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POST UTME EKSU 2018 Mathematics | Objective

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Question 1 View Details

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

Correct A. \(\frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4\)

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

C. \(\frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4^2\)

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

Correct Answer: A

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Question 2 View Details

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

Correct A. \(x < -\frac{5}{2}\) or \(x > \frac{3}{2}\)

B. \(x < -\frac{3}{2}\) or \(x > \frac{5}{2}\)

C. \(x < -\frac{5}{2}\) or \(x < \frac{3}{2}\)

D. \(x < -\frac{3}{2}\) or \(x < \frac{5}{2}\)

Correct Answer: A

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Question 3 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 + \(y - 3\)^\(2 = 4\) )

C. \(x - 3 \\)^2 + \(y - 2\)^\(2 = 16\) )

D. \(x - 3 \\)^2 + \(y - 2\)^\(2 = 4\) )

Correct Answer: A

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Question 4 View Details

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

A. \(x = \frac{\pi}{2}\)

Correct B. \(x = \frac{\pi}{4}\)

C. \(x = \frac{3\pi}{4}\)

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

Correct Answer: B

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Question 5 View Details

Find the equation of the line passing through the points ( (1, 2) ) and ( (3, 4) ).

Correct A. \(y = \frac{4}{2}x + \frac{2}{2}\)

B. \(y = \frac{4}{2}x - \frac{2}{2}\)

C. \(y = \frac{2}{2}x + \frac{4}{2}\)

D. \(y = \frac{2}{2}x - \frac{4}{2}\)

Correct Answer: A

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Question 6 View Details

Find the value of x in the equation \(\log_{10} x^2 \\)\(= 4 ).\)

Correct A. 10

B. 100

C. 1000

D. 10000

Correct Answer: A

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Question 7 View Details

A set A contains 3 elements. If we select 2 elements at random from set A, what is the probability that the selected elements are not distinct?

A. \(1/3\)

Correct B. \(1/2\)

C. \(2/3\)

D. \(3/4\)

Correct Answer: B

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Question 8 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. \(\frac{-x}{x^2 + 1\) ^2}\)\)

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

Correct Answer: A

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Question 9 View Details

A circle with center (0, 0) and radius 5 passes through the point (3, 4). Find the equation of the circle.

Correct A. \(x - 0\)^2 + \(y - 0\)^\(2 = 25\)

B. \(x - 3\)^2 + \(y - 4\)^\(2 = 25\)

C. \(x - 0\)^2 + \(y - 0\)^\(2 = 16\)

D. \(x - 3\)^2 + \(y - 4\)^\(2 = 16\)

Correct Answer: A

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Question 10 View Details

A sequence is defined by the formula \(a_n = 2n + 1\). Find the sum of the first 5 terms of the sequence.

A. 15

B. 20

C. 25

Correct D. 30

Correct Answer: D

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Question 11 View Details

Find the equation of the circle with center at ((2,3)) and radius (5).

Correct A. \(x-2 \\)^2 + \(y-3\)^\(2 = 25\) )

B. \(x-3 \\)^2 + \(y-2\)^\(2 = 25\) )

C. \(x+2 \\)^2 + \(y-3\)^\(2 = 25\) )

D. \(x-2 \\)^2 + \(y+3\)^\(2 = 25\) )

Correct Answer: A

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Question 12 View Details

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

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

B. \(x = \frac{3\pi}{4}\)

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

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

Correct Answer: A

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Question 13 View Details

Find the area under the curve \(y = x^2\) from \(x = 0\) to \(x = 4\).

Correct A. (16)

B. (32)

C. (64)

D. (128)

Correct Answer: A

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Question 14 View Details

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

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

B. (f'\((x) = 6x + 2x - 5)\)

C. (f'\((x) =\)\(6x^2 + 2x - 5)\)

D. (f'\((x) = 6x +\)\(2x^2 - 5)\)

Correct Answer: A

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Question 15 View Details

Solve the system of equations \(egin{cases}x + y = 2\x - y = 1\end{cases}\).

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

B. \(x = 1, y = 2\)

C. \(x = 2, y = 1\)

D. \(x = 2, y = 2\)

Correct Answer: A

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Question 16 View Details

Find 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 17 View Details

A circle with center (0, 0) and radius 5 passes through which of the following points?

Correct A. (3, 4)

B. (4, 3)

C. \(-3, 4\)

D. \(-4, 3\)

Correct Answer: A

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Question 18 View Details

A sequence is defined by the recurrence relation \(a_n = 2a_{n-1} + 1\) with initial term \(a_1 = 3\). Find the value of \(a_5\).

Correct A. 31

B. 32

C. 33

D. 34

Correct Answer: A

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Question 19 View Details

A set of 5 points is chosen at random from a circle of radius 10. What is the probability that the 5 points form a convex pentagon?

A. \(1/10\)

Correct B. \(1/5\)

C. \(1/2\)

D. \(3/4\)

Correct Answer: B

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Question 20 View Details

A vector ( mathbf{a} ) has magnitude 5 and direction \(30^circ\) counterclockwise from the positive x-axis. Find the x and y components of ( mathbf{a} ).

Correct A. 4.33, 2.5

B. 2.5, 4.33

C. 3, 4

D. 4, 3

Correct Answer: A

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Question 21 View Details

Find 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 22 View Details

A curve is defined by the equation (y = \(\frac{1}{\(x^2 + 1}\)\)\). Find the area under the curve between \\((y = frac{1}{x^2 + 1}\(x = 0\) and \(x = 1\).

Correct A. 0.5

B. 0.75

C. 1

D. 1.5

Correct Answer: A

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Question 23 View Details

A rectangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find the volume of the prism.

Correct A. 30

B. 50

C. 60

D. 70

Correct Answer: A

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Question 24 View Details

Solve the inequality \(x^2 - 4x - 5 > 0\).

Correct A. \(-\infty, -1\) \cup \(5, \infty\)

B. \(-\infty, 1\) \cup \(5, \infty\)

C. \(-\infty, -1\) \cup \(1, \infty\)

D. \(-\infty, 5\) \cup \(1, \infty\)

Correct Answer: A

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Question 25 View Details

Find the vector ( mathbf{a} ) that satisfies the equation \(\mathbf{a} \cdot \mathbf{b} = 10\) and \(\mathbf{a} \cdot \mathbf{c} = 20\), where \(\mathbf{b} = 2, 3, 4 \\) ) and \(\mathbf{c} = 1, 2, 3 \\) ).

Correct A. (5, 10, 15)

B. (10, 20, 30)

C. (15, 30, 45)

D. (20, 40, 60)

Correct Answer: A

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