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POST UTME CRAWFORD UNIVERSITY 2019 Mathematics | Objective

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Question 1 View Details

Determine the value of x in the equation $$1x = \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. $\frac{2\pi}{3}$

Correct Answer: D

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Question 2 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. $\frac{3\pi}{4}$

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

Correct Answer: A

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Question 3 View Details

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 View Details

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 View Details

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 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 7 View Details

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

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 View Details

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

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 View Details

Find the mean and standard 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 View Details

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 View Details

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 View Details

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 View Details

A rectangular 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 View Details

A set of exam scores has a mean of 80 and a standard 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 View Details

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 View Details

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 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 19 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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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