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POST UTME CRAWFORD UNIVERSITY 2020 Mathematics | Objective

Are you preparing for POST UTME CRAWFORD UNIVERSITY exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2020 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

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

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

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

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. 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

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

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

A histogram of exam scores has a mean of 75 and a s\tandard 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

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

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

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

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

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

Find the value of \( \sin \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

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

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

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

Find the value of \( \sin \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

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

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. \( x = \frac{3pi}{4} \)

D. \( x = \frac{5pi}{4} \)

Correct Answer: A

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Question 20

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

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

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

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

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

Find the derivative of the function f(x) = \frac{1}{x^2} u\sing 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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