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POST UTME JOSEPH AYO BABALOLA UNIVERSITY 2022 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 2022 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

Determine the equation of the circle with center \( -2, 3 \) and radius 4.

Correct A. \( x^2 + y^2 + 4x - 6y + 13 = 0 \)

B. \( x^2 + y^2 - 4x + 6y + 13 = 0 \)

C. \( x^2 + y^2 + 4x + 6y + 13 = 0 \)

D. \( x^2 + y^2 - 4x - 6y + 13 = 0 \)

Correct Answer: A

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Question 2

A survey of 100 students found that 70% of them preferred Mathematics, 20% preferred Science, and 10% preferred both. What is the probability that a randomly selected student prefers either Mathematics or Science?

Correct A. 0.85

B. 0.75

C. 0.65

D. 0.55

Correct Answer: A

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Question 3

Solve the inequality \( 2x^2 + 5x - 3 > 0 \).

Correct A. \( x < -1 \) or \( x > \frac{3}{2} \)

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

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

D. \( x < 3 \) or \( x > -\frac{1}{2} \)

Correct Answer: A

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Question 4

Find the equation of the line pas\sing through the points (2, 3) and (4, 5).

Correct A. \( y = \frac{1}{2}x + \frac{1}{2} \)

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

C. \( y = \frac{1}{2}x - \frac{1}{2} \)

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

Correct Answer: A

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Question 5

A car travels from city A to city B at an average speed of 60 km/h and returns at an average speed of 40 km/h. What is the average speed of the car for the entire trip?

A. 50 km/h

B. 55 km/h

Correct C. 60 km/h

D. 65 km/h

Correct Answer: C

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Question 6

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

A. 2

B. 4

Correct C. 6

D. 8

Correct Answer: C

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Question 7

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

A. 10

Correct B. 15

C. 20

D. 25

Correct Answer: B

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Question 8

A geometric sequence has first term \( a = 2 \) and common ratio \( r = 3 \). Find the sum of the first five terms.

Correct A. 325

B. 335

C. 345

D. 355

Correct Answer: A

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Question 9

Two events ( A ) and ( B ) are indep\endent. If ( P(A) = 0.4 ) and ( P(B) = 0.6 ), find the probability that both events occur.

A. 0.2

Correct B. 0.24

C. 0.28

D. 0.32

Correct Answer: B

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Question 10

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 = 20

C. \( x - 2 \)^2 + \( y - 3 \)^2 = 24

D. \( x - 2 \)^2 + \( y - 3 \)^2 = 28

Correct Answer: A

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Question 11

Let X be a random variable with probability density function f(x) = \( \frac{1}{2}e^{-|x|} \) for -∞ < x < ∞. Find the probability that X lies between -1 and 1.

A. 0

Correct B. 0.5

C. 1

D. 1.5

Correct Answer: B

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Question 12

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

Correct A. \( -∞, -3 \) ∪ (3, ∞)

B. \( -3, 3 \)

C. \( -∞, -3 \) ∪ (3, ∞) ∪ (0, 3)

D. \( -∞, -3 \) ∪ (3, ∞) ∪ (0, 3) ∪ (4, ∞)

Correct Answer: A

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Question 13

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

C. \( \frac{-2x^3}{\( x^2 + 1 \ \)^2} )

D. \( \frac{2x^3}{\( x^2 + 1 \ \)^2} )

Correct Answer: A

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Question 14

Solve the trigonometric equation \( \sin^2 x + \cos^2 x = 1 \) for (0 ≤ x ≤ 2pi).

Correct A. \( x = 0, \frac{pi}{2}, pi, \frac{3pi}{2} \)

B. \( x = 0, \frac{pi}{2}, pi, \frac{3pi}{2}, 2pi \)

C. \( x = 0, \frac{pi}{2}, pi, \frac{3pi}{2}, 2pi, \frac{5pi}{2} \)

D. \( x = 0, \frac{pi}{2}, pi, \frac{3pi}{2}, 2pi, \frac{5pi}{2}, \frac{7pi}{2} \)

Correct Answer: A

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Question 15

A particle moves along the x-axis with its position given by the equation (x(t) = 2t^2 - 5t + 1). Find the velocity of the particle at time \( t = 2 \).

A. 3

Correct B. 4

C. 5

D. 6

Correct Answer: B

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Question 16

Determine the value of x in the equation \( \sin\( 2x \ \) = \frac{1}{2} ) given that \( \sin\( x \ \) = \frac{\sqrt{3}}{2} ).

Correct A. \frac{\pi}{6}

B. \frac{\pi}{4}

C. \frac{\pi}{3}

D. \frac{\pi}{2}

Correct Answer: A

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Question 17

A binary operation \( * \) on the set of real numbers is defined as \( a * b = a^2 + b^2 \). Find the value of ( x ) such that \( x * \( x + 1 \ \) = 25 ).

A. 4

Correct B. 5

C. 6

D. 7

Correct Answer: B

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Question 18

In a circle with center ( O ) and radius ( 4 ), a chord ( AB ) is drawn such that \( OA = 3 \). Find the length of ( AB ).

A. 5

B. 6

Correct C. 7

D. 8

Correct Answer: C

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Question 19

A random experiment consists of rolling a fair six-sided die and then flipping a fair coin. If the outcome of the die roll is even, the coin is flipped twice. Otherwise, the coin is flipped once. What is the probability that the outcome of the die roll is even and the outcome of the coin flip is heads?

A. \frac{1}{6}

Correct B. \frac{1}{12}

C. \frac{1}{4}

D. \frac{1}{3}

Correct Answer: B

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Question 20

Find the value of ( x ) in the equation \( 2^x + 5^x = 100 \).

A. 2

B. 3

Correct C. 4

D. 5

Correct Answer: C

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Question 21

A solid right circular cone has a height of 12 cm and a base radius of 6 cm. Find the volume of the cone in terms of π.

A. \frac{288\pi}{\pi}

Correct B. \frac{288\pi}{3}

C. \frac{288\pi}{\pi}

D. \frac{288\pi}{3}

Correct Answer: B

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Question 22

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

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

Correct Answer: A

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Question 23

A histogram is constructed from the following data: 5, 7, 9, 11, 13, 15. Find the mean of the data.

A. 10

Correct B. 12

C. 14

D. 16

Correct Answer: B

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Question 24

Simplify the expression: \frac{2x^2 + 3x - 1}{x^2 - 4}

Correct A. \frac{2x + 1}{x - 2}

B. \frac{2x - 1}{x + 2}

C. \frac{2x + 1}{x + 2}

D. \frac{2x - 1}{x - 2}

Correct Answer: A

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Question 25

A right-angled triangle has a base of 5 cm and a height of 12 cm. Find the length of the hypotenuse.

A. 13

B. 15

Correct C. 17

D. 19

Correct Answer: C

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