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POST UTME BABCOCK UNIVERSITY 2020 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 2020 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

Solve for x in the equation \( \sin^2 x + \cos^2 x = 1 \).

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

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

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

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

Correct Answer: A

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Question 2

A random variable X has a probability distribution given by \( P\( X = x \ \) = \frac{1}{2} ) for \( x = 1, 2, 3, 4 \). Find the expected value of X.

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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Question 3

In the diagram below, ( ABC ) is a right-angled triangle with \( angle B = 90^circ \). If \( AB = 3 \) and \( BC = 4 \), find the length of ( AC ).

A. 5

B. 6

Correct C. 7

D. 8

Correct Answer: C

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Question 4

A histogram of the heights of students in a class is shown below. If the class has 50 students, find the median height.

A. 160

Correct B. 170

C. 180

D. 190

Correct Answer: B

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Question 5

A circle with center ( C ) and radius ( r ) is shown below. If \( OC = 6 \), find the length of ( AB ).

A. 4

Correct B. 6

C. 8

D. 10

Correct Answer: B

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Question 6

A cylindrical \tank with a radius of 5m and a height of 10m is filled with water. If the density of water is 1000 kg/m^3, calculate the volume of water in the \tank.

Correct A. 785.4 m^3

B. 785.4 m^2

C. 785.4 m

D. 785.4 km^3

Correct Answer: A

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Question 7

Solve the inequality: \frac{x-2}{x+1} > 0

Correct A. x < -1 or x > 2

B. x < -1 or x < 2

C. x > -1 or x < 2

D. x > -1 or x > 2

Correct Answer: A

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Question 8

Find the area under the curve y = 2x^2 + 3x - 1 from x = 0 to x = 2

Correct A. 14.67

B. 14.67 m^2

C. 14.67 km^2

D. 14.67 cm^2

Correct Answer: A

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Question 9

A bag contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?

A. 0.375

Correct B. 0.375 or 3/8

C. 0.375 or 1/3

D. 0.375 or 1/2

Correct Answer: B

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Question 10

The mean of 5 numbers is 12. If one of the numbers is 15, what is the mean of the remaining 4 numbers?

Correct A. 11.25

B. 11.25 or 45/4

C. 11.25 or 3/4

D. 11.25 or 1/4

Correct Answer: A

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Question 11

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

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 12

Solve for ( 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 13

Find the equation of the circle with center ( (3, 4) ) and radius ( 5 ).

Correct A. \( x - 3 \)^2 + \( y - 4 \)^2 = 25

B. \( x - 4 \)^2 + \( y - 3 \)^2 = 25

C. \( x - 3 \)^2 + \( y - 4 \)^2 = 30

D. \( x - 4 \)^2 + \( y - 3 \)^2 = 30

Correct Answer: A

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Question 14

Find the value of \( \sin \( 2x \ \) ) given that \( \sin \( x \ \) = \frac{3}{5} ) and \( \cos \( x \ \) = \frac{4}{5} ).

Correct A. \frac{24}{25}

B. \frac{24}{25}

C. \frac{24}{25}

D. \frac{24}{25}

Correct Answer: A

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Question 15

Find the sum of the first 10 terms of the geometric series with first term \( a = 2 \) and common ratio \( r = 3 \).

Correct A. 59049

B. 59049

C. 59049

D. 59049

Correct Answer: A

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Question 16

Determine the mean of the following data set: 2, 4, 6, 8, 10. If the mean is increased by 2, what is the new mean?

A. 6

Correct B. 8

C. 10

D. 12

Correct Answer: B

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Question 17

Solve the system of linear equations u\sing matrices:\n\( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 7 \ 10 \end{bmatrix} \)

Correct A. \( egin{bmatrix} 1 \ 2 \end{bmatrix} \)

B. \( egin{bmatrix} 2 \ 1 \end{bmatrix} \)

C. \( egin{bmatrix} 3 \ 4 \end{bmatrix} \)

D. \( egin{bmatrix} 4 \ 3 \end{bmatrix} \)

Correct Answer: A

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Question 18

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 + \( y - 3 \)^2 = 16 )

D. \( x - 3 \ \)^2 + \( y - 4 \)^2 = 16 )

Correct Answer: A

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Question 19

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. If the dis\tance between the two cities is 240 km, what is the average speed for the round trip?

A. 48

B. 50

Correct C. 52

D. 54

Correct Answer: C

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Question 20

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

Correct A. \( x = -2 \)

B. \( x = 2 \)

C. \( x = -1 \)

D. \( x = 1 \)

Correct Answer: A

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Question 21

A random sample of 25 students from a university had a mean height of 175.5 cm with a s\tandard deviation of 5.2 cm. Calculate the coefficient of variation (CV) of the sample.

A. 12.5%

Correct B. 15%

C. 17.5%

D. 20%

Correct Answer: B

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Question 22

Solve for 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 23

Find the determinant of the matrix \[ \begin{bmatrix} 2 & 3 & 1 \\ 4 & 1 & 2 \\ 3 & 2 & 1 \end{bmatrix} \].

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 24

A sequence is defined by the formula \( a_n = 2n + 1 \). Find the sum of the first 10 terms of the sequence.

A. 110

B. 120

Correct C. 130

D. 140

Correct Answer: C

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Question 25

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

A. 30

B. 40

Correct C. 50

D. 60

Correct Answer: C

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