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POST UTME COVENANT UNIVERSITY 2019 Mathematics | Objective

Prepare for your exams with POST UTME COVENANT UNIVERSITY questions? Reviewing past/model 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 View Details

Find the derivative of the function ( f(x) = \(\frac{1}{x^2 + 1}\)\)\) ) using the chain rule.

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

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

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

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

Correct Answer: A

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Question 2 View Details

Solve the system of linear equations using matrices:\nn\(egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 7 \ 11 \end{bmatrix}\)

Correct A. \(x = 3, y = 2\)

B. \(x = 2, y = 3\)

C. \(x = 1, y = 4\)

D. \(x = 4, y = 1\)

Correct Answer: A

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Question 3 View Details

Find the volume of the solid formed by revolving the region bounded by the curves \(y = x^2\) and \(y = 4 - x^2\) about the x-axis.

A. \(\frac{16\pi}{3}\)

Correct B. \(\frac{32\pi}{3}\)

C. \(\frac{64\pi}{3}\)

D. \(\frac{128\pi}{3}\)

Correct Answer: B

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Question 4 View Details

Solve the quadratic 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 5 View Details

Find the derivative of the function ( f(x) = \\(\sin^2\) x ) using the chain rule.

Correct A. ( f'\((x) = 2\)\sin x \cos x )

B. ( f'\((x) = 2\)\sin x )

C. ( f'\((x) = 2\)\cos x )

D. ( f'\((x) = 2\)\\(\sin^2\) x )

Correct Answer: A

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Question 6 View Details

In a circle of radius 8 cm, a chord of length 12 cm is drawn. Find the distance of the chord from the centre of the circle.

A. 4 cm

Correct B. 6 cm

C. 8 cm

D. 10 cm

Correct Answer: B

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Question 7 View Details

A matrix A has the property that when multiplied by any 3x3 matrix B, the product AB is a symmetric matrix. What is the value of the element in the first row and first column of matrix A?

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 8 View Details

The mean of 5 numbers is 12. If one of the numbers is 15, what is the sum of the other 4 numbers?

Correct A. 48

B. 50

C. 52

D. 54

Correct Answer: A

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Question 9 View Details

A line passes through the points (2, 3) and (4, 5). What is the equation of the line in slope-intercept form?

Correct A. \(y = x + 1\)

B. \(y = x - 1\)

C. \(y = -x + 1\)

D. \(y = x + 2\)

Correct Answer: A

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Question 10 View Details

A circle has a diameter of 10 cm. What is the area of the circle?

A. 50\pi

B. 75\pi

Correct C. 100\pi

D. 125\pi

Correct Answer: C

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Question 11 View Details

In the complex plane, the points \(z_1\) and \(z_2\) are represented by the complex numbers \(z_1 = 2 + 3i\) and \(z_2 = 4 - 5i\). Find the distance between the points \(z_1\) and \(z_2\).

Correct A. \(\sqrt{109}\)

B. \(\sqrt{121}\)

C. \(\sqrt{169}\)

D. \(\sqrt{289}\)

Correct Answer: A

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Question 12 View Details

A sequence is defined by the recurrence relation (a_\(n = 2a\)_{n-1} + 1\), where \(a_1 = 3\\((a_n = 2a_{n-1} + 1), where\). Find the value of \(a_{10}\).

Correct A. 1023

B. 1024

C. 1025

D. 1026

Correct Answer: A

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Question 13 View Details

In a circle with center \(O\) and radius \(5\), a chord (AB\) is drawn such that \(OA = 3\\((AB) is drawn such that\). Find the length of the chord \(AB\).

Correct A. \(\sqrt{91}\)

B. \(\sqrt{121}\)

C. \(\sqrt{169}\)

D. \(\sqrt{289}\)

Correct Answer: A

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Question 14 View Details

A right-angled triangle has sides of length \(3\), \(4\), and \(5\). Find the area of the triangle.

Correct A. 6

B. 12

C. 18

D. 24

Correct Answer: A

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Question 15 View Details

A set (S\) contains the elements \({1, 2, 3, 4, 5}\\((S) contains the elements\). Find the number of subsets of \(S\) that contain exactly two elements.

A. 5

Correct B. 10

C. 15

D. 20

Correct Answer: B

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Question 16 View Details

Find the equation of the circle with center at ((2,3)) and passing through the point ((6,8)).

Correct A. \(x-2 \\)^2 + \(y-3\)^\(2 = 5\) )

B. \(x-2 \\)^2 + \(y-3\)^\(2 = 10\) )

C. \(x-2 \\)^2 + \(y-3\)^\(2 = 15\) )

D. \(x-2 \\)^2 + \(y-3\)^\(2 = 20\) )

Correct Answer: A

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Question 17 View Details

Solve the system of equations using matrices: [ egin{cases} \(x + 2y - 3z = 7\) \\(2x - 3y + z = -2\)\ \(3x + y + 2z = 5\) \end{cases} ].

Correct A. \(x = 1, y = 2, z = 3\)

B. \(x = 2, y = 1, z = -1\)

C. \(x = 3, y = -1, z = 2\)

D. \(x = -1, y = 3, z = 1\)

Correct Answer: A

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Question 18 View Details

Find the value of [ \log_{10} left\(\frac{1}{\sqrt{2}} \right\) ].

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

B. \(-\frac{3}{2}\)

C. \(-\frac{1}{4}\)

D. \(-\frac{3}{4}\)

Correct Answer: A

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Question 19 View Details

Solve the inequality [ \(2x^2 - 5x - 3\) geq 0 ].

Correct A. \(x \leq -1\) or \(x \geq \frac{3}{2}\)

B. \(x \leq -1\) or \(x \leq \frac{3}{2}\)

C. \(x \geq -1\) or \(x \geq \frac{3}{2}\)

D. \(x \geq -1\) or \(x \leq \frac{3}{2}\)

Correct Answer: A

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Question 20 View Details

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

D. \(\frac{8}{25}\)

Correct Answer: A

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Question 21 View Details

Solve the inequality \(\frac{x^2 - 4}{x^2 - 9} > 0\) for ( x in mathbb{R} ).

Correct A. \(-\infty, -3 \\) cup (1, infty) )

B. \(-\infty, -3 \\) cup (1, 3) )

C. \(-\infty, -3 \\) cup (3, infty) )

D. \(-\infty, 1 \\) cup (3, infty) )

Correct Answer: A

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Question 22 View Details

Find the equation of the circle with center ( (2, 3) ) and radius ( 4 ) in the form \(x - h \\)^2 + \(y - k\)^\(2 = r\^2\) ).

Correct A. \(x - 2 \\)^2 + \(y - 3\)^\(2 = 16\) )

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

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

D. \(x - 2 \\)^2 + \(y - 3\)^\(2 = 49\) )

Correct Answer: A

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Question 23 View Details

If ( f(x) = \(\frac{x^2 - 4}{x^2 - 9}\)\)) ), find \(f -2 \\\() ), find (f -2\) ).

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

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

C. \(\frac{1}{3}\)

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

Correct Answer: A

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Question 24 View Details

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

Correct A. \(x = -2\)

B. \(x = -1\)

C. \(x = 1\)

D. \(x = 2\)

Correct Answer: A

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Question 25 View Details

Find the equation of the line passing through the points ( (1, 2) ) and ( (3, 4) ).

Correct A. \(y = 2x - 1\)

B. \(y = 2x + 1\)

C. \(y = 3x - 2\)

D. \(y = 3x + 2\)

Correct Answer: A

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