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POST UTME RSU 2020 Mathematics | Objective

Prepare for your exams with POST UTME RSU questions? Reviewing past/model 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.

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Question 1 View Details

Determine the value of \(int_{0}^{1} \frac{1}{x^2 + 1} dx\) using 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 View Details

A histogram is constructed from a dataset of exam scores. If the mean score is 75 and the standard deviation is 10, what is the probability that a randomly selected score will fall within 2 standard 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 View Details

Solve the equation \(x^2 + 4x + 4 = 0\) using 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 View Details

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 View Details

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 View Details

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 View Details

Solve the system of equations using 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 View Details

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 View Details

Find the derivative of the function ( f(x) = \(\frac{1}{x^2 + 1}\)\)\) ) using 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 View Details

Solve the trigonometric equation (2 \\(sin^2\) x + 3 \(1x - 1 = 0\) using the identity \\((2 sin^2 x + 3\)\(1x - 1 = 0\)\(\sin^2 x + \cos^2 x = 1\).

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

A histogram represents the distribution of exam scores. The histogram has a mean of 60 and a standard 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 View Details

Solve the equation \(2x + 5 = 11\).

Correct A. 3

B. 4

C. 5

D. 6

Correct Answer: A

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Question 21 View Details

Let \(X\) and \(Y\) be independent 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 \(P X+Y < 0\\(frac{1}{3}e^{-|y|}), respectively. Find\)\).

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 View Details

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 View Details

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 View Details

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 View Details

Find the value of (x\) that satisfies the equation \(x^2 + 4x + 4 = 0\\((x) that satisfies the equation\).

Correct A. \(x = -2\)

B. \(x = 2\)

C. \(x = -1\)

D. \(x = 1\)

Correct Answer: A

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