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POST UTME JOSEPH AYO BABALOLA UNIVERSITY 2020 Mathematics | Objective

Are you preparing for POST UTME JOSEPH AYO BABALOLA UNIVERSITY 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.

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Question 1

Find the area under the curve \( y = \frac{1}{2}x^2 \) from \( x = 0 \) to \( x = 4 \).

Correct A. ( 8 )

B. ( 16 )

C. ( 32 )

D. ( 64 )

Correct Answer: A

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Question 2

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

Correct A. \( x = \frac{pi}{4} \)

B. \( x = \frac{3pi}{4} \)

C. \( x = \frac{pi}{2} \)

D. \( x = \frac{5pi}{4} \)

Correct Answer: A

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Question 3

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

Correct A. ( f'(x) = -\frac{2}{x^3} )

B. ( f'(x) = \frac{2}{x^3} )

C. ( f'(x) = -\frac{1}{x^3} )

D. ( f'(x) = \frac{1}{x^3} )

Correct Answer: A

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Question 4

Solve the system of equations u\sing matrices:

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

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

C. \( x = 4, y = 5 \)

D. \( x = 5, y = 4 \)

Correct Answer: A

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Question 5

Find the determinant of the matrix \( egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \).

Correct A. ( 0 )

B. ( 1 )

C. ( 2 )

D. ( 3 )

Correct Answer: A

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Question 6

Find the derivative of the function ( f(x) = \frac{x^2 + 2x - 3}{x^2 - 4} ) u\sing the quotient rule.

A. \( \frac{\( 2x + 2 \)\( x^2 - 4 \ \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2} )

B. \( \frac{\( 2x + 2 \)\( x^2 - 4 \ \) + \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2} )

Correct C. \( \frac{\( 2x + 2 \)\( x^2 - 4 \ \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2} )

D. \( \frac{\( 2x + 2 \)\( x^2 - 4 \ \) + \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2} )

Correct Answer: C

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Question 7

A circle has a radius of 5 units. Find the equation of the circle in s\tandard form.

Correct A. \( x^2 + y^2 = 25 \)

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

C. \( x^2 - y^2 = 25 \)

D. \( x^2 + y^2 = 25 \)

Correct Answer: A

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Question 8

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

Correct A. \( \frac{14}{3} \)

B. \( \frac{14}{3} \)

C. \( \frac{14}{3} \)

D. \( \frac{14}{3} \)

Correct Answer: A

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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{2x}{\( x^2 + 1 \ \)^2} )

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

Correct Answer: A

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Question 10

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

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

B. \( y = x - 1 \)

C. \( y = x + 1 \)

D. \( y = x - 1 \)

Correct Answer: A

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Question 11

Solve for x in the equation \( \sin^2\( x \ \) + \cos^2(x) = 1 ) u\sing the identity \( \sin^2\( x \ \) + \cos^2(x) = 1 ).

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

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

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

D. x = \frac{5\pi}{4}

Correct Answer: A

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Question 12

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

A. 60

B. 70

Correct C. 80

D. 90

Correct Answer: C

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Question 13

Solve the quadratic equation \( x^2 + 5x + 6 = 0 \) u\sing the quadratic formula.

A. x = -2

Correct B. x = -3

C. x = 2

D. x = 3

Correct Answer: B

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Question 14

A circle has a radius of 4 cm. What is the area of the circle?

A. 50\pi

Correct B. 100\pi

C. 200\pi

D. 300\pi

Correct Answer: B

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Question 15

A car travels from city A to city B at an average speed of 60 km/h. If the dis\tance between the two cities is 240 km, how long does the trip take?

A. 4 hours

Correct B. 6 hours

C. 8 hours

D. 10 hours

Correct Answer: B

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Question 16

Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.

Correct A. 12155

B. 12345

C. 12567

D. 12890

Correct Answer: A

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Question 17

A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. What is the probability that a randomly selected score is between 60 and 90?

A. 0.68

Correct B. 0.72

C. 0.76

D. 0.80

Correct Answer: B

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Question 18

Solve the inequality \frac{x^2 - 4}{x + 2} > 0.

Correct A. x < -2 or x > 2

B. x > -2 or x < 2

C. x < -2 or x = 2

D. x > -2 or x = -2

Correct Answer: A

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Question 19

A fair six-sided die is rolled. What is the probability that the number rolled is a multiple of 3?

A. 1/2

Correct B. 1/3

C. 2/3

D. 1/6

Correct Answer: B

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Question 20

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

Correct A. 32

B. 64

C. 16

D. 128

Correct Answer: A

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Question 21

Given that \( \log_{10} \( x^2 \ \) = 4 ), find the value of ( x ) u\sing the change of base formula.

Correct A. 10

B. 20

C. 40

D. 80

Correct Answer: A

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Question 22

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

A. 60

B. 70

Correct C. 80

D. 90

Correct Answer: C

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

C. \( x - 4 \ \)^2 + \( y - 3 \)^2 = 16 )

D. \( x - 2 \ \)^2 + \( y - 4 \)^2 = 16 )

Correct Answer: A

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Question 24

A vector ( mathbf{a} ) has magnitude ( 5 ) and direction \( 60^\circ \) counterclockwise from the positive x-axis. Find the vector ( mathbf{a} ).

Correct A. \( 5\cos\( 60^\circ \ \) + 5\sin\( 60^\circ \) )

B. \( 5\cos\( 60^\circ \ \) - 5\sin\( 60^\circ \) )

C. \( 5\sin\( 60^\circ \ \) + 5\cos\( 60^\circ \) )

D. \( 5\sin\( 60^\circ \ \) - 5\cos\( 60^\circ \) )

Correct Answer: A

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Question 25

Two events ( A ) and ( B ) are indep\endent. If ( P(A) = 0.3 ) and ( P(B) = 0.4 ), find \( P\( A \cap B \ \) ).

Correct A. 0.12

B. 0.24

C. 0.36

D. 0.48

Correct Answer: A

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