{4}{5} ).

Correct A. \( \frac{24}{25} \)

B. \( \frac{16}{25} \)

C. \( \frac{20}{25} \)

D. \( \frac{12}{25} \)

Correct Answer: A

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Question 9

A sequence is defined by \( a_n = 2n + 1 \). Find the sum of the first 5 terms of the sequence.

A. ( 15 )

B. ( 25 )

Correct C. ( 35 )

D. ( 45 )

Correct Answer: C

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Question 10

A vector ( mathbf{a} ) has components \( a_x = 3 \) and \( a_y = 4 \). Find the magnitude of the vector.

A. ( 5 )

Correct B. ( 10 )

C. ( 15 )

D. ( 20 )

Correct Answer: B

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Question 11

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 that X + Y < 1.

A. 1/4

Correct B. 1/2

C. 3/4

D. 1

Correct Answer: B

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Question 12

Find the area under the curve y = 2x^2 + 3x - 4 from x = 0 to x = 2.

A. 20

B. 30

Correct C. 40

D. 50

Correct Answer: C

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Question 13

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

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

B. \frac{\pi}{2}

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

D. \pi

Correct Answer: A

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Question 14

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

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

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

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

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

Correct Answer: A

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Question 15

Determine the sum of the first 5 terms of the geometric series with first term a = 2 and common ratio r = 3.

Correct A. 2 + 6 + 18 + 54 + 162

B. 2 + 6 + 18 + 54 + 162 + 486

C. 2 + 6 + 18 + 54 + 162 + 486 + 1458

D. 2 + 6 + 18 + 54 + 162 + 486 + 1458 + 4374

Correct Answer: A

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Question 16

A random variable X has a probability distribution given by P(X) = \( 1/2 \)^k, where k = 0, 1, 2, ... . Find the expected value of X.

A. 1

B. 2

Correct C. \frac{1}{2}

D. \frac{2}{3}

Correct Answer: C

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Question 17

A cube has a side length of 5 cm. Find the volume of the cube in cubic centimeters.

Correct A. 125 cm^3

B. 250 cm^3

C. 500 cm^3

D. 1000 cm^3

Correct Answer: A

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Question 18

A 3x3 matrix A has the following elements: \[ A = \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix} \]. Find the determinant of A.

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 19

A histogram is shown below: \[ \text{Histogram of X} \]. Find the mean of X.

A. 10

Correct B. 20

C. 30

D. 40

Correct Answer: B

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Question 20

A random variable X has a probability distribution given by P(X) = \( 1/2 \)^k, where k = 0, 1, 2, ... . Find the variance of X.

Correct A. \frac{1}{4}

B. \frac{1}{2}

C. 1

D. 2

Correct Answer: A

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Question 21

Solve the inequality \( \frac{x}{x+1} > \frac{2}{3} \) for \( x > -1 \).

Correct A. x > 1

B. x > 2

C. x > 3

D. x > 4

Correct Answer: A

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Question 22

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

A. 4

Correct B. 6

C. 8

D. 10

Correct Answer: B

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Question 23

Solve the equation \( x^2 - 4x + 4 = 0 \).

Correct A. x = 2

B. x = 4

C. x = 0

D. x = 1

Correct Answer: A

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Question 24

Find the derivative of the function ( f(x) = x^3 - 2x^2 + x - 1 ).

Correct A. 3x^2 - 4x + 1

B. x^2 - 2x + 1

C. x^3 - 2x^2 + x

D. x^2 - 4x + 1

Correct Answer: A

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Question 25

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

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

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

C. x = \frac{\pi}{6}

D. x = \frac{\pi}{3}

Correct Answer: B

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