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POST UTME BABCOCK UNIVERSITY 2019 Mathematics | Objective

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Question 1 View Details

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

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Question 2 View Details

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

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Question 3 View Details

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

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Question 4 View Details

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

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Question 5 View Details

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

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Question 6 View Details

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

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Question 7 View Details

A histogram of exam scores has a mean of 75 and a standard 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

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Question 8 View Details

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

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Question 9 View Details

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

Correct A. 6x - 2

B. 6x + 2

C. \(3x^2 - 2\)

D. \(3x^2 + 2\)

Correct Answer: A

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Question 10 View Details

A rectangular 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

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Question 11 View Details

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

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Question 12 View Details

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

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Question 13 View Details

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

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Question 14 View Details

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

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Question 15 View Details

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

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Question 16 View Details

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

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Question 17 View Details

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

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Question 18 View Details

Find the derivative of the function ( f(x) = \(\frac{1}{x^2 + 1}\)\)\) \) using 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

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Question 19 View Details

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

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Question 20 View Details

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

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Question 21 View Details

Find the derivative of the function ( f(x) = \(\frac{1}\){\sqrt{1 - \(x^2}}\)\) ) using 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

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Question 22 View Details

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

Correct A. \(-∞, -3\) ∪ (1, ∞)

B. \(-∞, -1\) ∪ (3, ∞)

C. \(-∞, 1\) ∪ (3, ∞)

D. \(-∞, -3\) \cup \(-1, 1\)\)

Correct Answer: A

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Question 23 View Details

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

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Question 24 View Details

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

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Question 25 View Details

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

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