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POST UTME CRAWFORD UNIVERSITY 2017 Mathematics | Objective

Are you preparing for POST UTME CRAWFORD UNIVERSITY exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2017 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

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

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

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

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

Find the derivative of the function ( f(x) = \sin^2(x) ) u\sing 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

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

If ( f(x) = \frac{x^2 - 4}{x - 2} ), find ( f'(x) ) u\sing 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

A histogram of exam scores has a mean of 60 and a s\tandard 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

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

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

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

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

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

A set of exam scores has a mean of 75 and a s\tandard 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

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

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

Correct A. x > 4

B. x > 6

C. x > 8

D. x > 10

Correct Answer: A

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Question 17

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

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

Find the mean and s\tandard 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

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

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

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

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

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

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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