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POST UTME UNIPORT 2017 Mathematics | Objective

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Question 1 View Details

Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 24π \(cm^3\)

Correct B. 48π \(cm^3\)

C. 96π \(cm^3\)

D. 192π \(cm^3\)

Correct Answer: B

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Question 2 View Details

A box contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is not blue?

A. \(1/2\)

Correct B. \(2/3\)

C. \(3/5\)

D. \(4/7\)

Correct Answer: B

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Question 3 View Details

Solve the quadratic equation \(x^2 + 4x + 4 = 0\).

Correct A. \(x = -2\)

B. \(x = 2\)

C. \(x = -1\)

D. \(x = 1\)

Correct Answer: A

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Question 4 View Details

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

A. 5

Correct B. 6

C. 7

D. 8

Correct Answer: B

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Question 5 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 6 View Details

Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 50\pi \(cm^3\)

B. 75\pi \(cm^3\)

Correct C. 100\pi \(cm^3\)

D. 125\pi \(cm^3\)

Correct Answer: C

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Question 7 View Details

Solve the inequality \(\frac{x^2 - 4x - 5}{x^2 - 4x + 4}\)\)\\() > 0.\)

Correct A. \left\(-\infty, -1\right\) \cup \left\(1, \infty\right\)

B. \left\(-\infty, -1\right\) \cup \left\(1, 2\right\)

C. \left\(-\infty, -1\right\) \cup \left\(2, \infty\right\)

D. \left\(-\infty, 1\right\) \cup \left\(2, \infty\right\)

Correct Answer: A

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Question 8 View Details

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

Correct A. \(x - 1\)^2 + \(y + 2\)^\(2 = 10\)

B. \(x + 1\)^2 + \(y - 2\)^\(2 = 10\)

C. \(x - 2\)^2 + \(y + 1\)^\(2 = 10\)

D. \(x + 2\)^2 + \(y - 1\)^\(2 = 10\)

Correct Answer: A

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Question 9 View Details

Evaluate the definite integral \int_\(0^1\) \(x^2\) \sin x dx.

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

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

C. \(\frac{1}{2}\)\) - \(\frac{1}{3}\)\)

D. \(\frac{1}{2}\)\) + \(\frac{1}{3}\)\)

Correct Answer: A

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Question 10 View Details

Find the derivative of the function f(x) = \(\frac{x^2 + 2x - 3}{x^2 - 4x + 3}\)\)\) using the quotient rule.

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

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

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

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

Correct Answer: A

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Question 11 View Details

Find the equation of the circle with center at \(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 + \(y+3\)^\(2 = 32\) )

D. \(x+2 \\)^2 + \(y-3\)^\(2 = 32\) )

Correct Answer: A

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Question 12 View Details

Solve the system of equations using matrices:

Correct A. \(egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix}\)

B. \(egin{bmatrix} 2 & 1 \ 4 & 3 \end{bmatrix}\)

C. \(egin{bmatrix} 1 & 3 \ 2 & 4 \end{bmatrix}\)

D. \(egin{bmatrix} 3 & 1 \ 2 & 4 \end{bmatrix}\)

Correct Answer: A

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Question 13 View Details

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

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

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

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

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

Correct Answer: A

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Question 14 View Details

Solve the quadratic equation \(x^2 + 4x + 4 = 0\).

Correct A. \(x = -2\)

B. \(x = 2\)

C. \(x = -1\)

D. \(x = 1\)

Correct Answer: A

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Question 15 View Details

Find the area of the triangle with vertices at ((0,0)), ((3,0)), and ((0,4)).

Correct A. ( 6 )

B. ( 8 )

C. ( 10 )

D. ( 12 )

Correct Answer: A

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Question 16 View Details

Determine the volume of the frustum of a cone with a height of 10 cm, a lower base radius of 4 cm, and an upper base radius of 6 cm.

A. 20π cm³

Correct B. 30π cm³

C. 40π cm³

D. 50π cm³

Correct Answer: B

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Question 17 View Details

A random variable X has a probability distribution given by P\(X = 1 = 0.3\), P\(X = 2 = 0.4\), and P\(X = 3 = 0.3\). Find the probability that X is greater than 2.

A. 0.3

B. 0.4

Correct C. 0.5

D. 0.6

Correct Answer: C

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Question 18 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} \\)

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

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

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

Correct Answer: A

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Question 19 View Details

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

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

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

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

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

Correct Answer: A

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Question 20 View Details

A circle with a radius of 5 cm is inscribed in a square. Find the area of the square.

A. 25 cm²

B. 50 cm²

C. 75 cm²

Correct D. 100 cm²

Correct Answer: D

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Question 21 View Details

Find the volume of the frustum of a cone with height 8cm, lower base radius 4cm, and upper base radius 2cm.

A. 256\pi \(cm^3\)

B. 512\pi \(cm^3\)

Correct C. 768\pi \(cm^3\)

D. 1024\pi \(cm^3\)

Correct Answer: C

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Question 22 View Details

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

A. 50

B. 60

Correct C. 70

D. 80

Correct Answer: C

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Question 23 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 24 View Details

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

A. \(x = -4\)

Correct B. \(x = -2\)

C. \(x = 1\)

D. \(x = 4\)

Correct Answer: B

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Question 25 View Details

Find the determinant of the matrix \begin{bmatrix} 2 & 1 \ 4 & 3 \end{bmatrix}.

A. 5

Correct B. 6

C. 7

D. 8

Correct Answer: B

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