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POST UTME BABCOCK UNIVERSITY 2025 Mathematics | Objective

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Question 1 View Details

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 View Details

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 View Details

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 View Details

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 View Details

Two events A and B are independent. 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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 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 - 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 View Details

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 View Details

Find the equation of the line passing 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 View Details

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 View Details

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 View Details

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 View Details

A histogram is constructed with a mean of 25 and a standard 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 View Details

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 View Details

A random sample of 16 students from a population of 100 students has a mean height of 170 cm with a standard deviation of 5 cm. Calculate the standard 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 View Details

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

Correct A. -2

B. -1

C. 0

D. 1

Correct Answer: A

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Question 23 View Details

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 View Details

A rectangular 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 View Details

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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