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POST UTME NOUN 2023 Mathematics | Objective

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Question 1 View Details

Find the determinant of the matrix [ egin{array}{ccc} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{array} ].

Correct A. -3

B. 0

C. 3

D. 6

Correct Answer: A

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Question 2 View Details

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

A. 60

B. 70

Correct C. 80

D. 90

Correct Answer: C

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Question 3 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 4 View Details

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

Correct A. \(-∞, -1\) ∪ (3, ∞)

B. \(-∞, 1\) ∪ (3, ∞)

C. \(-∞, -3\) ∪ (1, ∞)

D. \(-∞, 3\) ∪ (1, ∞)

Correct Answer: A

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Question 5 View Details

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

Correct A. 2197

B. 2187

C. 2177

D. 2167

Correct Answer: A

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Question 6 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.

A. 24\pi

B. 48\pi

Correct C. 96\pi

D. 192\pi

Correct Answer: C

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Question 7 View Details

Solve the system of linear equations using matrices: \begin{align*} x + y + z &= 6 \ 2x - y + 3z &= 7 \ -x + 2y - z &= -2 \end{align*}

Correct A. \begin{pmatrix} 1 \ 2 \ -1 \end{pmatrix}

B. \begin{pmatrix} 2 \ -1 \ 3 \end{pmatrix}

C. \begin{pmatrix} 1 \ 2 \ -1 \end{pmatrix}

D. \begin{pmatrix} 2 \ -1 \ 3 \end{pmatrix}

Correct Answer: A

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Question 8 View Details

Find the derivative of the function \(f(x) = \frac{x^2 + 2x - 3}{x^2 - 4}\) using the quotient rule.

A. \(\frac{2x + 2}{x^2 - 4\) ^2}\)\)

Correct B. \(\frac{2x^2 + 4x - 6}{\) \(x^2 - 4\) ^2}\)\)

C. \(\frac{2x + 2}{x^2 - 4}\)\)\)

D. \(\frac{2x^2 + 4x - 6}{x^2 - 4}\)\)\)

Correct Answer: B

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Question 9 View Details

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

Correct A. \begin{pmatrix} -2 \ -2 \end{pmatrix}

B. \begin{pmatrix} -1 \ -4 \end{pmatrix}

C. \begin{pmatrix} -2 \ -2 \end{pmatrix}

D. \begin{pmatrix} -1 \ -4 \end{pmatrix}

Correct Answer: A

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Question 10 View Details

Find the surface area of the sphere with radius 5 cm.

A. 100\pi

B. 50\pi

Correct C. 200\pi

D. 250\pi

Correct Answer: C

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Question 11 View Details

Find the value of x in the equation \(egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ 1 \end{bmatrix} = egin{bmatrix} 7 \ 11 \end{bmatrix}\).

A. 3

B. 4

Correct C. 5

D. 6

Correct Answer: C

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Question 12 View Details

A circle with center (1, 2) and radius 3 passes through the point (6, 6). Find the equation of the circle.

Correct A. \(x - 1\)^2 + \(y - 2\)^\(2 = 9\)

B. \(x - 2\)^2 + \(y - 1\)^\(2 = 9\)

C. \(x - 1\)^2 + \(y - 2\)^\(2 = 16\)

D. \(x - 2\)^2 + \(y - 1\)^\(2 = 16\)

Correct Answer: A

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Question 13 View Details

Simplify the expression \(\frac{1}{2} \log_{10} x^2 \\) - \(\frac{1}{3}\)\) \log_{10} \(x^3\) ).

Correct A. \log_{10} (x)

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

C. \log_{10} \(x^3\)

D. \log_{10} \(x^4\)

Correct Answer: A

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Question 14 View Details

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

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

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

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

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

Correct Answer: A

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Question 15 View Details

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

Correct A. \(-∞, -1\) ∪ (3, ∞)

B. \(-∞, -3\) ∪ (1, ∞)

C. \(-∞, -1\) ∪ (1, ∞)

D. \(-∞, -3\) ∪ (3, ∞)

Correct Answer: A

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