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POST UTME CRAWFORD UNIVERSITY 2019 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 2019 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

Determine the value of x in the equation $ \tan x = \frac{1}{\sqrt{3}} $ if ( x ) lies in the second quadrant.

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

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

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

Correct D. $ \frac{2pi}{3} $

Correct Answer: D

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Question 2

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{3pi}{4} $

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

Correct Answer: A

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Question 3

Solve the system of equations $ egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 3 \ 7 \end{bmatrix} $.

Correct A. $ x = 1, y = 2 $

B. $ x = 2, y = 1 $

C. $ x = 3, y = 4 $

D. $ x = 4, y = 3 $

Correct Answer: A

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Question 4

A box contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?

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

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

Correct C. $ \frac{3}{5} $

D. $ \frac{2}{3} $

Correct Answer: C

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Question 5

Find the sum of the first 5 terms of the geometric progression ( 2, 6, 18, ... ).

Correct A. ( 62 )

B. ( 64 )

C. ( 66 )

D. ( 68 )

Correct Answer: A

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Question 6

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 7

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

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

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

C. \frac{-2}{$ x^2 + 1 $^2}

D. \frac{2}{$ x^2 + 1 $^2}

Correct Answer: A

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Question 8

In the coordinate plane, 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 9

Solve the trigonometric equation $\sin^2 x + \cos^2 x = 1$ for $x$ in the interval $[0, 2\pi]$.

Correct A. x = \frac{\pi}{4}, \frac{3\pi}{4}, \frac{5\pi}{4}, \frac{7\pi}{4}

B. x = \frac{\pi}{2}, \frac{3\pi}{2}

C. x = 0, \pi, 2\pi

D. x = \frac{\pi}{6}, \frac{5\pi}{6}

Correct Answer: A

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Question 10

Find the mean and s\tandard deviation of the data set $\{2, 4, 6, 8, 10\}$.

Correct A. \bar{x} = 6, \sigma = 2

B. \bar{x} = 6, \sigma = 4

C. \bar{x} = 6, \sigma = 6

D. \bar{x} = 6, \sigma = 8

Correct Answer: A

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Question 11

Find the area under the curve $ y = \frac{1}{2}x^2 + 3x - 4 $ from $ x = 1 $ to $ x = 3 $.

A. 20

B. 30

Correct C. 40

D. 50

Correct Answer: C

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Question 12

The equation of a circle is $ x^2 + y^2 - 4x + 6y + 9 = 0 $. Find the coordinates of the center of the circle.

Correct A. $ -2, -3 $

B. $ -1, -2 $

C. (2, 3)

D. (1, 2)

Correct Answer: A

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Question 13

Find the determinant of the matrix $ \begin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 3 & 4 & 2 \end{bmatrix} $.

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 14

A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find its volume.

A. 30

B. 40

Correct C. 50

D. 60

Correct Answer: C

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Question 15

A set of exam scores has a mean of 80 and a s\tandard deviation of 10. Find the z-score of a score of 90.

A. 0.5

B. 1

Correct C. 1.5

D. 2

Correct Answer: C

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Question 16

Find the volume of the frustum of a cone with height 6cm, lower base radius 4cm and upper base radius 2cm.

A. 48\pi cm^3

B. 64\pi cm^3

Correct C. 80\pi cm^3

D. 96\pi cm^3

Correct Answer: C

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Question 17

Solve for x: \log_{10} $ x^2 $ = 4.

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 18

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 19

Solve the inequality: 2x^2 + 5x - 3 > 0.

Correct A. x < -1 or x > \frac{3}{2}

B. x > -1 or x < \frac{3}{2}

C. x < -1 or x < \frac{3}{2}

D. x > -1 or x > \frac{3}{2}

Correct Answer: A

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Question 20

Find the area of the triangle with vertices (0, 0), (4, 0), and (0, 3).

Correct A. 6

B. 8

C. 10

D. 12

Correct Answer: A

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Question 21

Find the area under the curve $ y = \frac{1}{2}x^2 + 3x - 2 $ from $ x = 0 $ to $ x = 4 $.

A. 64

B. 72

Correct C. 80

D. 96

Correct Answer: C

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Question 22

Solve for ( x ) in the equation $ 2^x + 3^x = 5^x $.

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 23

A box contains 5 red balls and 3 blue balls. If 2 balls are drawn at random, what is the probability that both balls are blue?

Correct A. 1/7

B. 1/10

C. 1/14

D. 1/21

Correct Answer: A

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Question 24

Find the value of ( x ) in the equation $ x^2 + 4x + 4 = 0 $.

Correct A. -2

B. -1

C. 0

D. 1

Correct Answer: A

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Question 25

A company produces 200 units of a product per day. If the production \cost is $150 per unit, what is the total \cost of producing 500 units?

A. ₦75,000

B. ₦80,000

Correct C. ₦85,000

D. ₦90,000

Correct Answer: C

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