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POST UTME BABCOCK UNIVERSITY 2018 Mathematics | Objective

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Question 1 View Details

Find the equation of the plane passing through the points ((1,2,3)), ((4,5,6)), and ((7,8,9)).

Correct A. \(2x - 3y + z = 0\)

B. \(x + 2y - 3z = 0\)

C. \(3x - 2y + z = 0\)

D. \(x - 2y + 3z = 0\)

Correct Answer: A

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Question 2 View Details

Solve the inequality \(\frac{x^2 - 4}{x^2 - 9} > 0\).

Correct A. x in \( -infty, -3 \ cup (2, infty) )

B. x in \( -infty, -3 \ cup (3, infty) )

C. x in \( -infty, 2 \ cup (3, infty) )

D. x in \( -infty, -3 \ cup (2, 3) )

Correct Answer: A

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Question 3 View Details

A survey of 100 students found that 70% of them preferred Mathematics, 20% preferred Science, and 10% preferred both. What is the probability that a randomly selected student prefers either Mathematics or Science?

Correct A. \(\frac{9}{10}\)

B. \(\frac{8}{10}\)

C. \(\frac{7}{10}\)

D. \(\frac{6}{10}\)

Correct Answer: A

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Question 4 View Details

A rectangular box has a length of 10 cm, a width of 5 cm, and a height of 8 cm. Find the volume of the box in cubic centimeters.

Correct A. ( 400 )

B. ( 500 )

C. ( 600 )

D. ( 800 )

Correct Answer: A

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Question 5 View Details

In the diagram below, the area of triangle ABC is 12 square units. If the base of the triangle is 4 units, find the height of the triangle.

Correct A. ( 3 )

B. ( 4 )

C. ( 6 )

D. ( 8 )

Correct Answer: A

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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. \(\frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4\)

B. \(\frac{1}{2} \times 4^2 + 3 \times 4 - 2\)

C. \(\frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4^2\)

D. \(\frac{1}{2} \times 4^2 + 3 \times 4^3 - 2 \times 4\)

Correct Answer: A

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Question 7 View Details

A rectangular prism has a length of 6 cm, a width of 4 cm, and a height of 3 cm. Find the volume of the prism.

A. 6 cm × 4 cm × 3 cm

B. 6 cm × 4 cm + 3 cm

Correct C. 6 cm × 4 cm × 3 cm

D. 6 cm + 4 cm × 3 cm

Correct Answer: C

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Question 8 View Details

Solve the equation \(2^x + 2^x = 128\).

Correct A. \(x = 7\)

B. \(x = 6\)

C. \(x = 5\)

D. \(x = 4\)

Correct Answer: A

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Question 9 View Details

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 10 View Details

A cone has a base radius of 4 cm and a height of 6 cm. Find the volume of the cone.

Correct A. \(\frac{1}{3} \pi r^2 h\)

B. \(\frac{1}{3} \pi r h\)

C. \(\frac{1}{3} \pi r^2\)

D. \(\frac{1}{3} \pi r\)

Correct Answer: A

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Question 11 View Details

Find the value of \(\frac{d}{dx}\left \frac{1}{x^2}\right\)\).

Correct A. -\(\frac{2}{x^3}\)\)\)

B. +\(\frac{2}{x^3}\)\)\)

C. -\(\frac{1}{x^3}\)\)\)

D. +\(\frac{1}{x^3}\)\)\)

Correct Answer: A

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Question 12 View Details

Solve the equation \(\log_2 x-1\) + \log_2\(x+1\)\(= 2\)\).

Correct A. \(x = 3\)

B. \(x = 2\)

C. \(x = 1\)

D. \(x = 4\)

Correct Answer: A

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Question 13 View Details

A circle with center \(C\) and radius \(r\) has equation \(x-h\)^2 + \(y-k\)^\(2 = r\^2\)\). Find the equation of the circle with center \(C -2,3\)\) and radius \(r = 4\).

Correct A. \(x+2\)^2 + \(y-3\)^\(2 = 16\)

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

C. \(x+2\)^2 + \(y+3\)^\(2 = 16\)

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

Correct Answer: A

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Question 14 View Details

Find the value of \(\int_0^1 x^2 dx\).

Correct A. \(\frac{1}{3}\)\)

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

C. 1

D. \(\frac{2}{3}\)\)

Correct Answer: A

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Question 15 View Details

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

Correct A. \(x < -1\)\text{ or } \(x > 3\)

B. \(x < 1\) \text{ or } \(x > 3\)

C. \(x < 1\) \text{ or } \(x < 3\)

D. \(x > 1\) \text{ or } \(x < 3\)

Correct Answer: A

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Question 16 View Details

Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.

Correct A. 12155

B. 12158

C. 12161

D. 12164

Correct Answer: A

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Question 17 View Details

A rectangular solid has a length of 6 cm, a width of 4 cm, and a height of 3 cm. Find its volume.

Correct A. 72

B. 80

C. 88

D. 96

Correct Answer: A

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Question 18 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. \(x < 3/2\)\) or x > -1

D. \(x > 3/2\)\) or x < -1

Correct Answer: A

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Question 19 View Details

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

Correct A. 6x - 2

B. 6x + 2

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

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

Correct Answer: A

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Question 20 View Details

A right triangle has a hypotenuse of length 10 cm and one leg of length 6 cm. Find the length of the other leg.

Correct A. 8

B. 6

C. 4

D. 2

Correct Answer: A

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Question 21 View Details

Solve the inequality \((2x^2 + 5x - 3\) > 0\) for ( x ) in the interval \(-\\((2x^2 + 5x - 3 > 0) for ( x ) in the interval \infty, \infty \\) ).

Correct A. \(\frac{-5 + \sqrt{49}\)}{4}\)

B. \(\frac{-5 - \sqrt{49}\)}{4}\)

C. \(\frac{-5 + \sqrt{25}\)}{4}\)

D. \(\frac{-5 - \sqrt{25}\)}{4}\)

Correct Answer: A

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Question 22 View Details

A sequence is defined by \(a_n = 2n^2 - 3n + 1\). Find the sum of the first five terms of the sequence.

Correct A. 120

B. 130

C. 140

D. 150

Correct Answer: A

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Question 23 View Details

A set of data is given by the following table. Find the mean of the data.

A. 25

Correct B. 30

C. 35

D. 40

Correct Answer: B

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Question 24 View Details

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

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 25 View Details

A polynomial is defined by ( p(x) = \((x^3 - 2x^2 + x - 1\)\) ). Find the value of \(p -1 \\((x^3 - 2x^2 + x - 1) ). Find the value of \\) ).

Correct A. -3

B. -2

C. -1

D. 0

Correct Answer: A

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