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POST UTME UNIPORT 2019 Mathematics | Objective

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Question 1 View Details

Find the volume of the solid formed by rotating the region bounded by \(y = x^2\) and \(y = 4x\) about the x-axis.

Correct A. \(\frac{256}{15}\)\)\pi

B. \(\frac{64}{3}\)\)\pi

C. \(\frac{32}{3}\)\)\pi

D. \(\frac{16}{3}\)\)\pi

Correct Answer: A

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Question 2 View Details

Solve the inequality \(\frac{2x-1}{x+2} > 0\).

Correct A. \(-\infty,-2)\cup \frac{1}{2},\infty \\)

B. \(-\infty,-2)\cup \frac{1}{2},\infty \\)

C. \(-\infty,-2)\cup \frac{1}{2},\infty \\)

D. \(-\infty,-2)\cup \frac{1}{2},\infty \\)

Correct Answer: A

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Question 3 View Details

Find the area of the triangle with vertices \(A(0,0), B(3,0), C(1,2)\).

A. 4

Correct B. 6

C. 8

D. 10

Correct Answer: B

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Question 4 View Details

Find the derivative of the function \(f(x) = \frac{1}{x^2+1}\).

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 5 View Details

Find the determinant of the matrix \(\begin{bmatrix}1&2&3\4&5&6\7&8&9\end{bmatrix}\).

Correct A. 0

B. 1

C. -1

D. 2

Correct Answer: A

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Question 6 View Details

Find the derivative of the function ( f(x) = \(\frac{1}\){\sqrt{\(x^2 + 1}}\)\) ) using the chain rule.

Correct A. f'\((x) =\)\(\frac{-x}\){ \(x^2 + 1\) \)^{\(3/2\)}}\)

B. f'\((x) =\)\(\frac{x}\){ \(x^2 + 1\) \)^{\(3/2\)}}\)

C. f'\((x) =\)\(\frac{1}\){ \(x^2 + 1\) \)^{\(3/2\)}}\)

D. f'\((x) =\)\(\frac{-1}\){ \(x^2 + 1\) \)^{\(3/2\)}}\)

Correct Answer: A

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Question 7 View Details

Solve the inequality \(2x^2 - 5x - 3 > 0\) using the quadratic formula.

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

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

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

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

Correct Answer: A

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Question 8 View Details

Find the sum of the first 5 terms of the geometric series \(2 + 6 + 18 + \ldots\).

Correct A. \(2 + 6 + 18 + 54 + 162 = 242\)

B. \(2 + 6 + 18 + 54 + 162 = 242\)

C. \(2 + 6 + 18 + 54 + 162 = 242\)

D. \(2 + 6 + 18 + 54 + 162 = 242\)

Correct Answer: A

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Question 9 View Details

Solve the system of linear equations \(x + y = 3\) and \(2x - 3y = -5\).

Correct A. \(x = 2\), \(y = 1\)

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

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

D. \(x = -1\), \(y = 2\)

Correct Answer: A

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Question 10 View Details

Find the area of the triangle with vertices ( A(1, 2) ), ( B(3, 4) ), and ( C(2, 1) ).

Correct A. 5

B. 10

C. 15

D. 20

Correct Answer: A

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Question 11 View Details

Solve for (x\) in the equation [ \\(tan 2x =\)\\((x) in the equation [ \(\frac{1}\){\(\sqrt{3}\)}\) ] given that \(0^circ \le x \le 90^circ\).

Correct A. \(30^circ\)

B. \(45^circ\)

C. \(60^circ\)

D. \(75^circ\)

Correct Answer: A

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Question 12 View Details

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

A. \(x^2 + y^2 - 4x - 6y + 13 = 0\)

Correct B. \(x^2 + y^2 - 4x - 6y + 25 = 0\)

C. \(x^2 + y^2 - 4x - 6y + 9 = 0\)

D. \(x^2 + y^2 - 4x - 6y + 1 = 0\)

Correct Answer: B

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Question 13 View Details

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

Correct A. x in \(-\infty, -1 \cup 3, \infty\)\)

B. x in \(-\infty, 1 \cup 3, \infty\)\)

C. x in \(-\infty, -3 \cup 1, \infty\)\)

D. x in \(-\infty, 3 \cup 1, \infty\)\)

Correct Answer: A

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Question 14 View Details

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

Correct A. \(10^4\)

B. \(10^2\)

C. \(10^{-2}\)

D. \(10^{-4}\)

Correct Answer: A

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Question 15 View Details

Find the mean of the data set [ 2, 4, 6, 8, 10 ].

A. \(6\)

Correct B. \(8\)

C. \(10\)

D. \(12\)

Correct Answer: B

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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

Solve for y in the equation \(y = \frac{1}{2} 3x + 5 \\) ) when \(x = 2\).

A. 4

Correct B. 6

C. 8

D. 10

Correct Answer: B

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Question 18 View Details

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

Correct A. 50.24

B. 100.48

C. 150.72

D. 201.06

Correct Answer: A

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Question 19 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 20 View Details

A set of numbers has a mean of 10 and a standard deviation of 2. Find the probability that a randomly selected number from the set is greater than 12.

A. 0.5

B. 0.6

C. 0.7

Correct D. 0.8

Correct Answer: D

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Question 21 View Details

Determine the value of \(\int_{0}^{\frac{\pi}{2}} \frac{\sin^2 x}{\cos^2 x + \sin^2 x} dx\).

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

B. \(\frac{\pi}{2}\)\)

C. \(\frac{\pi}{3}\)\)

D. \(\frac{\pi}{6}\)\)

Correct Answer: A

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Question 22 View Details

Solve the equation \(\frac{1}{2} \log_{10} x^2\)\(= 4\)\) for \(x\).

A. 10

Correct B. 100

C. 1000

D. 10000

Correct Answer: B

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Question 23 View Details

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

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

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

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

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

Correct Answer: A

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Question 24 View Details

A particle moves in a straight line with a velocity given by (v(t) = \(2t^2 - 5t + 3\)\). Find the acceleration at time \(t = 2\\((v(t) = 2t^2 - 5t + 3). Find the acceleration at time\) seconds.

Correct A. 4

B. -3

C. 2

D. -2

Correct Answer: A

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Question 25 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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