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POST UTME COVENANT UNIVERSITY 2019 Mathematics | Objective

Are you preparing for POST UTME COVENANT UNIVERSITY exams? Reviewing past 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

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

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

Correct Answer: A

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Question 2

Solve the system of linear equations u\sing matrices:\n\n$ 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

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{16pi}{3} $

Correct B. $ \frac{32pi}{3} $

C. $ \frac{64pi}{3} $

D. $ \frac{128pi}{3} $

Correct Answer: B

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Question 4

Solve the quadratic 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 5

Find the derivative of the function ( f(x) = \sin^2 x ) u\sing 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

In a circle of radius 8 cm, a chord of length 12 cm is drawn. Find the dis\tance 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

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

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

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

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

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 dis\tance 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

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

Correct A. 1023

B. 1024

C. 1025

D. 1026

Correct Answer: A

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Question 13

In a circle with center $O$ and radius $5$, a chord $AB$ is drawn such that $OA = 3$. 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

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

A set $S$ contains the elements ${1, 2, 3, 4, 5}$. 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

Find the equation of the circle with center at ((2,3)) and pas\sing 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

Solve the system of equations u\sing 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

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

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

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

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

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

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

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

Find the equation of the line pas\sing 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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