POST UTME REDEEMERS UNIVERSITY 2018 Mathematics | Objective

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Question 1 View Details
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 View Details
Solve for x in the equation \(2^x + 2^x = 128\).
A. 4
Correct B. 5
C. 6
D. 7

Correct Answer: B

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Question 3 View Details
Find the determinant of the matrix \(egin{bmatrix} 2 & 1 \ 4 & 3 \end{bmatrix}\).
A. 1
B. 2
C. 3
Correct D. 4

Correct Answer: D

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Question 4 View Details
A random experiment has two possible outcomes: A and B. The probability of outcome A is 0.4, and the probability of outcome B is 0.6. If the experiment is repeated 100 times, how many times can we expect outcome A to occur?
Correct A. 40
B. 50
C. 60
D. 70

Correct Answer: A

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Question 5 View Details
A set of numbers has a mean of 20 and a standard deviation of 5. If the set contains 10 numbers, what is the sum of the numbers?
A. 200
B. 250
C. 300
Correct D. 350

Correct Answer: D

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Question 6 View Details
Find the derivative of the function ( f(x) = \(\frac{1}{2}\)\) \log_{10} \(x^2 + 1\) ) using the chain rule.
A. x \log_{10} \(x^2 + 1\)
B. \(\frac{x}{x^2 + 1}\)\)\)
Correct C. \(\frac{1}{2}\)\) \(\frac{2x}{x^2 + 1}\)\)\)
D. \(\frac{x}{2 x^2 + 1\) }\)\)

Correct Answer: C

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Question 7 View Details
A fair six-sided die is rolled. What is the probability that the number obtained is greater than 4, given that the number obtained is an even number?
A. \(\frac{1}{3}\)\)
Correct B. \(\frac{2}{3}\)\)
C. \(\frac{1}{2}\)\)
D. \(\frac{2}{5}\)\)

Correct Answer: B

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Question 8 View Details
Solve the inequality \(2x^2 + 5x - 3 > 0\) using the quadratic formula.
A. \left\(- \frac{5}{4}, \frac{3}{2} \right\)
B. \left\(- \infty, - \frac{3}{2} \right\) \cup \left\(\frac{3}{2}, \infty \right\)
C. \left\(- \frac{3}{2}, \frac{3}{2} \right\)
Correct D. \left\(- \infty, \frac{3}{2} \right\) \cup \left\(\frac{3}{2}, \infty \right\)

Correct Answer: D

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Question 9 View Details
Find the area under the curve \(y = x^2 - 2x + 1\) from \(x = 0\) to \(x = 2\) using integration.
A. \(\frac{1}{3}\)\)
B. \(\frac{2}{3}\)\)
Correct C. \(\frac{4}{3}\)\)
D. \(\frac{5}{3}\)\)

Correct Answer: C

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Question 10 View Details
A circle with center ( C(2, 3) ) and radius \(r = 4\) is drawn on a coordinate plane. What is the equation of the circle?
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 11 View Details
Determine the value of x in the equation \(\frac{1}{2}x^2 + 5x - 3 = 0\).
A. -2
Correct B. 2
C. 4
D. 6

Correct Answer: B

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Question 12 View Details
Solve for y in the equation \(y = \frac{1}{2} \log_{10} x^2 \\) + 3 ).
Correct A. \(\frac{1}{2}\)\) \log_{10} \(x^2\) + 3
B. \(\frac{1}{2}\)\) \log_{10} \(x^2\) - 3
C. \(\frac{1}{2}\)\) \log_{10} \(x^2\) + 5
D. \(\frac{1}{2}\)\) \log_{10} \(x^2\) - 5

Correct Answer: A

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Question 13 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 14 View Details
Solve the inequality \(2x - 5 > 3\).
Correct A. \(x > 4\)
B. \(x < 4\)
C. \(x > 2\)
D. \(x < 2\)

Correct Answer: A

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Question 15 View Details
Find the value of x in the equation \(x^2 + 4x + 4 = 0\).
A. -2
Correct B. 2
C. 4
D. 6

Correct Answer: B

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Question 16 View Details
Find the area under the curve \(y = \frac{1}{2}x^2 + 3x - 2\) from \(x = 0\) to \(x = 4\).
A. 40
B. 50
Correct C. 60
D. 70

Correct Answer: C

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Question 17 View Details
Solve the inequality \(2x^2 + 5x - 3 > 0\).
Correct A. x < -1 or \(x > 3/2\)\)
B. x < -1 or \(x < 3/2\)\)
C. x > -1 or \(x > 3/2\)\)
D. x > -1 or \(x < 3/2\)\)

Correct Answer: A

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Question 18 View Details
Find the determinant of the matrix \(\begin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 3 & 1 & 2 \end{bmatrix}\).
A. 0
B. 4
Correct C. -4
D. 8

Correct Answer: C

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Question 19 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 20 View Details
Find the mean of the data set: 2, 4, 6, 8, 10.
A. 6
B. 8
Correct C. 10
D. 12

Correct Answer: C

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Question 21 View Details
Let \(X\) and \(Y\) be independent random variables with probability density functions (f_\(X(x) = 2x\)\) for \(0 < x < 1\\((f_X(x) = 2x) for\) and (f_\(Y(y) = \(3y^2\)\)\) for \(0 < y < 1\\((f_Y(y) = 3y^2) for\). Find \(P X > Y\)\).
Correct A. \(\frac{1}{4}\)\)
B. \(\frac{1}{2}\)\)
C. \(\frac{3}{4}\)\)
D. \(\frac{5}{8}\)\)

Correct Answer: A

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Question 22 View Details
Find the sum of the infinite geometric series \(\sum_{n = 1}^\infty \frac{2}{3^n}\).
A. \(\frac{2}{3}\)\)
Correct B. \(\frac{4}{9}\)\)
C. \(\frac{6}{9}\)\)
D. \(\frac{8}{9}\)\)

Correct Answer: B

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Question 23 View Details
In the diagram below, (ABCD\) is a rectangle, \(E\\((ABCD) is a rectangle,\) is the midpoint of \(AB\), and \(F\) is the midpoint of (CD\). If \(AB = 6\\((CD). If\) and \(CD = 8\), find the area of the shaded region.
A. 12
Correct B. 16
C. 20
D. 24

Correct Answer: B

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Question 24 View Details
Solve the inequality \(|x - 2| > 3\).
Correct A. \(x < -1\) or \(x > 5\)
B. \(x < -1\) or \(x > 2\)
C. \(x < 2\) or \(x > 5\)
D. \(x < 1\) or \(x > 5\)

Correct Answer: A

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Question 25 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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