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POST UTME OAU 2021 Mathematics | Objective

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Question 1 View Details

Let \(\mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix}\) and \(\mathbf{b} = egin{pmatrix} -1 \ 4 \end{pmatrix}\). Find the projection of ( mathbf{b} ) onto ( mathbf{a} ).

A. \(egin{pmatrix} 0 \ 0 \end{pmatrix}\)

Correct B. \(egin{pmatrix} 1 \ 2 \end{pmatrix}\)

C. \(egin{pmatrix} -1 \ 2 \end{pmatrix}\)

D. \(egin{pmatrix} 1 \ -2 \end{pmatrix}\)

Correct Answer: B

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Question 2 View Details

In the diagram below, ( AB ) is a diameter of the circle with center ( O ). If angle \(AOB = 60\^{circ}\), find the measure of ( angle ACB ).

A. \(30^{circ}\)

B. \(45^{circ}\)

Correct C. \(60^{circ}\)

D. \(90^{circ}\)

Correct Answer: C

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Question 3 View Details

Solve the 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 4 View Details

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

Correct A. -1

B. 1

C. 2

D. 3

Correct Answer: A

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Question 5 View Details

In the sequence ( 1, 2, 4, 8, 16, ... ), find the next term.

A. 32

Correct B. 64

C. 128

D. 256

Correct Answer: B

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Question 6 View Details

Determine the value of x in the equation \(\frac{x}{2} + \frac{3}{4} = \frac{7}{8}\).

A. 1

B. 2

C. 3

Correct D. 4

Correct Answer: D

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Question 7 View Details

A histogram is constructed with the following data: 5, 7, 9, 11, 13. What is the mean of the data?

A. 9

Correct B. 10

C. 11

D. 12

Correct Answer: B

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Question 8 View Details

Find the volume of the sphere \(x^2 + y^2 + z^2 = 4\) using the method of cylindrical shells.

A. 16\pi

B. 32\pi

Correct C. 48\pi

D. 64\pi

Correct Answer: C

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Question 9 View Details

A vector \(\vec{a} = 2\hat{i} + 3\hat{j}\) is rotated by an angle of 30 degrees. What is the magnitude of the rotated vector?

A. 3.61

B. 4.24

Correct C. 4.47

D. 4.58

Correct Answer: C

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Question 10 View Details

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

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

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

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

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

Correct Answer: A

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Question 11 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 \(cm^3\)

Correct B. 48\pi \(cm^3\)

C. 96\pi \(cm^3\)

D. 192\pi \(cm^3\)

Correct Answer: B

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Question 12 View Details

Solve for x in the equation \(x^4 - 6x^2 + 8 = 0\).

Correct A. \(x =\)\pm 2

B. \(x =\)\pm \(\sqrt{2}\)

C. \(x =\)\pm 2\sqrt{2}

D. \(x =\)\pm 4

Correct Answer: A

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Question 13 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 + \(y - 3\)^\(2 = 25\)

C. \(x - 2\)^2 + \(y - 3\)^\(2 = 36\)

D. \(x - 2\)^2 + \(y - 3\)^\(2 = 49\)

Correct Answer: A

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Question 14 View Details

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

Correct A. x \leq -1 \text{ or } x \geq \(\frac{3}{2}\)\)

B. x \leq -1 \text{ or } x \geq 1

C. x \leq -1 \text{ or } x \geq 2

D. x \leq 1 \text{ or } x \geq 2

Correct Answer: A

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Question 15 View Details

Find the area under the curve \(y = x^2\) from \(x = 0\) to \(x = 4\).

A. 64

B. 128

Correct C. 192

D. 256

Correct Answer: C

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Question 16 View Details

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

A. 14

Correct B. 16

C. 18

D. 20

Correct Answer: B

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Question 17 View Details

In the diagram below, 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 18 View Details

Two events A and B are independent. If P(A) = 0.4 and P(B) = 0.6, find P(\(A \cap B\)).

Correct A. 0.24

B. 0.36

C. 0.48

D. 0.64

Correct Answer: A

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Question 19 View Details

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

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

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

C. 1

D. 2

Correct Answer: A

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Question 20 View Details

Find the value of x in the equation: \log_{10} \(x^2 = 4\).

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 21 View Details

Solve the quadratic equation \(x^2 + 4x - 5 = 0\) using the quadratic formula. What is the value of ( x )?

A. 1

B. -5

Correct C. 2

D. -2

Correct Answer: C

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Question 22 View Details

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

A. 16π

Correct B. 32π

C. 64π

D. 128π

Correct Answer: B

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Question 23 View Details

A circle has a diameter of 10 cm. Find the area of the circle.

Correct A. 25π

B. 50π

C. 100π

D. 200π

Correct Answer: A

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Question 24 View Details

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

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

B. x < -1 or \(x > 3\)

C. \(x < 1\) or \(x > 3\)

D. x < -3 or \(x < 1\)

Correct Answer: A

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Question 25 View Details

Find the derivative of the function ( f(x) = \(3x^2 + 2x - 5\) ).

Correct A. 6x + 2

B. 6x - 2

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

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

Correct Answer: A

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