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POST UTME BABCOCK UNIVERSITY 2025 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 2025 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

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

A. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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Question 2

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 < -1 or x < 3/2

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

Correct Answer: A

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Question 3

Find the mean of the following data set: 2, 4, 6, 8, 10.

A. 6

Correct B. 8

C. 10

D. 12

Correct Answer: B

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Question 4

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

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 5

Two events A and B are indep\endent. If P(A) = 0.4 and P(B) = 0.6, find P(A and B).

Correct A. 0.2

B. 0.4

C. 0.6

D. 0.8

Correct Answer: A

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Question 6

Find the volume of the solid formed by rotating the region bounded by the curves y = 2x^2 + 1, y = 0, and x = 1 about the x-axis.

Correct A. π/3

B. π/2

C. π/4

D. π/6

Correct Answer: A

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Question 7

A random variable X has a probability distribution given by P\( X = 1 \) = 1/4, P\( X = 2 \) = 1/2, and P\( X = 3 \) = 1/4. Find the expected value of X.

Correct A. 1.5

B. 2

C. 2.5

D. 3

Correct Answer: A

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Question 8

The mean of a set of 5 numbers is 10. If one of the numbers is 15, find the sum of the remaining 4 numbers.

Correct A. 35

B. 40

C. 45

D. 50

Correct Answer: A

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Question 9

A histogram of the heights of 20 students in a class is shown below. If the class has 10 boys and 10 girls, find the probability that a randomly selected student is taller than 170 cm.

A. 0.4

Correct B. 0.5

C. 0.6

D. 0.7

Correct Answer: B

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Question 10

A binary number 1011 is converted to decimal. Find the decimal equivalent.

A. 11

B. 12

Correct C. 13

D. 14

Correct Answer: C

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Question 11

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

Correct A. \( \frac{pi}{2} \)

B. \( \frac{pi}{4} \)

C. \( \frac{pi}{6} \)

D. \( \frac{pi}{8} \)

Correct Answer: A

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Question 12

Solve for ( x ) in the equation \( 2^x + 3^x = 5^x \).

A. \( x = 1 \)

Correct B. \( x = 2 \)

C. \( x = 3 \)

D. \( x = 4 \)

Correct Answer: B

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Question 13

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 + \( y - 2 \)^2 = 16 )

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

Correct Answer: A

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Question 14

Find the value of \( \log_{10} \( 1000 \ \) ).

A. ( 3 )

Correct B. ( 4 )

C. ( 5 )

D. ( 6 )

Correct Answer: B

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Question 15

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

Correct A. \( y = 2x - 1 \)

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

C. \( y = 3x - 2 \)

D. \( y = 3x + 2 \)

Correct Answer: A

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Question 16

In a binary system, what is the value of the number represented by the sequence 1011?

A. 3

Correct B. 5

C. 7

D. 9

Correct Answer: B

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Question 17

Solve for x in the equation \( \frac{1}{2}x^2 + 3x - 2 = 0 \)

A. 1

Correct B. -2

C. 4

D. -1

Correct Answer: B

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Question 18

Find the determinant of the matrix \( egin{bmatrix} 2 & 1 \ 4 & 3 \end{bmatrix} \)

Correct A. 5

B. 6

C. 7

D. 8

Correct Answer: A

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Question 19

A histogram is constructed with a mean of 25 and a s\tandard deviation of 5. What is the value of the area of the histogram?

A. 100

Correct B. 200

C. 300

D. 400

Correct Answer: B

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Question 20

A vector ( vec{a} ) has a magnitude of 5 and is directed at an angle of 30° to the x-axis. What is the value of the y-component of the vector?

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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Question 21

A random sample of 16 students from a population of 100 students has a mean height of 170 cm with a s\tandard deviation of 5 cm. Calculate the s\tandard error of the mean.

Correct A. 1.25 cm

B. 2.5 cm

C. 3.75 cm

D. 5 cm

Correct Answer: A

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Question 22

Solve the quadratic equation \( x^2 + 4x + 4 = 0 \) u\sing the quadratic formula.

Correct A. -2

B. -1

C. 0

D. 1

Correct Answer: A

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Question 23

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

A. 50.24 cm^2

Correct B. 100.48 cm^2

C. 200.96 cm^2

D. 25.13 cm^2

Correct Answer: B

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Question 24

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. 50 cm^3

C. 60 cm^3

D. 70 cm^3

Correct Answer: A

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Question 25

A vector \( \vec{a} \) has a magnitude of 5 units and makes an angle of 60° with the positive x-axis. Find the x-component of the vector.

Correct A. 2.5 units

B. 3.75 units

C. 4.33 units

D. 5 units

Correct Answer: A

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