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POST UTME AFE BABALOLA UNIVERSITY 2022 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. ( 8 )

B. ( 16 )

C. ( 32 )

D. ( 64 )

Correct Answer: A

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Question 2 View Details

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

A. \(x = -1\)

Correct B. \(x = 3\)

C. \(x = -3\)

D. \(x = 1\)

Correct Answer: B

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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

Find the vector ( mathbf{v} ) such that \(\mathbf{v} \cdot \mathbf{i} = 3\) and \(\mathbf{v} \cdot \mathbf{j} = -2\).

Correct A. \(\mathbf{v} = 3\mathbf{i} - 2\mathbf{j}\)

B. \(\mathbf{v} = 3\mathbf{i} + 2\mathbf{j}\)

C. \(\mathbf{v} = -3\mathbf{i} + 2\mathbf{j}\)

D. \(\mathbf{v} = -3\mathbf{i} - 2\mathbf{j}\)

Correct Answer: A

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Question 5 View Details

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

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

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

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

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

Correct Answer: A

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Question 6 View Details

A cylindrical tank with a radius of 7m and a height of 10m is filled with water. If the density of water is 1000 \(kg/m\^3\\(tank with a radius of 7m and a height of 10m is filled with water. If the density of water is 1000 (kg/m\), calculate the volume of water in the \tank.

Correct A. 1490π \(m^3\)

B. 1400π \(m^3\)

C. 1500π \(m^3\)

D. 1600π \(m^3\)

Correct Answer: A

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Question 7 View Details

A die is rolled twice. If the first roll results in a 4, what is the probability that the second roll will result in an even number?

Correct A. \(1/2\)

B. \(1/3\)

C. \(2/3\)

D. \(1/4\)

Correct Answer: A

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Question 8 View Details

A sequence is defined as: 2, 6, 12, 20, ... . What is the next term in the sequence?

Correct A. 30

B. 28

C. 32

D. 29

Correct Answer: A

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Question 9 View Details

A polynomial function is defined as:\(f(x) = \((x^3 - 6x^2 + 11x - 6\)\)\). What is the value of f\(-1\\((x^3 - 6x^2 + 11x - 6). What is the value of f\)?

Correct A. -24

B. -23

C. -25

D. -26

Correct Answer: A

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Question 10 View Details

A curve is defined as:\((y = 2x\)\^2 + 3x - 4\). What is the derivative of the curve at \\((y = 2x^2 + 3x - 4\(x = 1\)?

Correct A. 7

B. 6

C. 8

D. 9

Correct Answer: A

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Question 11 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 12 View Details

A rectangular prism has a length of 6 cm, a width of 4 cm, and a height of 3 cm. Find its volume.

Correct A. 72

B. 80

C. 90

D. 100

Correct Answer: A

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Question 13 View Details

The mean of a set of numbers is 25. If the sum of the numbers is 100, find the standard deviation.

A. 5

Correct B. 10

C. 15

D. 20

Correct Answer: B

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Question 14 View Details

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

A. 0

Correct B. -2

C. -1

D. 1

Correct Answer: B

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Question 15 View Details

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

A. 314

Correct B. 314.16

C. 314.16

D. 314.16

Correct Answer: B

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Question 16 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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Question 17 View Details

Find the volume of the cylinder with a radius of 4 cm and a height of 6 cm.

Correct A. 150.32

B. 150.32

C. 150.32

D. 150.32

Correct Answer: A

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Question 18 View Details

Find the surface area of the sphere with a radius of 6 cm.

Correct A. 452.39

B. 452.39

C. 452.39

D. 452.39

Correct Answer: A

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Question 19 View Details

Find the area of the circle with a radius of 5 cm.

Question 20 View Details

Solve the quadratic equation \(x^2 + 5x + 6 = 0\) using the quadratic formula.

Correct A. x = -2 or x = -3

B. \(x = 2\) or \(x = 3\)

C. x = -1 or x = -6

D. \(x = 1\) or \(x = 6\)

Correct Answer: A

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Question 21 View Details

A binary operation (\ast\) is defined as \\((ast\(a ast b = a^2 + b^2\). Find the value of \(2 \\(ast b = a^2 + b^2). Find the value of \ast 3\).

A. 13

Correct B. 25

C. 9

D. 4

Correct Answer: B

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Question 22 View Details

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

A. 10

Correct B. 15

C. 20

D. 25

Correct Answer: B

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Question 23 View Details

A sequence is defined as \(a_n = 2n + 1\). Find the sum of the first five terms of the sequence.

A. 15

B. 20

C. 25

Correct D. 30

Correct Answer: D

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Question 24 View Details

A geometric progression has a first term of 2 and a common ratio of 3. Find the sum of the first five terms of the progression.

A. 1210

B. 1230

Correct C. 1250

D. 1270

Correct Answer: C

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Question 25 View Details

A vector ( mathbf{a} ) has a magnitude of 5 and makes an angle of 60° with the positive x-axis. Find the x-component of the vector.

A. 2.5

Correct B. 3.75

C. 4.33

D. 5.00

Correct Answer: B

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