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Subject

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POST UTME AAUA 2020 Mathematics | Objective

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Question 1 View Details

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

Correct A. \(\frac{16}{3}\)

B. \(\frac{32}{3}\)

C. \(\frac{64}{3}\)

D. \(\frac{128}{3}\)

Correct Answer: A

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Question 2 View Details

Solve for ( x ) in the equation \(2x^2 + 5x - 3 = 0\).

A. \(x = -\frac{3}{2}\)

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

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

D. \(x = \frac{3}{2}\)

Correct Answer: B

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Question 3 View Details

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

Correct A. \(\frac{32\pi}{3}\)

B. \(\frac{64\pi}{3}\)

C. \(\frac{128\pi}{3}\)

D. \(\frac{256\pi}{3}\)

Correct Answer: A

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Question 4 View Details

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

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

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

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

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

Correct Answer: A

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Question 5 View Details

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

Correct A. \(y = \frac{1}{2}x + \frac{1}{2}\)

B. \(y = \frac{1}{2}x - \frac{1}{2}\)

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

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

Correct Answer: A

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Question 6 View Details

Find the value of \(int_{0}^{2} 2x^2 + 3x - 1 \\) dx ).

A. 4

B. 6

Correct C. 8

D. 10

Correct Answer: C

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Question 7 View Details

Solve the matrix equation \(egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix}\).

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

B. \(x = 2\), \(y = 3\)

C. \(x = 3\), \(y = 4\)

D. \(x = 4\), \(y = 5\)

Correct Answer: A

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Question 8 View Details

Find the sum of the first 5 terms of the geometric progression 2, 6, 18, ...

A. 62

B. 64

Correct C. 66

D. 68

Correct Answer: C

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Question 9 View Details

A histogram is constructed from the following data: 2, 4, 6, 8, 10. Find the mean of the data.

A. 5

Correct B. 6

C. 7

D. 8

Correct Answer: B

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Question 10 View Details

Find the value of \(\frac{d}{dx} x^3 - 3x^2 + 2x - 1 \\) ).

Correct A. \(3x^2 - 6x + 2\)

B. \(3x^2 - 6x + 1\)

C. \(3x^2 - 6x - 1\)

D. \(3x^2 + 6x - 1\)

Correct Answer: A

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Question 11 View Details

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

Correct A. text{Equation: } \(x + 2\)^2 + \\(text{Equation:} (x + 2\(y - 3\)^\(2 = 16\)

B. text{Equation: } \(x - 2\)^2 + \\(text{Equation:} (x - 2\(y + 3\)^\(2 = 16\)

C. text{Equation: } \(x + 2\)^2 + \\(text{Equation:} (x + 2\(y + 3\)^\(2 = 16\)

D. text{Equation: } \(x - 2\)^2 + \\(text{Equation:} (x - 2\(y - 3\)^\(2 = 16\)

Correct Answer: A

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Question 12 View Details

Solve the inequality \(\frac{x}{2}\)\) - \(3 > 2\).

Correct A. \(x > 10\)

B. \(x < 10\)

C. \(x > 4\)

D. \(x < 4\)

Correct Answer: A

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Question 13 View Details

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

Correct A. 768\pi \text{ cm}^3

B. 512\pi \text{ cm}^3

C. 384\pi \text{ cm}^3

D. 256\pi \text{ cm}^3

Correct Answer: A

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Question 14 View Details

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

Correct A. \(y =\)\(\frac{2}{3}\)\) x + \(\frac{1}{3}\)\)

B. \(y =\)\(\frac{3}{2}\)\) x - 1

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

D. \(y =\)\(\frac{2}{3}\)\) x - 2

Correct Answer: A

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Question 15 View Details

Find the mean of the numbers 2, 4, 6, 8, 10.

Correct A. 6

B. 8

C. 10

D. 12

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.

A. 24\pi

B. 32\pi

Correct C. 48\pi

D. 64\pi

Correct Answer: C

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Question 17 View Details

Solve for 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 18 View Details

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

A. 50\pi

Correct B. 100\pi

C. 200\pi

D. 300\pi

Correct Answer: B

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Question 19 View Details

A right-angled triangle has a hypotenuse of length 10 cm and one leg of length 6 cm. Find the length of the other leg.

A. 4

B. 6

Correct C. 8

D. 12

Correct Answer: C

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Question 20 View Details

A rectangular prism has a length of 8 cm, a width of 5 cm, and a height of 3 cm. Find the volume of the prism.

A. 120

B. 150

Correct C. 180

D. 200

Correct Answer: C

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Question 21 View Details

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

Correct A. 16

B. 32

C. 64

D. 128

Correct Answer: A

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Question 22 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 23 View Details

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

Correct A. \left\(x - 2 \right\)^2 + \left\(y - 3 \right\)^\(2 = 16\)

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

C. \left\(x - 4 \right\)^2 + \left\(y - 3 \right\)^\(2 = 16\)

D. \left\(x - 2 \right\)^2 + \left\(y - 4 \right\)^\(2 = 16\)

Correct Answer: A

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Question 24 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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Question 25 View Details

Find the area of the triangle with vertices ( (0, 0) ), ( (3, 0) ), and ( (0, 4) ).

A. 6

Correct B. 12

C. 18

D. 24

Correct Answer: B

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