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POST UTME REDEEMERS UNIVERSITY 2021 Mathematics | Objective

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Question 1 View Details

Solve the inequality \(\frac{x^2 - 4}{x + 2} \geq 0\) for ( x in mathbb{R} ).

Correct A. \(x \leq -2\) or ( x geq 2 )

B. \(x > -2\) and \(x < 2\)

C. \(x < -2\) or \(x > 2\)

D. \(x = -2\) or \(x = 2\)

Correct Answer: A

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Question 2 View Details

Find the equation of the circle with center \(C -2, 3 \\) ) and radius \(r = 4\).

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 3 View Details

A histogram of exam scores is shown below. Find the mean score.

Correct A. \(\frac{1}{2}\)

B. \(\frac{3}{4}\)

C. \(\frac{5}{6}\)

D. \(\frac{7}{8}\)

Correct Answer: A

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Question 4 View Details

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

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

B. \(x = \frac{\pi}{2}\) or \(x = \frac{3\pi}{2}\)

C. \(x = \frac{\pi}{4}\) or \(x = \frac{7\pi}{4}\)

D. \(x = \frac{\pi}{2}\) or \(x = \frac{5\pi}{2}\)

Correct Answer: A

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Question 5 View Details

A curve is defined by the equation (y = \(\frac{1}{\(x^2 + 1}\)\)\). Find the equation of the \\((y = frac{1}{x^2 + 1}\tangent line at the point \(1, \frac{1}{2} \\) ).

Correct A. \(y = x - \frac{1}{2}\)

B. \(y = x + \frac{1}{2}\)

C. \(y = -x + \frac{1}{2}\)

D. \(y = x + \frac{1}{2}\)

Correct Answer: A

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Question 6 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. \(x = \frac{5\pi}{4}\)

Correct Answer: A

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Question 7 View Details

Find the volume of the frustum of a cone with height 10cm, lower base radius 4cm, and upper base radius 2cm.

Correct A. \(\frac{1}{3} \pi 4^2 + 2^2 + 4 \cdot 2 \cdot 4 \\) )

B. \(\frac{1}{3} \pi 4^2 + 2^2 - 4 \cdot 2 \cdot 4 \\) )

C. \(\frac{1}{3} \pi 4^2 + 2^2 + 2 \cdot 4 \cdot 2 \\) )

D. \(\frac{1}{3} \pi 4^2 + 2^2 - 2 \cdot 4 \cdot 2 \\) )

Correct Answer: A

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Question 8 View Details

Solve the inequality \(2x^2 + 5x - 3 > 0\).

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

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

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

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

Correct Answer: A

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Question 9 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 10 View Details

Solve the system of equations \(x + y = 2\) and \(xy = 1\).

Correct A. \(x = 1, y = 1\)

B. \(x = 1, y = -1\)

C. \(x = -1, y = 1\)

D. \(x = -1, y = -1\)

Correct Answer: A

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Question 11 View Details

Determine the value of x in the equation \(\frac{x}{2} + 5 = 11\).

Correct A. 6

B. 8

C. 10

D. 12

Correct Answer: A

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Question 12 View Details

Solve for y in the equation \(y^2 + 4y - 5 = 0\).

A. -5

Correct B. -1

C. 1

D. 5

Correct Answer: B

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Question 13 View Details

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

Correct A. 6x + 2

B. 6x - 2

C. 3x + 2

D. 3x - 2

Correct Answer: A

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Question 14 View Details

A circle has a radius of 4 cm. Find the area of the circle.

Correct A. 16\pi

B. 32\pi

C. 64\pi

D. 128\pi

Correct Answer: A

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Question 15 View Details

A right-angled triangle has a hypotenuse of 10 cm and one leg of 6 cm. Find the length of the other leg.

A. 4

B. 6

Correct C. 8

D. 12

Correct Answer: C

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Question 16 View Details

Find the determinant of the matrix [ egin{pmatrix} 2 & 3 \ 4 & 5 \end{pmatrix} ].

A. 1

Correct B. -1

C. 2

D. 3

Correct Answer: B

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Question 17 View Details

A circle has a diameter of 10 cm. Find the area of the circle.

A. 50\pi

Correct B. 100\pi

C. 200\pi

D. 250\pi

Correct Answer: B

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Question 18 View Details

Solve the equation [ \(2x + 5 = 11\) ].

Correct A. 3

B. 2

C. 4

D. 5

Correct Answer: A

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Question 19 View Details

Find the probability of drawing two aces from a deck of 52 cards.

A. \(\frac{1}{52}\)\)

B. \(\frac{1}{26}\)\)

C. \(\frac{1}{51}\)\)

Correct D. \(\frac{1}{52}\)\) \cdot \(\frac{1}{51}\)\)

Correct Answer: D

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Question 20 View Details

Solve the inequality [ \(2x - 5 > 3\) ].

Correct A. \(x > 4\)

B. \(x < 4\)

C. \(x > 3\)

D. \(x < 3\)

Correct Answer: A

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Question 21 View Details

Let X and Y be independent events with P(X) = 0.4 and P(Y) = 0.6. Find P(\(X \cap Y\)).

Correct A. 0.24

B. 0.36

C. 0.48

D. 0.60

Correct Answer: A

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Question 22 View Details

Solve for x in the equation \(x^2 - 6x - 8 = 0\).

A. 2

Correct B. -2

C. 4

D. -4

Correct Answer: B

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Question 23 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. \(-\frac{1}{x^2 + 1\) \ ^2}\)\) )

D. \(\frac{1}{x^2 + 1\) \ ^2}\)\) )

Correct Answer: A

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Question 24 View Details

A set A contains 5 elements, and a set B contains 3 elements. Find the number of elements in the union of sets A and B.

A. 8

Correct B. 10

C. 12

D. 15

Correct Answer: B

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Question 25 View Details

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

A. 62

Correct B. 64

C. 66

D. 68

Correct Answer: B

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