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POST UTME CRAWFORD UNIVERSITY 2025 Mathematics | Objective

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Question 1 View Details

Find the volume of the solid formed by revolving the region bounded by the curves $y = x\^2$, $y = 0$, and $x = 2$ about the x-axis.

Correct A. $\frac{32\pi}{5}$\)

B. $\frac{64\pi}{5}$\)

C. $\frac{128\pi}{5}$\)

D. $\frac{256\pi}{5}$\)

Correct Answer: A

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Question 2 View Details

Solve the inequality $\frac{x^2 - 4}{x^2 + 4}$\)\$) > 0.$

Correct A. $-\infty, -2$ \cup $-2, 2$ \cup $2, \infty$

B. $-\infty, -2$ \cup $2, \infty$

C. $-2, 2$

D. $-\infty, 2$ \cup $2, \infty$

Correct Answer: A

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Question 3 View Details

Find the derivative of the function f(x) = $\frac{x^2 + 2x - 3}{x^2 - 4}$\)\) using the quotient rule.

Correct A. $\frac{2x + 2 x^2 - 4 - x^2 + 2x - 3$ (2x)}{ $x^2 - 4$ ^2}\)\)

B. $\frac{2x + 2 x^2 - 4 - x^2 + 2x - 3$ (2x)}{ $x^2 - 4$ ^2}\)\)

C. $\frac{2x + 2 x^2 - 4 - x^2 + 2x - 3$ (2x)}{ $x^2 - 4$ ^2}\)\)

D. $\frac{2x + 2 x^2 - 4 - x^2 + 2x - 3$ (2x)}{ $x^2 - 4$ ^2}\)\)

Correct Answer: A

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Question 4 View Details

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

Correct A. $x = -2$

B. $x = -1$

C. $x = 1$

D. $x = 2$

Correct Answer: A

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Question 5 View Details

Find the sum of the first 5 terms of the geometric series with first term 2 and common ratio 3.

Correct A. 2 + 6 + 18 + 54 + 162

B. 2 + 6 + 18 + 54 + 162

C. 2 + 6 + 18 + 54 + 162

D. 2 + 6 + 18 + 54 + 162

Correct Answer: A

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Question 6 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. 48\pi

B. 64\pi

Correct C. 80\pi

D. 96\pi

Correct Answer: C

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Question 7 View Details

Solve for x in the equation $\log_{10} x^2$$= 4$\).

A. $10^4$

Correct B. $10^8$

C. $10^12$

D. $10^16$

Correct Answer: B

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Question 8 View Details

A circle passes through the points (2, 3) and (4, 5). Find the equation of the circle.

Correct A. $x - 3$^2 + $y - 4$^$2 = 5\^2$

B. $x - 2$^2 + $y - 3$^$2 = 4\^2$

C. $x - 4$^2 + $y - 5$^$2 = 3\^2$

D. $x - 5$^2 + $y - 3$^$2 = 4\^2$

Correct Answer: A

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Question 9 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 10 View Details

Solve the system of equations $x + y = 4$ and $x - y = 2$.

Correct A. $x = 3$, $y = 1$

B. $x = 1$, $y = 3$

C. $x = 2$, $y = 2$

D. $x = 4$, $y = 0$

Correct Answer: A

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Question 11 View Details

Determine the value of x in the equation $\sin^2 x + \cos^2 x = 1$ if $$1x = \frac{3}{5}$.

A. $\frac{\sqrt{16}}{5}$

B. $\frac{\sqrt{9}}{5}$

C. $\frac{\sqrt{25}}{5}$

Correct D. $\frac{\sqrt{36}}{5}$

Correct Answer: D

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Question 12 View Details

Find the area under the curve $y = \frac{1}{x^2 + 1}$ from $x = 0$ to $x = 1$.

Correct A. $\frac{\pi}{4}$

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

C. $\frac{\pi}{6}$

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

Correct Answer: A

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Question 13 View Details

Solve the inequality $\frac{x^2 - 4x + 3}{x^2 - 2x - 3} > 0$.

Correct A. $x < -1$ or $x > 3$

B. $x < 1$ or $x > 3$

C. $x < -1$ or $x < 3$

D. $x > 1$ or $x < 3$

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. $y = 2x - 1$

B. $y = 2x + 1$

C. $y = x - 1$

D. $y = x + 1$

Correct Answer: A

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Question 15 View Details

Solve the equation $x^3 - 6x^2 + 11x - 6 = 0$.

Correct A. $x = 1$ or $x = 2$ or $x = 3$

B. $x = 1$ or $x = 2$ or $x = 4$

C. $x = 1$ or $x = 3$ or $x = 4$

D. $x = 2$ or $x = 3$ or $x = 4$

Correct Answer: A

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Question 16 View Details

Find the area under the curve $y = \frac{1}{x^2}$ from $x = 1$ to $x = 2$.

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

B. $\frac{1}{3}$

C. $\frac{1}{4}$

D. $\frac{1}{5}$

Correct Answer: A

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Question 17 View Details

Solve the inequality $|x - 2| \geq 3$.

Correct A. $x \leq -1$ or ( x geq 5 )

B. ( x leq 1 ) or ( x geq 5 )

C. $x \leq -1$ or ( x geq 4 )

D. ( x leq 0 ) or ( x geq 4 )

Correct Answer: A

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Question 18 View Details

Find the derivative of the function (f(x) = $\frac{1}{x^2 + 1}$\)\)).

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

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

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

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

Correct Answer: A

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Question 19 View Details

Solve the equation $2 \sin^2 x + 3 $1x - 2 = 0$.

Correct A. $\(1x = -1$ or 1x = $\frac{2}{3}$\)

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

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

D. $\(1x = \frac{1}{2}$ or 1x = -$\frac{2}{3}$\)

Correct Answer: A

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Question 20 View Details

Find the area of the triangle with vertices (A(1, 2)), (B(3, 4)), and (C(2, 1)).

Correct A. ( 5 )

B. ( 10 )

C. ( 15 )

D. ( 20 )

Correct Answer: A

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Question 21 View Details

Find the derivative of the function ( f(x) = $\frac{1}${\sqrt{$x^2 + 1}}$\) ) using the chain rule.

Correct A. $\frac{-x}${ $x^2 + 1$ \)^{$3/2$}}\)

B. $\frac{x}${ $x^2 + 1$ \)^{$3/2$}}\)

C. $\frac{1}${ $x^2 + 1$ \)^{$3/2$}}\)

D. $\frac{-1}${ $x^2 + 1$ \)^{$3/2$}}\)

Correct Answer: A

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Question 22 View Details

Solve for x in the equation $2^x + 2^x = 2^{x+1}$.

Correct A. $x = 1$

B. $x = 2$

C. $x = 3$

D. $x = 4$

Correct Answer: A

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Question 23 View Details

A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?

A. $\frac{1}{6}$\)

B. $\frac{2}{6}$\)

C. $\frac{3}{6}$\)

Correct D. $\frac{4}{6}$\)

Correct Answer: D

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Question 24 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 25 View Details

Solve for x in the equation $2^x = 16$.

Correct A. $x = 2$

B. $x = 3$

C. $x = 4$

D. $x = 5$

Correct Answer: A

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