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POST UTME AAUA 2022 Mathematics | Objective

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Question 1 View Details

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

A. 16\pi

B. 32\pi

Correct C. 64\pi

D. 128\pi

Correct Answer: C

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Question 2 View Details

If f(x) = \(\frac{1}{x^2 + 1}\)\)\), find f'(x).

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

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

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

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

Correct Answer: A

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Question 3 View Details

Solve the equation \\(\sin^2\) x + \\(\cos^2\) \(x = 1\) for x in the interval [0, 2\pi].

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

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

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

D. \(\frac{5\pi}{4}\)\)

Correct Answer: A

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Question 4 View Details

Find the area under the curve \(y = x\^3 - 6x^2 + 9x + 2\) from \(x = 0\) to \(x = 2\).

A. 10

B. 20

Correct C. 30

D. 40

Correct Answer: C

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Question 5 View Details

A circle with radius 4 cm is inscribed in a square. Find the area of the square.

A. 16

B. 32

Correct C. 64

D. 128

Correct Answer: C

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Question 6 View Details

Solve the inequality (\(\frac{x}{x-2}\(> 2\)\) for \\((frac{x}{x-2} > 2\(x > 2\)\).

A. \(x > 4\)

Correct B. \(x > 6\)

C. \(x > 8\)

D. \(x > 10\)

Correct Answer: B

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Question 7 View Details

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

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

B. \(y = 2x + 1\)

C. \(y = x + 2\)

D. \(y = x - 2\)

Correct Answer: A

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Question 8 View Details

A set ( A ) contains the elements ( 1, 2, 3, 4, 5 ). Find the number of subsets of ( A ) that contain exactly three elements.

A. 10

B. 15

Correct C. 20

D. 25

Correct Answer: C

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Question 9 View Details

Find the sum of the infinite geometric series \(1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + ldots\).

A. 2

Correct B. 4

C. 8

D. 16

Correct Answer: B

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Question 10 View Details

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

Correct A. \(x = -2\)

B. \(x = 2\)

C. \(x = -1\)

D. \(x = 1\)

Correct Answer: A

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Question 11 View Details

Find the area under the curve \(y = 2x\^2 + 3x - 4\) from \(x = 0\) to \(x = 2\).

A. 12

Correct B. 16

C. 20

D. 24

Correct Answer: B

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Question 12 View Details

Solve the system of equations using matrices: \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 5 \\ 11 \end{bmatrix}.

Correct A. \begin{bmatrix} 1 \\ 2 \end{bmatrix}

B. \begin{bmatrix} 2 \\ 3 \end{bmatrix}

C. \begin{bmatrix} 3 \\ 4 \end{bmatrix}

D. \begin{bmatrix} 4 \\ 5 \end{bmatrix}

Correct Answer: A

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Question 13 View Details

Find the equation of the circle with center (2, 3) and radius 4.

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

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

C. \(x - 3\)^2 + \(y - 2\)^\(2 = 25\)

D. \(x - 4\)^2 + \(y - 3\)^\(2 = 36\)

Correct Answer: B

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Question 14 View Details

Solve for x in the equation \(2^x\) + \\((3^x\)\(= 5\)\\()^x\).

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 15 View Details

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

A. \(\vec{r} = \begin{bmatrix} 1 \\ 2 \end{bmatrix} + t\begin{bmatrix} 1 \\ 1 \end{bmatrix}\)

Correct B. \(\vec{r} = \begin{bmatrix} 1 \\ 2 \end{bmatrix} + t\begin{bmatrix} 2 \\ 3 \end{bmatrix}\)

C. \(\vec{r} = \begin{bmatrix} 1 \\ 2 \end{bmatrix} + t\begin{bmatrix} 3 \\ 4 \end{bmatrix}\)

D. \(\vec{r} = \begin{bmatrix} 1 \\ 2 \end{bmatrix} + t\begin{bmatrix} 4 \\ 5 \end{bmatrix}\)

Correct Answer: B

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Question 16 View Details

Find the area under the curve \(y = \frac{1}{2}x^2 + 3x - 2\) from \(x = 0\) to \(x = 4\).

A. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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Question 17 View Details

Solve the equation \(2^x + 3^x = 5^x\) for ( x ).

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 18 View Details

A circle has a radius of 5 cm. Find the area of the circle.

A. 50

B. 75

Correct C. 100

D. 125

Correct Answer: C

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Question 19 View Details

A die is rolled. Find the probability that the number obtained is greater than 4.

Correct A. \(1/6\)

B. \(1/3\)

C. \(1/2\)

D. \(2/3\)

Correct Answer: A

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Question 20 View Details

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

A. \(y = x + 1\)

B. \(y = x - 1\)

Correct C. \(y = 2x - 1\)

D. \(y = 2x + 1\)

Correct Answer: C

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Question 21 View Details

In a binary operation (*\) on the set of vectors \(\\((*) on the set of vectors \mathbb{R}^2), the operation is defined as ((mathbf{a}, mathbf{b}) mapsto mathbf{a} cdot mathbf{b}). If \(\mathbf{a} = 1, 2 \\(), the operation is defined as ((mathbf{a}, mathbf{b}) mapsto mathbf{a} cdot mathbf{b}). If (\\)) and \(\mathbf{b} = 3, 4\)), find \(\mathbf{a} * \\()), find (\mathbf{b}\).

A. 7

Correct B. 11

C. 13

D. 15

Correct Answer: B

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Question 22 View Details

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

A. 8π/3

Correct B. 16π/3

C. 32π/3

D. 64π/3

Correct Answer: B

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Question 23 View Details

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

A. 2

B. 4

Correct C. 8

D. 16

Correct Answer: C

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Question 24 View Details

Find the surface area of the sphere with radius 5.

A. 50π

B. 100π

Correct C. 150π

D. 200π

Correct Answer: C

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Question 25 View Details

Solve the inequality \(\frac{x}{x - 1} > 1\).

Correct A. \(-∞, 0\) ∪ (1, ∞)

B. \(-∞, 1\) ∪ (1, ∞)

C. \(-∞, 0\) ∪ (1, 2)

D. \(-∞, 1\) ∪ (2, ∞)

Correct Answer: A

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