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POST UTME CRAWFORD UNIVERSITY 2020 Mathematics | Objective

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Question 1 View Details

Determine the value of 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 2 View Details

Solve for y in the equation $y = \frac{1}{2} \tan^{-1} \left \frac{2x}{1-x^2} \right \$ ).

A. $\frac{1}{2}$\) \$\tan^{-1}$ (2x)

Correct B. $\frac{1}{2}$\) \$\tan^{-1}$ \left$\frac{2x}{1-x^2} \right$

C. \$\tan^{-1}$ (2x)

D. \$\tan^{-1}$ \left$\frac{2x}{1-x^2} \right$

Correct Answer: B

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Question 3 View Details

Find the area of the triangle with vertices A(1, 2), B(3, 4), and C(5, 6).

A. 10

B. 20

Correct C. 30

D. 40

Correct Answer: C

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Question 4 View Details

A car travels from city A to city B at an average speed of 60 $(km/h$\) and returns at an average speed of 40 $km/h\\((km/h) and returns at an average speed of 40$. What is the average speed for the round trip?

A. 50

B. 60

C. 70

Correct D. 80

Correct Answer: D

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Question 5 View Details

A population of bacteria doubles every 2 hours. If there are initially 100 bacteria, how many bacteria will there be after 6 hours?

A. 1000

B. 2000

C. 4000

Correct D. 8000

Correct Answer: D

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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. 24π cm³

Correct B. 48π cm³

C. 96π cm³

D. 192π cm³

Correct Answer: B

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Question 7 View Details

A histogram of exam scores has a mean of 75 and a standard deviation of 5. If the scores are normally distributed, what is the probability that a randomly selected score is between 70 and 80?

A. 0.135

B. 0.341

Correct C. 0.674

D. 0.954

Correct Answer: C

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Question 8 View Details

Find the determinant of the matrix [ egin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 5 \ 6 & 3 & 7 \end{bmatrix} ].

Correct A. -10

B. 0

C. 10

D. 20

Correct Answer: A

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Question 9 View Details

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

Correct A. -2

B. -1

C. 0

D. 1

Correct Answer: A

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Question 10 View Details

A vector [ mathbf{a} = egin{bmatrix} 2 \ 3 \ 4 \end{bmatrix} ] is rotated by 90° about the x-axis. Find the new vector [ mathbf{a}' ].

Correct A. [ egin{bmatrix} 2 \ -3 \ 4 \end{bmatrix} ]

B. [ egin{bmatrix} 2 \ 3 \ -4 \end{bmatrix} ]

C. [ egin{bmatrix} 2 \ 4 \ 3 \end{bmatrix} ]

D. [ egin{bmatrix} 2 \ -4 \ 3 \end{bmatrix} ]

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 $x = 4$.

Correct A. $\frac{1}{2} \left \frac{4^3}{3} + 3 \cdot 4^2 - 2 \cdot 4 \right \$ - \left$\frac{1}{2} \cdot 0^2 + 3 \cdot 0 - 2 \right$

B. $\frac{1}{2} \left \frac{4^3}{3} + 3 \cdot 4^2 - 2 \cdot 4 \right \$ + \left$\frac{1}{2} \cdot 0^2 + 3 \cdot 0 - 2 \right$

C. $\frac{1}{2} \left \frac{4^3}{3} + 3 \cdot 4^2 - 2 \cdot 4 \right \$

D. $\frac{1}{2} \left \frac{4^3}{3} + 3 \cdot 4^2 - 2 \cdot 4 \right \$ + 2 \)

Correct Answer: A

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Question 12 View Details

Solve for ( x ) in the equation $\begin{vmatrix} 2 & 3 & 1 \ 4 & 1 & 3 \ 2 & 0 & 1 \ \end{vmatrix} = 0$.

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

B. $x = -\frac{1}{2} \$

C. $x = 1 \$

D. $x = -1 \$

Correct Answer: A

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Question 13 View Details

Find the value of $$1\left \frac{3\pi}{4} \right \$ \cos \left$\frac{\pi}{4} \right$ + \cos \left$\frac{3\pi}{4} \right$ \sin \left$\frac{\pi}{4} \right$ ).

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

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

C. $\frac{1}{\sqrt{2}} \$

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

Correct Answer: A

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Question 14 View Details

Solve the inequality $\frac{1}{x+1} + \frac{1}{x-1} \geq \frac{1}{2} \$.

Correct A. $x \leq -1 \$ or $x \geq 1 \$

B. $x > -1 \$ and $x < 1 \$

C. $x < -1 \$ or $x > 1 \$

D. $x \geq -1 \$ and $x \leq 1 \$

Correct Answer: A

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Question 15 View Details

Find the value of $\log_{10} \left \frac{1000}{100} \right \$.

Correct A. $2 \$

B. $1 \$

C. $3 \$

D. $4 \$

Correct Answer: A

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Question 16 View Details

Solve the equation $\sqrt{x+1} + \sqrt{x-1} = 2 \$.

A. $x = 1 \$

Correct B. $x = 3 \$

C. $x = 5 \$

D. $x = 7 \$

Correct Answer: B

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Question 17 View Details

Find the value of $$1\left \frac{\pi}{6} \right \$ \cos \left$\frac{\pi}{3} \right$ - \cos \left$\frac{\pi}{6} \right$ \sin \left$\frac{\pi}{3} \right$ ).

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

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

C. $\frac{\sqrt{3}}{2} \$

D. $\frac{1}{\sqrt{2}} \$

Correct Answer: VIEW ANSWER

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Question 18 View Details

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

A. 64π cm³

Correct B. 128π cm³

C. 256π cm³

D. 512π cm³

Correct Answer: B

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Question 19 View Details

Solve for x in the equation $\sin^2 x + \cos^2 x = 1$.

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

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

C. $x = \frac{3\pi}{4}$

D. $x = \frac{5\pi}{4}$

Correct Answer: A

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Question 20 View Details

A bag contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is not blue?

Correct A. $\frac{2}{3}$

B. $\frac{3}{4}$

C. $\frac{4}{5}$

D. $\frac{5}{6}$

Correct Answer: A

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Question 21 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 22 View Details

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

A. $x = 2$

Correct B. $x = 4$

C. $x = 8$

D. $x = 16$

Correct Answer: B

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Question 23 View Details

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

Correct A. \boxed{ x - 2 ^2 + y - $3 ^2 = 16$}

B. $x - 2$^2 + $y - 3$^$2 = 20$

C. $x - 2$^2 + $y - 3$^$2 = 12$

D. $x - 2$^2 + $y - 3$^$2 = 8$

Correct Answer: A

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Question 24 View Details

Solve for x in the equation $\frac{1}{2}$\) \log_{10} \$(x^2$$= 3.$\)

Correct A. \boxed{$x = 1000$}

B. $x = 100$

C. $x = 10$

D. $x = 1$

Correct Answer: A

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Question 25 View Details

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

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

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

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

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

Correct Answer: A

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