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POST UTME CRAWFORD UNIVERSITY 2017 Mathematics | Objective

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Question 1 View Details

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

A. 2x\(x^2 + 1\) - \(2x^2\)

Correct B. 2x\(x^2 + 1\) + \(2x^2\)

C. 2x\(x^2 + 1\) - \(x^2\)

D. 2x\(x^2 + 1\) + \(x^2\)

Correct Answer: B

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Question 2 View Details

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

Correct A. \(-∞, -1\) ∪ (3, ∞)

B. \(-∞, -3\) ∪ (1, ∞)

C. \(-∞, 1\) ∪ (3, ∞)

D. \(-∞, -3\) ∪ (1, ∞)

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(0, 4) ).

Correct A. 6

B. 12

C. 18

D. 24

Correct Answer: A

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Question 4 View Details

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

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

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

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

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

Correct Answer: A

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Question 5 View Details

Find the derivative of the function ( f(x) = \\(\sin^2(x)\) ) using the chain rule.

Correct A. 2\sin\(x)\cos(x\)

B. -2\sin\(x)\cos(x\)

C. 2\\(\sin^2\)\(x)\cos(x\)

D. -2\\(\sin^2\)\(x)\cos(x\)

Correct Answer: A

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Question 6 View Details

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

Correct A. \(\frac{1}{2}\)

B. ( 3 )

C. ( 4 )

D. ( 5 )

Correct Answer: A

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Question 7 View Details

If ( f(x) = \(\frac{x^2 - 4}{x - 2}\)\)\) ), find ( f'(x) ) using the chain rule.

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

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

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

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

Correct Answer: A

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Question 8 View Details

A histogram of exam scores has a mean of 60 and a standard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is greater than 70?

A. 0.5

B. 0.6

Correct C. 0.7

D. 0.8

Correct Answer: C

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Question 9 View Details

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

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

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

Correct C. \(x - 2 \\)^2 + \(y - 3\)^\(2 = 36\) )

D. \(x - 2 \\)^2 + \(y - 3\)^\(2 = 49\) )

Correct Answer: C

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Question 10 View Details

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

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 11 View Details

Find the value of k such that the equation \(x^2 + kx + 16 = 0\) has equal roots.

A. 4

Correct B. -4

C. 8

D. -8

Correct Answer: B

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Question 12 View Details

Solve the trigonometric equation \(\sin^2 x + \cos^2 x = 1\) for x in the interval \([0, 2\\\() for x in the interval ([0, 2\pi]\).

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

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

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

D. \pi

Correct Answer: A

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Question 13 View Details

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

A. 4

Correct B. 6

C. 8

D. 10

Correct Answer: B

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Question 14 View Details

A set of exam scores has a mean of 75 and a standard deviation of 10. What is the z-score of a score of 85?

A. 0.5

Correct B. 1

C. 1.5

D. 2

Correct Answer: B

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Question 15 View Details

Solve the equation \(2^x = 32\) for x.

A. 5

Correct B. 6

C. 7

D. 8

Correct Answer: B

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Question 16 View Details

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

Correct A. \(x > 4\)

B. \(x > 6\)

C. \(x > 8\)

D. \(x > 10\)

Correct Answer: A

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Question 17 View Details

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

A. 27

Correct B. 30

C. 33

D. 36

Correct Answer: B

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Question 18 View Details

Solve the system of equations \(egin{cases} x + y = 4 \ 2x - 3y = 5 \end{cases}\).

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

B. \(x = 3\), \(y = 1\)

C. \(x = 4\), \(y = 0\)

D. \(x = 5\),\(y = -1\)

Correct Answer: A

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Question 19 View Details

Find the mean and standard deviation of the data set ( { 2, 4, 6, 8, 10 } ).

Correct A. \(mean = 6\), std \(dev = 2\)

B. \(mean = 4\), std \(dev = 2\)

C. \(mean = 2\), std \(dev = 4\)

D. \(mean = 8\), std \(dev = 6\)

Correct Answer: A

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Question 20 View Details

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

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 21 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 22 View Details

A circle has a diameter of 10 cm. Find the area of the circle.

A. 50

B. 75

Correct C. 100

D. 125

Correct Answer: C

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Question 23 View Details

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

A. 5

Correct B. 6

C. 7

D. 8

Correct Answer: B

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Question 24 View Details

Find the derivative of the function \(y = 3x^2 + 2x - 5\).

Correct A. 6x + 2

B. 3x + 1

C. 2x - 3

D. x - 2

Correct Answer: A

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Question 25 View Details

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

A. 2

B. 3

Correct C. 4

D. 5

Correct Answer: C

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