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Subject

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POST UTME CRAWFORD UNIVERSITY 2018 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 2018 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

Let X and Y be indep\endent events with P(X) = 0.4 and P(Y) = 0.6. Find P(X ∩ Y).

Correct A. 0.2

B. 0.24

C. 0.3

D. 0.36

Correct Answer: A

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Question 2

Solve the quadratic equation \( x^2 + 5x + 6 = 0 \).

Correct A. \( x = -2 \)

B. \( x = -3 \)

C. \( x = 2 \)

D. \( x = 3 \)

Correct Answer: A

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Question 3

A binary operation ( odot ) on the set of real numbers is defined as \( a odot b = ab + 2 \). Find ( 3 odot 4 ).

A. 14

B. 16

Correct C. 18

D. 20

Correct Answer: C

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Question 4

Let ( f(x) = 2x^2 + 3x - 1 ). Find the value of \( f\( -2 \ \) ).

Correct A. -11

B. -9

C. -7

D. -5

Correct Answer: A

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Question 5

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

Correct A. \( x > 4 \)

B. \( x < 4 \)

C. \( x > 3 \)

D. \( x < 3 \)

Correct Answer: A

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Question 6

Find the determinant of the matrix [ egin{pmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{pmatrix} ].

A. 0

B. 1

Correct C. 2

D. 3

Correct Answer: C

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Question 7

Solve the inequality [ 2x^2 + 5x - 3 > 0 ].

Correct A. \( -∞, -1 \) ∪ (3, ∞)

B. \( -∞, -3 \) ∪ (1, ∞)

C. \( -∞, -1 \) ∪ (1, ∞)

D. \( -∞, 1 \) ∪ (3, ∞)

Correct Answer: A

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Question 8

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

A. -\frac{2x}{\( x^2 + 1 \)^2}

Correct B. \frac{2x}{\( x^2 + 1 \)^2}

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

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

Correct Answer: B

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Question 9

Solve the system of equations [ egin{cases} x + y = 2 \ 2x - y = 3 \end{cases} ].

Correct A. \{ (1, 1) \}

B. \{ (2, 0) \}

C. \{ (1, 0) \}

D. \{ (0, 2) \}

Correct Answer: A

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Question 10

Find the area of the triangle with vertices [ A(1, 2), B(3, 4), C(5, 6) ].

Correct A. 10

B. 20

C. 30

D. 40

Correct Answer: A

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Question 11

Let X and Y be indep\endent random variables with probability density functions f_X(x) and f_Y(y), respectively. If E(X) = 2 and E(Y) = 3, find E(XY).

Correct A. 6

B. 12

C. 18

D. 24

Correct Answer: A

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Question 12

Find the determinant of the matrix A = egin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 5 \ 6 & 3 & 7 \end{bmatrix}.

A. -1

Correct B. 1

C. 2

D. 3

Correct Answer: B

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Question 13

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

A. 0.25

B. 0.5

C. 0.75

Correct D. 0.9

Correct Answer: D

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Question 14

Find the derivative of the function f(x) = \( 2x^2 + 3x - 1 \) / \( x^2 + 1 \) u\sing the quotient rule.

A. \( 4x + 3 \) / \( x^2 + 1 \)

Correct B. \( 4x^2 + 3x - 1 \) / \( x^2 + 1 \)^2

C. \( 8x + 6 \) / \( x^2 + 1 \)^2

D. \( 8x^2 + 6x - 2 \) / \( x^2 + 1 \)^3

Correct Answer: B

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Question 15

A vector ℓ = 2ℓ + 3℔, where ℓ = ℓi + ℔j. Find the magnitude of ℓ.

A. 5

B. 10

Correct C. 15

D. 20

Correct Answer: C

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Question 16

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

Correct A. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4 \)

B. \( \frac{1}{2} \times 4^2 + 3 \times 4 - 2 \)

C. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4^2 \)

D. \( \frac{1}{2} \times 4^2 + 3 \times 4^3 - 2 \)

Correct Answer: A

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Question 17

Find the equation of the line pas\sing through the points ( (2, 3) ) and ( (4, 5) ).

Correct A. \( y = \frac{5-3}{4-2}x + \frac{3 \times 4 - 5 \times 2}{4-2} \)

B. \( y = \frac{5-3}{4-2}x + \frac{3 \times 2 - 5 \times 4}{4-2} \)

C. \( y = \frac{5-3}{4-2}x + \frac{3 \times 4 + 5 \times 2}{4-2} \)

D. \( y = \frac{5-3}{4-2}x + \frac{3 \times 2 + 5 \times 4}{4-2} \)

Correct Answer: A

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Question 18

Find the volume of the cylinder with radius ( 4 ) and height ( 6 ).

Correct A. \( pi \times 4^2 \times 6 \)

B. \( pi \times 4^2 \times 6^2 \)

C. \( pi \times 4^2 \times 6^3 \)

D. \( pi \times 4^3 \times 6^2 \)

Correct Answer: A

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Question 19

Find the determinant of the matrix \( egin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix} \).

Correct A. \( 2 \times 5 - 3 \times 4 \)

B. \( 2 \times 4 - 3 \times 5 \)

C. \( 2 \times 3 - 4 \times 5 \)

D. \( 2 \times 4 - 5 \times 3 \)

Correct Answer: A

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Question 20

Find the area of the circle with radius ( 4 ).

Correct A. \( pi \times 4^2 \)

B. \( pi \times 4^3 \)

C. \( pi \times 4^4 \)

D. \( pi \times 4^5 \)

Correct Answer: A

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Question 21

Let X and Y be indep\endent random variables with probability density functions f_X(x) = 2x, 0 < x < 1, and f_Y(y) = 3y^2, 0 < y < 1. Find P\( X > Y \).

Correct A. \frac{1}{2}

B. \frac{1}{3}

C. \frac{2}{3}

D. \frac{3}{4}

Correct Answer: A

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Question 22

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

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 23

Simplify the expression \sqrt[3]{64x^3y^3} u\sing the properties of radicals.

Correct A. 4x^3y^3

B. 4xy

C. 4x^3y

D. 4x^3y^3

Correct Answer: A

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Question 24

Find the volume of the solid formed by revolving the region bounded by y = x^2, x = 0, and x = 2 about the x-axis.

Correct A. \frac{32\pi}{3}

B. \frac{16\pi}{3}

C. \frac{64\pi}{3}

D. \frac{128\pi}{3}

Correct Answer: A

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Question 25

Find the surface area of the solid formed by revolving the region bounded by y = x^2, x = 0, and x = 2 about the x-axis.

A. 16\pi

Correct B. 32\pi

C. 64\pi

D. 128\pi

Correct Answer: B

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