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POST UTME AFE BABALOLA UNIVERSITY 2021 Mathematics | Objective

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Question 1 View Details

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 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 3 View Details

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 View Details

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 View Details

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 View Details

Find the derivative of the function ( f(x) = $\frac{1}{2x^2 + 3x - 1}$\)\) ) using 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 View Details

Solve the inequality $2x^2 + 3x - 1 > 0$ using 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 View Details

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 View Details

Solve the system of equations $x + y = 2$ and $xy = 1$ using 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 View Details

Find the derivative of the function ( f(x) = \$\sin^2$ x ) using 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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

Find the value of ($12\theta$ if \$($12theta$$1\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 View Details

Determine the value of x in the equation $\frac{1}{2}x^2 + 5x - 3 = 0$ using 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 View Details

Find the area under the curve $y = $1x$ 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 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 19 View Details

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 View Details

Determine the value of x in the equation $x^2 + 4x - 5 = 0$ using 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 View Details

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

A. 12

B. 14

Correct C. 16

D. 18

Correct Answer: C

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Question 22 View Details

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 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 24 View Details

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

Correct A. 55

B. 65

C. 75

D. 85

Correct Answer: A

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Question 25 View Details

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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