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POST UTME BABCOCK UNIVERSITY 2021 Mathematics | Objective

Are you preparing for POST UTME BABCOCK UNIVERSITY exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2021 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

A random variable X has a probability distribution given by P\( X = 1 \) = 0.3, P\( X = 2 \) = 0.4, and P\( X = 3 \) = 0.3. What is the expected value of X?

Correct A. 1.1

B. 1.2

C. 1.3

D. 1.4

Correct Answer: A

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Question 2

Solve the equation \( x^2 + 4x + 4 = 0 \) u\sing the quadratic formula. What is the value of x?

Correct A. -2

B. -1

C. 1

D. 2

Correct Answer: A

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Question 3

In the diagram below, what is the value of x?

A. 3

Correct B. 4

C. 5

D. 6

Correct Answer: B

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Question 4

A function f(x) is defined as f(x) = 2x^2 + 3x - 1. What is the value of f\( -2 \)?

Correct A. -5

B. -4

C. -3

D. -2

Correct Answer: A

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Question 5

Solve the trigonometric equation \( 2 \sin^2 x + 3 \sin x - 2 = 0 \) for x in the interval [0, 2\pi].

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

B. \frac{\pi}{3}

C. \frac{\pi}{2}

D. \frac{5\pi}{6}

Correct Answer: A

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Question 6

Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).

A. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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Question 7

Solve for ( x ) in the equation \( \left| x - 2 \right| + \left| x + 1 \right| = 3 \).

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 8

Find the value of \( \sin \left\( \arc\cos \frac{3}{5} \right \ \) ).

A. 0.6

Correct B. 0.8

C. 0.4

D. 0.2

Correct Answer: B

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Question 9

A fair six-sided 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 10

Find the sum of the first 10 terms of the geometric series \( 2x^2 + 3x + 1 \).

Correct A. 200x^2 + 300x + 10

B. 100x^2 + 150x + 5

C. 50x^2 + 75x + 2.5

D. 25x^2 + 37.5x + 1.25

Correct Answer: A

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Question 11

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

A. 0.25

Correct B. 0.5

C. 0.75

D. 1

Correct Answer: B

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Question 12

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

Correct A. 0.5

B. 1

C. 1.5

D. 2

Correct Answer: A

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Question 13

The equation of a circle is given by \( x^2 + y^2 - 6x + 4y + 4 = 0 \). Find the center and radius of the circle.

Correct A. Center: \( 3, -2 \), Radius: 2

B. Center: (2, 3), Radius: 3

C. Center: (3, 2), Radius: 2

D. Center: \( 2, -3 \), Radius: 3

Correct Answer: A

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Question 14

Solve the inequality \( |x - 2| > 3 \).

Correct A. \( -∞, -1 \) ∪ (4, ∞)

B. \( -∞, 1 \) ∪ (4, ∞)

C. \( -∞, -1 \) ∪ (1, ∞)

D. \( -∞, 4 \) ∪ (1, ∞)

Correct Answer: A

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Question 15

Find the mean and s\tandard deviation of the data set {2, 4, 6, 8, 10}.

Correct A. Mean: 6, S\tandard Deviation: 2

B. Mean: 5, S\tandard Deviation: 2

C. Mean: 6, S\tandard Deviation: 3

D. Mean: 5, S\tandard Deviation: 3

Correct Answer: A

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Question 16

A random sample of 25 students from a population of 500 students has a mean height of 170 cm with a s\tandard deviation of 5 cm. Calculate the s\tandard error of the mean.

A. 2.5 cm

Correct B. 3.5 cm

C. 4.5 cm

D. 5.5 cm

Correct Answer: B

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Question 17

A circle has a diameter of 10 cm. Find the area of the circle.

Correct A. 78.5 cm^2

B. 87.5 cm^2

C. 97.5 cm^2

D. 107.5 cm^2

Correct Answer: A

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Question 18

Find the derivative of the function f(x) = 3x^2 + 2x - 5.

Correct A. 6x + 2

B. 6x - 2

C. 3x + 2

D. 3x - 2

Correct Answer: A

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Question 19

A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find the volume of the prism.

Correct A. 30 cm^3

B. 40 cm^3

C. 50 cm^3

D. 60 cm^3

Correct Answer: A

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Question 20

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

Correct A. x < -1 or x > 3/2

B. x < 1 or x > -3/2

C. x < -3/2 or x > 1

D. x < 3/2 or x > -1

Correct Answer: A

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Question 21

A circle has a radius of 4 cm. Find the circumference of the circle.

Correct A. 25.13 cm

B. 26.18 cm

C. 27.23 cm

D. 28.28 cm

Correct Answer: A

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Question 22

Find the derivative of the function f(x) = x^3 - 2x^2 + x - 1.

Correct A. 3x^2 - 4x + 1

B. 3x^2 - 4x - 1

C. 3x^2 + 4x + 1

D. 3x^2 + 4x - 1

Correct Answer: A

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Question 23

A rec\tangular prism has a length of 6 cm, a width of 4 cm, and a height of 3 cm. Find the surface area of the prism.

Correct A. 104 cm^2

B. 114 cm^2

C. 124 cm^2

D. 134 cm^2

Correct Answer: A

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Question 24

Find the volume of the solid formed by rotating the region bounded by the curves y = x^2, y = 0, and x = 2 about the x-axis.

A. 32\pi

B. 64\pi

Correct C. 128\pi

D. 256\pi

Correct Answer: C

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Question 25

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

Correct A. \[\( -\infty, -3 \) \cup (1, \infty)\]

B. \[\( -\infty, -3 \) \cup (1, \infty)\]

C. \[\( -\infty, -3 \) \cup (1, \infty)\]

D. \[\( -\infty, -3 \) \cup (1, \infty)\]

Correct Answer: A

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