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Subject

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POST UTME AFE BABALOLA UNIVERSITY 2020 Mathematics | Objective

Are you preparing for POST UTME AFE 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

Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).

Correct A. 10

B. 100

C. 1000

D. 10000

Correct Answer: A

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Question 2

Find the value of \( \frac{1}{2} \int_{0}^{1} x^2 dx \).

Correct A. 0.5

B. 1

C. 1.5

D. 2

Correct Answer: A

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Question 3

A circle has a radius of 5cm. Find the area of the circle.

A. 25π

Correct B. 50π

C. 75π

D. 100π

Correct Answer: B

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Question 4

A die is rolled. What is the probability that the number obtained is greater than 4?

A. 1/6

B. 1/3

C. 1/2

Correct D. 2/3

Correct Answer: D

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Question 5

Solve the equation \( 2x^2 + 5x - 3 = 0 \).

A. -1/2

Correct B. 1/2

C. -3

D. 3

Correct Answer: B

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Question 6

Find the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 7

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 8

A vector ( mathbf{a} ) has a magnitude of 5 units and makes an angle of 30° with the positive x-axis. Find the x and y components of ( mathbf{a} ).

Correct A. x = 4.33, y = 2.5

B. x = 2.5, y = 4.33

C. x = 3.54, y = 2.5

D. x = 2.5, y = 3.54

Correct Answer: A

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Question 9

A right-angled triangle has a hypotenuse of length 10 units and one leg of length 6 units. Find the length of the other leg.

Correct A. 8

B. 6

C. 4

D. 2

Correct Answer: A

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Question 10

Solve the inequality \( x^2 - 4x + 4 > 0 \).

A. x < 2

Correct B. x > 2

C. x < 1

D. x > 1

Correct Answer: B

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Question 11

Let X be a random variable with probability density function f(x) = \\begin{cases} 2x & 0 < x < 1 \\ 0 & \text{otherwise} \\end{cases}. Find the probability that X is greater than 0.5.

Correct A. 0.25

B. 0.5

C. 0.75

D. 1.0

Correct Answer: A

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Question 12

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

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

Correct Answer: A

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Question 13

Solve the inequality x^2 - 4x - 5 > 0.

Correct A. \( -\infty, -1 \) \cup \( 5, \infty \)

B. \( -\infty, 1 \) \cup \( 5, \infty \)

C. \( -\infty, -1 \) \cup (1, 5)

D. \( -\infty, 1 \) \cup \( -5, \infty \)

Correct Answer: A

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Question 14

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

Correct A. \frac{8}{3}

B. \frac{16}{3}

C. \frac{24}{3}

D. \frac{32}{3}

Correct Answer: A

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Question 15

Solve the equation \sin^2 x + \cos^2 x = 1.

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

B. x = \frac{\pi}{2}

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

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

Correct Answer: A

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Question 16

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

Correct A. \( -infty, -2 \ \) cup (2, infty) )

B. \( -infty, -2 \ \) cup (2, infty) ) and \( x = -2 \)

C. \( -infty, -2 \ \) cup (2, infty) ) and \( x = 2 \)

D. \( -infty, -2 \ \) cup (2, infty) )

Correct Answer: A

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Question 17

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} )

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

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

Correct Answer: A

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Question 18

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

A. 60

Correct B. 70

C. 80

D. 90

Correct Answer: B

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Question 19

Solve the equation \( 2^x + 2^x = 2^{x+1} \) for ( x in mathbb{R} ).

A. \( x = 0 \)

Correct B. \( x = 1 \)

C. \( x = -1 \)

D. \( x = 2 \)

Correct Answer: B

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Question 20

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) = \sin(x) )

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

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

Correct Answer: A

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Question 21

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

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

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

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

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

Correct Answer: C

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Question 22

A set of 10 numbers has a mean of 20. If 5 is added to each number, what is the new mean?

A. 22

Correct B. 25

C. 28

D. 30

Correct Answer: B

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Question 23

Find the volume of the frustum of a cone with radii 6 cm and 3 cm and height 8 cm.

A. 120\pi

B. 150\pi

Correct C. 180\pi

D. 200\pi

Correct Answer: C

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Question 24

A sequence is defined by the formula \( a_n = 2n^2 - 5n + 1 \). Find the sum of the first 5 terms.

A. 15

B. 20

Correct C. 25

D. 30

Correct Answer: C

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Question 25

A histogram has a mean of 25 and a s\tandard deviation of 5. If the data is normally distributed, what is the probability that a randomly selected value is greater than 30?

A. 0.1587

B. 0.3413

C. 0.5000

Correct D. 0.8413

Correct Answer: D

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