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POST UTME MADONNA UNIVERSITY 2018 Mathematics | Objective

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Question 1 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 2 View Details

Evaluate the definite integral \(int_{0}^{2} 2x^3 - 3x^2 + x - 1 \\) dx ).

A. ( 2 )

B. ( 4 )

Correct C. ( 6 )

D. ( 8 )

Correct Answer: C

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Question 3 View Details

A set of exam scores has a mean of 75 and a standard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score will be between 60 and 90?

A. ( 0.9544 )

Correct B. ( 0.9772 )

C. ( 0.9987 )

D. ( 0.9999 )

Correct Answer: B

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Question 4 View Details

Find the derivative of the function ( f(x) = \(\sqrt{2x^2 + 3x - 1}\)\) ) using the chain rule.

Correct A. ( f'\((x) =\)\(\frac{4x + 3}\){\sqrt{\(2x^2 + 3x - 1}}\)\) )

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

C. ( f'\((x) =\)\(\frac{4x + 3}{2x^2 + 3x - 1}\)\)\) )

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

Correct Answer: A

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Question 5 View Details

Solve the system of linear equations using the method of substitution: \(2x + 3y = 7\) and \(x - 2y = -3\).

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 6 View Details

In a quadratic equation of the form \(ax^2 + bx + c = 0\), if the sum of the roots is 6 and the product of the roots is 12, find the equation.

Correct A. \(x^2 - 6x + 12 = 0\)

B. \(x^2 + 6x + 12 = 0\)

C. \(x^2 - 12x + 6 = 0\)

D. \(x^2 + 12x + 6 = 0\)

Correct Answer: A

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Question 7 View Details

A circle has a radius of 4 cm. If a chord is drawn such that the distance from the center of the circle to the chord is 3 cm, find the length of the chord.

A. 5 cm

Correct B. 6 cm

C. 7 cm

D. 8 cm

Correct Answer: B

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Question 8 View Details

A bag contains 5 red marbles, 4 blue marbles, and 3 green marbles. If a marble is drawn at random, what is the probability that it is blue?

A. \(1/3\)

Correct B. \(1/4\)

C. \(1/5\)

D. \(2/5\)

Correct Answer: B

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Question 9 View Details

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

Correct A. 32

B. 64

C. 128

D. 256

Correct Answer: A

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Question 10 View Details

A line passes through the points ( (2, 3) ) and ( (4, 5) ). Find the equation of the line.

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

B. \(y = x - 1\)

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

D. \(y = x + 2\)

Correct Answer: A

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Question 11 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 12 View Details

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

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

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

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

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

Correct Answer: A

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Question 13 View Details

A vector ( mathbf{a} ) has components \(a_1 = 2\) and \(a_2 = 3\). Find the magnitude of the vector.

A. 3.60555

Correct B. 4.1231

C. 5.19615

D. 6.32455

Correct Answer: B

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Question 14 View Details

A histogram has a mean of 25 and a standard deviation of 5. Find the value of the 80th percentile.

A. 30

B. 32

Correct C. 35

D. 40

Correct Answer: C

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Question 15 View Details

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

Correct A. \(-2, 0\)

B. \(-1, 1\)

C. \(-2, 2\)

D. \(-1, -1\)

Correct Answer: A

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Question 16 View Details

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

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

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

C. ( f'\((x) =\)\(\frac{1}\){\(\sqrt{x}\)}\) )

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

Correct Answer: B

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Question 17 View Details

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

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

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

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

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

Correct Answer: A

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Question 18 View Details

Find the sum of the first 5 terms of the geometric series \(2x + 4x^2 + 8x^3 + ..\)..

Correct A. \(2x + 4x^2 + 8x^3 + 16x^4 + 32x^5\)

B. \(2x + 4x^2 + 8x^3 + 16x^4\)

C. \(2x + 4x^2 + 8x^3 + 16x^4 + 32x^5 + 64x^6\)

D. \(2x + 4x^2 + 8x^3 + 16x^4 + 32x^5 + 64x^6\)

Correct Answer: A

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Question 19 View Details

Solve the matrix equation \(egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix}\).

Correct A. \(x = 2, y = 3\)

B. \(x = 3, y = 2\)

C. \(x = 1, y = 4\)

D. \(x = 4, y = 1\)

Correct Answer: A

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Question 20 View Details

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

A. \(x = 10\)

Correct B. \(x = 100\)

C. \(x = 1000\)

D. \(x = 10000\)

Correct Answer: B

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Question 21 View Details

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

A. \(2 < x\)\(< 3\)

Correct B. \(x > 3\)

C. \(x < 2\)

D. \(x = 3\)

Correct Answer: B

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Question 22 View Details

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

A. 36

B. 45

Correct C. 54

D. 63

Correct Answer: C

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Question 23 View Details

Solve the system of equations using matrices: \(2x + 3y = 7\) and \(x - 2y = -3\).

Correct A. \begin{bmatrix} 1 \ 2 \end{bmatrix}

B. \begin{bmatrix} 2 \ -1 \end{bmatrix}

C. \begin{bmatrix} -1 \ 1 \end{bmatrix}

D. \begin{bmatrix} 0 \ 0 \end{bmatrix}

Correct Answer: A

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Question 24 View Details

Find the sum of the first 10 terms of the geometric series \(2x^2 + 3x - 1\) with common ratio \(r = -2\).

A. 0

B. 1

Correct C. -1

D. 2

Correct Answer: C

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Question 25 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. 2

D. 3

Correct Answer: A

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