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POST UTME AFE BABALOLA UNIVERSITY 2021 Mathematics | Objective

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Question 1

Solve the inequality $ x-2 \ $^2 geq 4), where x is a real number.

Correct A. \left$ x-2\right $^2 \geq 4

B. \left$ x-2\right $^2 < 4

C. x \geq 2

D. x < 2

Correct Answer: A

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Question 2

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 3

A set of 5 consecutive integers has a median of 8. What is the sum of the integers?

A. 120

Correct B. 125

C. 130

D. 135

Correct Answer: B

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Question 4

A sequence is defined by the formula an = 2n + 1. Find the sum of the first 10 terms of the sequence.

A. 220

Correct B. 225

C. 230

D. 235

Correct Answer: B

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Question 5

A bag contains 5 red marbles, 4 blue marbles, and 3 green marbles. If a marble is drawn at random, what is the probability that it is blue?

A. \frac{1}{3}

Correct B. \frac{2}{5}

C. \frac{4}{12}

D. \frac{1}{2}

Correct Answer: B

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Question 6

Find the derivative of the function ( f(x) = \frac{1}{2x^2 + 3x - 1} ) u\sing the quotient rule.

Correct A. f'(x) = \frac{-2x + 3}{$ 2x^2 + 3x - 1 $^2}

B. f'(x) = \frac{2x + 3}{$ 2x^2 + 3x - 1 $^2}

C. f'(x) = \frac{2x - 3}{$ 2x^2 + 3x - 1 $^2}

D. f'(x) = \frac{2x + 1}{$ 2x^2 + 3x - 1 $^2}

Correct Answer: A

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Question 7

Solve the inequality $ 2x^2 + 3x - 1 > 0 $ u\sing the quadratic formula.

Correct A. x < -1/2 or x > 1/2

B. x < -1/2 or x < 1/2

C. x > -1/2 or x < 1/2

D. x < -1/2 or x > 1/2

Correct Answer: A

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Question 8

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

Correct A. \frac{28\pi}{3}

B. \frac{32\pi}{3}

C. \frac{40\pi}{3}

D. \frac{48\pi}{3}

Correct Answer: A

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Question 9

Solve the system of equations $ x + y = 2 $ and $ xy = 1 $ u\sing substitution.

Correct A. x = 1, y = 1

B. x = 1, y = -1

C. x = -1, y = 1

D. x = -1, y = -1

Correct Answer: A

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Question 10

Find the derivative of the function ( f(x) = \sin^2 x ) u\sing the chain rule.

Correct A. f'(x) = 2 \sin x \cos x

B. f'(x) = 2 \sin x \cos x + \sin^2 x

C. f'(x) = 2 \sin x \cos x - \sin^2 x

D. f'(x) = 2 \sin x \cos x - 2 \sin^2 x

Correct Answer: A

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Question 11

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

A. 64\pi cm^3

Correct B. 128\pi cm^3

C. 256\pi cm^3

D. 512\pi cm^3

Correct Answer: B

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Question 12

Solve for x in the equation $\begin{vmatrix} 2 & 3 \ 4 & 5 \ \end{vmatrix} = \begin{vmatrix} x & 3 \ 4 & 5 \ \end{vmatrix} $.

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 13

Find the sum of the first 10 terms of the geometric progression 3, 6, 12, ...

A. 1240

B. 1245

Correct C. 1247

D. 1249

Correct Answer: C

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Question 14

Solve the equation $x^2 + 4x + 4 = 0$.

Correct A. -2

B. -1

C. 1

D. 2

Correct Answer: A

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Question 15

Find the value of $\sin 2\theta$ if $\sin \theta = \frac{3}{5}$.

A. \frac{3}{5}

B. \frac{4}{5}

C. \frac{6}{5}

Correct D. \frac{12}{5}

Correct Answer: D

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Question 16

Determine the value of x in the equation $ \frac{1}{2}x^2 + 5x - 3 = 0 $ u\sing the quadratic formula.

A. $ x = -10 $

B. $ x = 6 $

Correct C. $ x = -\frac{3}{2} $

D. $ x = \frac{1}{2} $

Correct Answer: C

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Question 17

Find the area under the curve $ y = \sin x $ from $ x = 0 $ to $ x = \frac{pi}{2} $.

A. $ \frac{1}{2} $

B. $ \frac{pi}{2} $

Correct C. $ \frac{1}{2} pi $

D. $ \frac{2}{pi} $

Correct Answer: C

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Question 18

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 19

Find the determinant of the matrix $ egin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix} $.

Correct A. ( 1 )

B. ( 2 )

C. ( 3 )

D. ( 4 )

Correct Answer: A

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Question 20

Determine the value of x in the equation $ x^2 + 4x - 5 = 0 $ u\sing the quadratic formula.

A. $ x = -5 $

Correct B. $ x = 1 $

C. $ x = -1 $

D. $ x = 5 $

Correct Answer: B

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Question 21

In the number base $8$, what is the value of the expression $[5]_8 + [7]_8$?

A. 12

B. 14

Correct C. 16

D. 18

Correct Answer: C

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Question 22

Solve for $x$: $\frac{1}{x} + \frac{1}{x+1} = \frac{1}{2}$

A. 1

Correct B. -1

C. 2

D. -2

Correct Answer: B

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Question 23

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 24

Let $S_n = 1 + 2 + 3 + \cdots + n$. Find the value of $S_{10}$.

Correct A. 55

B. 65

C. 75

D. 85

Correct Answer: A

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Question 25

Find the value of $\log_{10} $ x^2 $ = 4$.

A. 4

B. 10

C. 100

Correct D. 1000

Correct Answer: D

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