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POST UTME OSUSTECH 2021 Mathematics | Objective

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Question 1 View Details

Find the volume of the solid formed by revolving the region bounded by the curves \(y = x^2\) and \(y = 4x\) about the x-axis.

A. 64\pi

Correct B. 128\pi

C. 256\pi

D. 512\pi

Correct Answer: B

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Question 2 View Details

Solve the system of equations: \begin{align*} x+y+z&=3 \ 2x+3y+4z&=7 \ 3x+2y+z&=5 \end{align*}

Correct A. \(x = 1\), \(y = 1\), \(z = 1\)

B. \(x = 2\), \(y = 1\), \(z = 0\)

C. \(x = 1\), \(y = 2\), \(z = 0\)

D. \(x = 0\), \(y = 1\), \(z = 2\)

Correct Answer: A

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Question 3 View Details

Find the area of the triangle with vertices \(A(2,3), B(4,5),\) and \(C(6,7)\).

Correct A. 10

B. 20

C. 30

D. 40

Correct Answer: A

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Question 4 View Details

Solve the inequality: \begin{align*} \(2x^2 + 5x - 3\) &\ge 0 \end{align*}

Correct A. xle-1 \text{ or } xgefrac{3}{2}

B. xle-1 \text{ or } xgefrac{1}{2}

C. xle-1 \text{ or } xgefrac{3}{4}

D. xle-1 \text{ or } xgefrac{1}{4}

Correct Answer: A

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Question 5 View Details

Find the value of (\(12\theta\) if \\((\)12theta\(\(1\theta = \frac{1}{3}\) and 1\\(theta =\)\frac{2\sqrt{5}}{5}\).

Correct A. \(\frac{4}{3}\)\)

B. \(\frac{4}{5}\)\)

C. \(\frac{5}{4}\)\)

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

Correct Answer: A

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Question 6 View Details

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

Correct A. ( f'\((x) =\)\(\frac{x^2 - 4\) 2x + 3 - \(x^2 + 3x - 2\) (2x)}{ \(x^2 - 4\) ^2}\)\) )

B. ( f'\((x) =\)\(\frac{x^2 - 4\) 2x + 3 - \(x^2 + 3x - 2\) (2x)}{ \(x^2 - 4\) ^2}\)\) )

C. ( f'\((x) =\)\(\frac{x^2 - 4\) 2x + 3 + \(x^2 + 3x - 2\) (2x)}{ \(x^2 - 4\) ^2}\)\) )

D. ( f'\((x) =\)\(\frac{x^2 - 4\) 2x + 3 - \(x^2 + 3x - 2\) (2x)}{ \(x^2 - 4\) ^2}\)\) )

Correct Answer: A

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Question 7 View Details

Solve for ( x ) in the equation \(\log_{10} x^2 \\)\(= 4 ).\)

A. \(x = 10^2\)

Correct B. \(x = 10^4\)

C. \(x = 10^{-2}\)

D. \(x = 10^{-4}\)

Correct Answer: B

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Question 8 View Details

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

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

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

C. \(\frac{\pi}{6}\)

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

Correct Answer: A

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Question 9 View Details

A histogram of exam scores has a mean of 60 and a standard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 50 and 70?

A. 0.68

Correct B. 0.84

C. 0.95

D. 0.99

Correct Answer: B

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Question 10 View Details

Simplify the expression \(\frac{2^3 \cdot 3^2}{2^2 \cdot 3^4}\).

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

B. \(\frac{1}{3^4}\)

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

D. \(\frac{1}{2^4}\)

Correct Answer: A

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Question 11 View Details

Let \(\mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix}\) and \(\mathbf{b} = egin{pmatrix} 1 \ -2 \end{pmatrix}\). Find the projection of ( mathbf{b} ) onto ( mathbf{a} ).

Correct A. \begin{pmatrix} 0.8 \\ 1.2 \end{pmatrix}

B. \begin{pmatrix} 1.2 \\ -0.8 \end{pmatrix}

C. \begin{pmatrix} 0.6 \\ 0.9 \end{pmatrix}

D. \begin{pmatrix} 0.4 \\ 0.7 \end{pmatrix}

Correct Answer: A

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Question 12 View Details

Find the volume of the solid formed by revolving the region bounded by \(y = x^2\) and \(x = 1\) about the x-axis.

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

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

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

D. \(\frac{5}{3}\)\)\pi

Correct Answer: C

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Question 13 View Details

A fair six-sided die is rolled. What is the probability that the number rolled is a multiple of 3?

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

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

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

Correct D. \(\frac{1}{6}\)\)

Correct Answer: D

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Question 14 View Details

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

Correct A. \(x + y + z = 6\)

B. \(x - y - z = 0\)

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

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

Correct Answer: A

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Question 15 View Details

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

Correct A. \(-\infty, -1\) \cup \(5, \infty\)

B. \(-\infty, 1\) \cup \(5, \infty\)

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

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

Correct Answer: A

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Question 16 View Details

Find the volume of the frustum of a cone with height 8 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 256\pi \(cm^3\)

B. 512\pi \(cm^3\)

Correct C. 768\pi \(cm^3\)

D. 1024\pi \(cm^3\)

Correct Answer: C

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Question 17 View Details

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

Correct A. \left\(-\infty, -3\right\) \cup \left\(2, \infty\right\)

B. \left\(-\infty, -3\right\) \cup \left\(-3, 2\right\) \cup \left\(2, \infty\right\)

C. \left\(-\infty, -3\right\) \cup \left\(2, \infty\right\)

D. \left\(-\infty, -3\right\) \cup \left\(-3, 2\right\)

Correct Answer: A

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Question 18 View Details

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

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 19 View Details

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

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

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

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

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

Correct Answer: B

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Question 20 View Details

Find the sum of the infinite geometric series \sum_{\(n = 1\)}^\infty \(\frac{1}{2^n}\)\)\).

Correct A. 1

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

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

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

Correct Answer: A

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Question 21 View Details

Solve the quadratic equation \(x^2 + 5x + 6 = 0\) using the quadratic formula. What is the value of ( x )?

A. 2

Correct B. -3

C. -2

D. 1

Correct Answer: B

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Question 22 View Details

A circle with center ( C ) and radius ( r ) passes through the points ( A ) and ( B ). If \(CA = 3\) and \(CB = 4\), what is the value of ( r )?

Correct A. 5

B. 3

C. 4

D. 2

Correct Answer: A

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Question 23 View Details

Find the determinant of the matrix \(\begin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix}\).

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 24 View Details

A vector \(\vec{a}\) has components \(a_1 = 2) and \(a_2 = 3\). If \\() and (a_2 = 3\(vec{b}\) is a unit vector in the same direction as \(\\(vec{b}) is a unit vector in the same direction as \vec{a}\), what is the value of \(b_1\)?

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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Question 25 View Details

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

Correct A. \(-∞, -1\) ∪ (3, ∞)

B. \(-∞, -3\) ∪ (1, ∞)

C. \(-∞, 1\) ∪ (3, ∞)

D. \(-∞, -3\) ∪ (1, ∞)

Correct Answer: A

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