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POST UTME CALEB UNIVERSITY 2024 Mathematics | Objective

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Question 1 View Details

Solve for x in the equation \(\frac{1}{2}x^2 + 5x - 3 = 0\) using the quadratic formula.

A. \(x = \frac{-5 \pm \sqrt{25 + 6}}{1} \\)

B. \(x = \frac{-5 \pm \sqrt{25 - 6}}{1} \\)

Correct C. \(x = \frac{-5 \pm \sqrt{25 + 12}}{1} \\)

D. \(x = \frac{-5 \pm \sqrt{25 - 12}}{1} \\)

Correct Answer: C

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Question 2 View Details

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

Correct A. \(2 1-4 \\) - 3\(8-6\) + 1\(8-3\) )

B. \(2 1-2 \\) - 3\(4-6\) + 1\(12-9\) )

C. \(2 1-2 \\) - 3\(4-3\) + 1\(8-12\) )

D. \(2 1-2 \\) - 3\(4-3\) + 1\(12-8\) )

Correct Answer: A

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Question 3 View Details

A binary operation (\odot\) is defined as \\((odot\(a odot b = a^2 + b^2\). Find the value of \(2 \\(odot b = a^2 + b^2). Find the value of \odot 3 \odot 4\).

Correct A. \(2^2 + 3^2 + 4^2\)

B. \(2^2 + 3^2 - 4^2\)

C. \(2^2 - 3^2 + 4^2\)

D. \(2^2 - 3^2 - 4^2\)

Correct Answer: A

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Question 4 View Details

A bag contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is not blue?

Correct A. \(\frac{5}{8}\)

B. \(\frac{3}{8}\)

C. \(\frac{2}{8}\)

D. \(\frac{1}{8}\)

Correct Answer: A

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Question 5 View Details

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

Correct A. \(x < -1 \\) or \(x > \frac{3}{2} \\)

B. \(x < -1 \\) or \(x < \frac{3}{2} \\)

C. \(x > -1 \\) or \(x > \frac{3}{2} \\)

D. \(x > -1 \\) or \(x < \frac{3}{2} \\)

Correct Answer: A

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Question 6 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-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 7 View Details

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

A. 25

Correct B. 30

C. 35

D. 40

Correct Answer: B

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Question 8 View Details

Solve the system of equations using matrices:

Correct A. \(egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix}\)

B. \(egin{bmatrix} 2 & 1 \ 4 & 3 \end{bmatrix}\)

C. \(egin{bmatrix} 1 & 3 \ 2 & 4 \end{bmatrix}\)

D. \(egin{bmatrix} 3 & 1 \ 2 & 4 \end{bmatrix}\)

Correct Answer: A

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Question 9 View Details

Find the volume of the cylinder with radius 6 and height 8.

A. ( 48pi )

B. ( 64pi )

Correct C. ( 96pi )

D. ( 128pi )

Correct Answer: C

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Question 10 View Details

Simplify the expression \(\frac{1}{2} \log_{10} x^2 \\) ).

Correct A. \(\frac{1}{2} \log_{10} x\)

B. \(\log_{10} x\)

C. \(\frac{1}{2} \log_{10} x^2 \\) )

D. \(\log_{10} x^2 \\) )

Correct Answer: A

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Question 11 View Details

Given the matrix A = egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix}, find the determinant of A.

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 12 View Details

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

A. 0

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

Correct C. \(\frac{\pi}{4}\)\)

D. \(\frac{3\pi}{4}\)\)

Correct Answer: C

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Question 13 View Details

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

Correct A. 59048

B. 59049

C. 59050

D. 59051

Correct Answer: A

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Question 14 View Details

A histogram of exam scores has a mean of 75 and a standard deviation of 10. What is the probability that a randomly selected score is between 60 and 90?

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

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

C. \(\frac{3}{4}\)\)

D. \(\frac{5}{6}\)\)

Correct Answer: B

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Question 15 View Details

Convert the decimal number 0.5 to a \fraction in lowest terms.

Correct A. \(\frac{1}{2}\)\)

B. \(\frac{1}{3}\)\)

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

D. \(\frac{3}{4}\)\)

Correct Answer: A

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Question 16 View Details

Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.

Correct A. \(\frac{1}{3}\)\)\pi (6) \(4^2 + 2^2 + 4\cdot 2\)

B. \(\frac{1}{3}\)\)\pi (6) \(4^2 + 2^2 - 4\cdot 2\)

C. \(\frac{1}{3}\)\)\pi (6) \(4^2 - 2^2 + 4\cdot 2\)

D. \(\frac{1}{3}\)\)\pi (6) \(4^2 - 2^2 - 4\cdot 2\)

Correct Answer: A

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Question 17 View Details

Solve the system of linear equations using matrices: \begin{bmatrix} 2 & 1 \\ 1 & 2 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 3 \\ 4 \end{bmatrix}.

Correct A. \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 1 \\ 2 \end{bmatrix}

B. \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 2 \\ 1 \end{bmatrix}

C. \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 3 \\ 4 \end{bmatrix}

D. \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 4 \\ 3 \end{bmatrix}

Correct Answer: A

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Question 18 View Details

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

Correct A. \(\frac{8}{3}\)\) + 3 - 1

B. \(\frac{8}{3}\)\) - 3 - 1

C. \(\frac{8}{3}\)\) + 3 + 1

D. \(\frac{8}{3}\)\) - 3 + 1

Correct Answer: A

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Question 19 View Details

Simplify the expression \(\frac{\sqrt{12}}{\sqrt{3}}\).

Correct A. 2\sqrt{3}

B. \(\sqrt{3}\)

C. \(\sqrt{12}\)

D. \(\sqrt{3}\) + \(\sqrt{12}\)

Correct Answer: A

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Question 20 View Details

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

Correct A. \(x = -2\)

B. \(x = -1\)

C. \(x = 1\)

D. \(x = 2\)

Correct Answer: A

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Question 21 View Details

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

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 22 View Details

Solve the inequality \(|x-2| > 3\).

Correct A. \(-∞, -1\) ∪ (5, ∞)

B. \(-∞, -1\) ∪ (1, ∞)

C. \(-∞, 1\) ∪ (5, ∞)

D. \(-∞, -1\) ∪ (2, ∞)

Correct Answer: A

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Question 23 View Details

Find the volume of the solid formed by revolving the region bounded by \(y = x^2\), \(y = 0\)\), and \(x = 2\) about the x-axis.

Correct A. \(\frac{32\pi}{5}\)\)

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

C. \(\frac{32\pi}{3}\)\)

D. \(\frac{64\pi}{5}\)\)

Correct Answer: A

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Question 24 View Details

A set of 5 numbers has a mean of 10 and a standard deviation of 2. Find the probability that a randomly selected number from this set is greater than 12.

Correct A. 0.25

B. 0.5

C. 0.75

D. 0.9

Correct Answer: A

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Question 25 View Details

Solve the equation \(\frac{x^2}{x-1} = 2\).

A. \(x = 1\)

Correct B. \(x = 2\)

C. \(x = 3\)

D. \(x = 4\)

Correct Answer: B

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