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POST UTME RSU 2020 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 2020 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

Determine the value of $ int_{0}^{1} \frac{1}{x^2 + 1} dx $ u\sing the method of substitution.

Correct A. \frac{\pi}{2}

B. \frac{\pi}{4}

C. \frac{\pi}{6}

D. \frac{\pi}{8}

Correct Answer: A

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Question 2

A histogram is constructed from a dataset of exam scores. If the mean score is 75 and the s\tandard deviation is 10, what is the probability that a randomly selected score will fall within 2 s\tandard deviations of the mean?

A. 0.9544

B. 0.9772

Correct C. 0.9987

D. 0.9999

Correct Answer: C

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Question 3

Solve the equation $ x^2 + 4x + 4 = 0 $ u\sing the quadratic formula.

Correct A. x = -2

B. x = -1

C. x = 0

D. x = 1

Correct Answer: A

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Question 4

A circle has a radius of 4 cm. Find the area of the circle.

A. 50.24 cm^2

Correct B. 100.48 cm^2

C. 200.96 cm^2

D. 50.24 cm^2

Correct Answer: B

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Question 5

A polynomial function is defined as ( f(x) = 2x^3 - 5x^2 + 3x - 1 ). Find the derivative of the function.

Correct A. f'(x) = 6x^2 - 10x + 3

B. f'(x) = 6x^2 - 10x + 2

C. f'(x) = 6x^2 - 10x - 3

D. f'(x) = 6x^2 - 10x - 2

Correct Answer: A

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Question 6

Find the value of x in the equation $ \frac{1}{2}x + 5 = 11 $ in base 8.

Correct A. 22

B. 23

C. 24

D. 25

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} 3 \ 7 \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

A histogram of exam scores is shown below. If the mean score is 60, find the value of the upper limit of the interval.

A. 65

Correct B. 70

C. 75

D. 80

Correct Answer: B

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Question 9

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{1}{$ x^2 + 1 $^2}

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

Correct Answer: A

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Question 10

Solve the trigonometric equation $ 2 \sin^2 x + 3 \cos x - 1 = 0 $ u\sing the identity $ \sin^2 x + \cos^2 x = 1 $.

Correct A. \sin x = \frac{1}{2}

B. \cos x = \frac{1}{2}

C. \sin x = \frac{1}{3}

D. \cos x = \frac{1}{3}

Correct Answer: A

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Question 11

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

Correct A. $ \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ $ )

B. $ \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ $ + 2 )

C. $ \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ $ - 2 )

D. $ \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ $ + 4 )

Correct Answer: A

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Question 12

Solve the matrix equation $ egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix} $.

Correct A. $ egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 2 \ 3 \end{bmatrix} $

B. $ egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 3 \ 2 \end{bmatrix} $

C. $ egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 4 \ 5 \end{bmatrix} $

D. $ egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 4 \end{bmatrix} $

Correct Answer: A

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Question 13

Find the sum of the first 10 terms of the geometric progression ( 2, 6, 18, ldots ).

Correct A. $ 2 left\( \frac{3^{10} - 1}{3 - 1} \right \ $ )

B. $ 2 left\( \frac{3^{10} + 1}{3 + 1} \right \ $ )

C. $ 2 left\( \frac{3^{10} - 1}{3 + 1} \right \ $ )

D. $ 2 left\( \frac{3^{10} + 1}{3 - 1} \right \ $ )

Correct Answer: A

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Question 14

Find the mean deviation of the data set ( 2, 4, 6, 8, 10 ).

Correct A. $ \frac{1}{5} left\( 2 + 4 + 6 + 8 + 10 \right \ $ )

B. $ \frac{1}{5} left\( 2 + 4 + 6 + 8 + 10 \right \ $ - 6 )

C. $ \frac{1}{5} left\( 2 + 4 + 6 + 8 + 10 \right \ $ + 6 )

D. $ \frac{1}{5} left\( 2 + 4 + 6 + 8 + 10 \right \ $ - 10 )

Correct Answer: A

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Question 15

Solve the polynomial equation $ x^3 - 6x^2 + 11x - 6 = 0 $.

Correct A. $ x = 1, 2, 3 $

B. $ x = 1, 3, 4 $

C. $ x = 2, 3, 4 $

D. $ x = 1, 2, 5 $

Correct Answer: A

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Question 16

Determine the mean of the following dataset: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

Correct A. 6

B. 5

C. 7

D. 8

Correct Answer: A

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Question 17

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

Correct A. 2

B. 4

C. 10

D. 20

Correct Answer: A

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Question 18

Find the area under the curve $ y = x^2 $ from $ x = 0 $ to $ x = 4 $.

Correct A. 64

B. 32

C. 16

D. 8

Correct Answer: A

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Question 19

A histogram represents the distribution of exam scores. The histogram has a mean of 60 and a s\tandard deviation of 10. If the highest score is 90, what is the lowest score?

Correct A. 30

B. 40

C. 50

D. 60

Correct Answer: A

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Question 20

Solve the equation $ 2x + 5 = 11 $.

Correct A. 3

B. 4

C. 5

D. 6

Correct Answer: A

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Question 21

Let $X$ and $Y$ be indep\endent random variables with probability density functions $f_X(x) = \frac{1}{2}e^{-|x|}$ and $f_Y(y) = \frac{1}{3}e^{-|y|}$, respectively. Find $P$ X+Y<0 $$.

Correct A. \frac{1}{6}

B. \frac{1}{3}

C. \frac{1}{2}

D. \frac{2}{3}

Correct Answer: A

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Question 22

Solve the system of linear equations $\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 3 \\ 7 \end{bmatrix}$.

Correct A. \begin{bmatrix} 1 \\ -1 \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 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 + 3 $^2 + $ y - 2 $^2 = 16

D. $ x - 3 $^2 + $ y + 2 $^2 = 16

Correct Answer: A

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Question 24

Solve the inequality $\frac{2x + 1}{x - 1} > 0$.

Correct A. x < -\frac{1}{2} \text{ or } x > 1

B. x < -1 \text{ or } x > 1

C. x < 1 \text{ or } x > -\frac{1}{2}

D. x < -\frac{1}{2} \text{ or } x < 1

Correct Answer: A

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Question 25

Find the value of $x$ that satisfies the 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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