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POST UTME DELSU 2020 Mathematics | Objective

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Question 1 View Details

Solve for x in the equation $\frac{1}{2}x^2 + 5x - 3 = 0$.

A. $x = -10$

B. $x = 3$

Correct C. $x = -3$

D. $x = 10$

Correct Answer: C

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Question 2 View Details

Find the area under the curve $y = x^2 + 2x - 3$ from $x = 0$ to $x = 2$.

Correct A. $\frac{14}{3}$

B. $\frac{16}{3}$

C. $\frac{18}{3}$

D. $\frac{20}{3}$

Correct Answer: A

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Question 3 View Details

In the diagram below, find the value of ( vec{a} cdot vec{b} ).

Correct A. ( 0 )

B. ( 1 )

C. ( 2 )

D. ( 3 )

Correct Answer: A

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Question 4 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 + $y - 3$^$2 = 20$ )

C. $x - 2 \$^2 + $y - 3$^$2 = 24$ )

D. $x - 2 \$^2 + $y - 3$^$2 = 28$ )

Correct Answer: A

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Question 5 View Details

Solve the inequality $x^2 + 4x - 5 > 0$.

Correct A. $x < -5$ or $x > 1$

B. $x < -1$ or $x > 5$

C. $x < 1$ or $x > 5$

D. $x < -5$ or $x < 1$

Correct Answer: A

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Question 6 View Details

Find the derivative of the function ( f(x) = $\frac{1}{2x^2 + 5x + 3}$\)\) ) using the quotient rule.

Correct A. $\frac{-2x + 5}{2x^2 + 5x + 3$ \ ^2}\)\) )

B. $\frac{2x + 5}{2x^2 + 5x + 3$ \ ^2}\)\) )

C. $\frac{2x - 5}{2x^2 + 5x + 3$ \ ^2}\)\) )

D. $\frac{-2x - 5}{2x^2 + 5x + 3$ \ ^2}\)\) )

Correct Answer: A

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Question 7 View Details

A histogram of exam scores has a mean of 75 and a standard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected student scored above 90?

A. 0.1587

B. 0.3413

C. 0.4772

Correct D. 0.6745

Correct Answer: D

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Question 8 View Details

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

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

B. $x = \frac{\pi}{4}, \frac{5\pi}{4}$

C. $x = \frac{\pi}{4}, \frac{7\pi}{4}$

D. $x = \frac{\pi}{4}, \frac{9\pi}{4}$

Correct Answer: A

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Question 9 View Details

A rectangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. What is its volume?

Correct A. 30

B. 40

C. 50

D. 60

Correct Answer: A

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Question 10 View Details

Find the determinant of the matrix $egin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix}$.

Correct A. 1

B. -1

C. 2

D. 3

Correct Answer: A

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Question 11 View Details

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

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

B. $x = \frac{\pi}{4}$

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

D. $x = \frac{\pi}{4} + \frac{\pi}{2}$

Correct Answer: A

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Question 12 View Details

A set A is defined as A = { x in mathbb{R} : \$(x^2 - 4x + 3$$= 0$\) }. Find the number of elements in set A.

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 13 View Details

The mean of a data set is 25 and the standard deviation is 3. Find the sum of the squares of the deviations from the mean.

Correct A. 900

B. 1000

C. 1100

D. 1200

Correct Answer: A

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Question 14 View Details

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

A. $\frac{16}{15}$\) pi

B. $\frac{32}{15}$\) pi

Correct C. $\frac{64}{15}$\) pi

D. $\frac{128}{15}$\) pi

Correct Answer: C

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Question 15 View Details

Evaluate the definite integral $int_{0}^{1} x^2 $1x , dx$.

Correct A. $\frac{1}{2}$\) - $\frac{1}{3}$\)

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

C. $\frac{1}{2}$\) - $\frac{1}{4}$\)

D. $\frac{1}{2}$\) + $\frac{1}{4}$\)

Correct Answer: A

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Question 16 View Details

Determine the mean of the following data set: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

A. 5

Correct B. 6

C. 7

D. 8

Correct Answer: B

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Question 17 View Details

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

A. $$1x \$$= 1 )$

B. $$1x \$$= 1 )$

Correct C. $$1x \$ = \cos(x) )

D. $$1x \$ = -\cos(x) )

Correct Answer: C

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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

A rectangular box has a length of 6 cm, a width of 4 cm, and a height of 3 cm. Find its volume.

Correct A. 72 $cm^3$

B. 48 $cm^3$

C. 36 $cm^3$

D. 24 $cm^3$

Correct Answer: A

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Question 20 View Details

Find the derivative of the function ( f(x) = $3x^2 + 2x - 5$ ).

Correct A. ( f'$(x) = 6x + 2 )$

B. ( f'$(x) = 6x - 2 )$

C. ( f'$(x) = 6x + 4 )$

D. ( f'$(x) = 6x - 4 )$

Correct Answer: A

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Question 21 View Details

Find the sum of the infinite geometric series with first term $1/2$ and common ratio $1/4$.

Correct A. 1

B. $3/4$

C. $5/8$

D. $7/16$

Correct Answer: A

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Question 22 View Details

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

Correct A. $x <$$-3/2$ or $x > 1/2$\)

B. $x <$$-1/2$ or $x > 3/2$\)

C. $x < 1/2$\) or x > $-3/2$

D. $x < 3/2$\) or x > $-1/2$

Correct Answer: A

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Question 23 View Details

Find the area of the region bounded by the parabola (y = x\^2\) and the line \$(y = x^2\(y = 2x$.

Correct A. $4/3$

B. $2/3$

C. $1/3$

D. $4/5$

Correct Answer: A

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Question 24 View Details

Solve the system of equations $x + y = 2$ and $xy = 1$.

Correct A. (1, 1)

B. $1, -1$

C. $-1, 1$

D. $-1, -1$

Correct Answer: A

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Question 25 View Details

Find the equation of the circle with center (1, 2) and radius 3.

Correct A. $x - 1$^2 + $y - 2$^$2 = 9$

B. $x + 1$^2 + $y - 2$^$2 = 9$

C. $x - 1$^2 + $y + 2$^$2 = 9$

D. $x + 1$^2 + $y + 2$^$2 = 9$

Correct Answer: A

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