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POST UTME JOSEPH AYO BABALOLA UNIVERSITY 2022 Mathematics | Objective

Prepare for your exams with POST UTME JOSEPH AYO BABALOLA UNIVERSITY questions? Reviewing past/model 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.

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Question 1 View Details

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 View Details

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 View Details

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 View Details

Find the equation of the line passing 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 View Details

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 \(km/h\\((km/h) and returns at an average speed of 40\). 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 View Details

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 View Details

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 View Details

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 View Details

Two events ( A ) and ( B ) are independent. 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 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 + \(y - 3\)^\(2 = 20\)

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 View Details

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 View Details

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 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. \(\frac{-2x^2}{\) \(x^2 + 1\) \ ^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 View Details

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

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

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

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

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

Correct Answer: A

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Question 15 View Details

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 \(t = 2\\((2t^2 - 5t + 1)). Find the velocity of the particle at time\).

A. 3

Correct B. 4

C. 5

D. 6

Correct Answer: B

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Question 16 View Details

Determine the value of x in the equation \(\(12x \\) = \(frac{1}{2}\)\) ) given that \\(frac{1}{2})\(\)1x \\) = \(\frac{\sqrt{3}}{2}\) ).

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 View Details

A binary operation (*\) on the set of real numbers is defined as \(a * b = a^2 + b^2\\((*) on the set of real numbers is defined as\). 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 View Details

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 View Details

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 View Details

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 View Details

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

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

Correct Answer: A

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Question 23 View Details

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 View Details

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 View Details

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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