Exam Body

Year

Subject

Paper Type

POST UTME BABCOCK UNIVERSITY 2019 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 2019 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

Determine the value of x in the equation [ \sin^2(x) + \cos^2(x) = 1 ].

Correct A. \pi/2

B. \pi/4

C. \pi/6

D. \pi/8

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 2

Find the area under the curve [ y = \frac{1}{x} \] from [ x = 1 \] to [ x = 2 \].

A. \log(2)

B. \log(1)

Correct C. \log(2) - \log(1)

D. \log(1) - \log(2)

Correct Answer: C

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 3

A sequence is defined as [ a_n = \frac{1}{n} \]. Find the sum of the first 5 terms of the sequence.

A. \frac{1}{1} + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5}

B. \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \frac{1}{6}

Correct C. \frac{1}{1} + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5}

D. \frac{1}{1} + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{6}

Correct Answer: C

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 4

A set of 5 numbers has a mean of 10. If 2 is added to each number, what is the new mean?

A. 8

B. 10

Correct C. 12

D. 14

Correct Answer: C

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 5

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

A. 16\pi

B. 32\pi

Correct C. 64\pi

D. 128\pi

Correct Answer: C

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 6

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

Correct A. 12

B. 16

C. 20

D. 24

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 7

A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 90?

A. 0.5

B. 0.6

Correct C. 0.7

D. 0.8

Correct Answer: C

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 8

Solve the inequality \( x^2 - 4x + 3 > 0 \).

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

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

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

D. (1, 3)

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 9

Find the derivative of the function ( f(x) = 3x^2 - 2x + 1 ) u\sing the chain rule.

Correct A. 6x - 2

B. 6x + 2

C. 3x^2 - 2

D. 3x^2 + 2

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 10

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

A. 30

B. 40

Correct C. 50

D. 60

Correct Answer: C

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 11

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

Correct A. \( \frac{1}{3}\( 4^3 + 12 cdot 4^2 - 8 cdot 4 \ \) )

B. \( \frac{1}{3}\( 4^3 + 12 cdot 4^2 + 8 cdot 4 \ \) )

C. \( \frac{1}{3}\( 4^3 - 12 cdot 4^2 - 8 cdot 4 \ \) )

D. \( \frac{1}{3}\( 4^3 - 12 cdot 4^2 + 8 cdot 4 \ \) )

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 12

A bakery sells a total of 480 loaves of bread per day. They make a profit of ₦5 per loaf of bread. If they sell a total of ₦2400 per day, what is the ratio of the number of loaves of bread they sell to the number of loaves of bread they do not sell?

Correct A. 1:239

B. 1:239

C. 1:239

D. 1:239

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 13

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

A. \( \frac{2}{3} pi \)

Correct B. \( \frac{4}{3} pi \)

C. \( \frac{8}{3} pi \)

D. \( \frac{16}{3} pi \)

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 14

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

A. \( \frac{1}{4} \)

B. \( \frac{1}{2} \)

Correct C. \( \frac{3}{8} \)

D. \( \frac{5}{8} \)

Correct Answer: C

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 15

Find the surface area of the solid formed by rotating the region bounded by the curves \( y = x^2 \) and \( y = 2x \) about the x-axis.

A. ( 4 pi )

Correct B. ( 8 pi )

C. ( 16 pi )

D. ( 32 pi )

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 16

Find the area under the curve \( y = \frac{1}{2}x^2 - 3x + 5 \) from \( x = 0 \) to \( x = 4 \).

A. 20

B. 25

Correct C. 30

D. 35

Correct Answer: C

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 17

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

Correct A. \left\( -\infty, -\frac{3}{2} \right \) \cup \left\( \frac{1}{2}, \infty \right \)

B. \left\( -\infty, \frac{1}{2} \right \) \cup \left\( \frac{3}{2}, \infty \right \)

C. \left\( -\infty, -\frac{1}{2} \right \) \cup \left\( \frac{3}{2}, \infty \right \)

D. \left\( -\infty, \frac{1}{2} \right \) \cup \left\( -\frac{3}{2}, \infty \right \)

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 18

Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} \) u\sing the chain rule.

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

Correct B. \frac{2x}{\( x^2 + 1 \)^2}

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

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

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 19

A box contains 5 red balls and 3 blue balls. If 2 balls are drawn at random, what is the probability that both balls are red?

Correct A. \frac{5}{8}

B. \frac{3}{8}

C. \frac{1}{4}

D. \frac{1}{2}

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 20

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

Correct A. \left\( -2, 2 \right \)

B. \left\( -2 \right \)

C. \left\( 2 \right \)

D. \left\( -2, -1 \right \)

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 21

Find the derivative of the function ( f(x) = \frac{1}{\sqrt{1 - x^2}} ) u\sing the chain rule.

Correct A. f'(x) = \frac{x}{\( 1 - x^2 \)^{3/2}}

B. f'(x) = \frac{-x}{\( 1 - x^2 \)^{3/2}}

C. f'(x) = \frac{1}{\( 1 - x^2 \)^{3/2}}

D. f'(x) = \frac{-1}{\( 1 - x^2 \)^{3/2}}

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 22

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

Correct A. \( -∞, -3 \) ∪ (1, ∞)

B. \( -∞, -1 \) ∪ (3, ∞)

C. \( -∞, 1 \) ∪ (3, ∞)

D. \( -∞, -3 \) ∪ \( -1, 1 \)

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 23

A box contains 5 red balls and 3 blue balls. If 2 balls are drawn at random, what is the probability that at least one blue ball is drawn?

A. \frac{3}{8}

Correct B. \frac{5}{8}

C. \frac{1}{2}

D. \frac{3}{4}

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 24

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

B. 12

C. 13

D. 14

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 25

Convert the decimal number 0.75 to a \fraction in its simplest form.

Correct A. \frac{3}{4}

B. \frac{1}{4}

C. \frac{3}{5}

D. \frac{2}{3}

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Master the Exam!

You've seen a preview, but there are thousands more questions plus AI tutor to break down complex solutions.

Unlock Full Access Available for Android & Windows

Help others prepare! Share this practice hub:

Chat with Support