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POST UTME VERITAS UNIVERSITY 2019 Mathematics | Objective

Are you preparing for POST UTME VERITAS UNIVERSITY exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2019 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

Determine the value of x in the equation \( \tan x = \frac{1}{\sqrt{3}} \) if ( x ) lies in the first quadrant.

Correct A. \( \frac{pi}{6} \)

B. \( \frac{pi}{4} \)

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

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

Correct Answer: A

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Question 2

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

A. -1

Correct B. 1

C. 2

D. 3

Correct Answer: B

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Question 3

A random experiment has two indep\endent events, A and B. If P(A) = 0.4 and P(B) = 0.6, find P(A ∩ B).

A. 0.2

Correct B. 0.24

C. 0.3

D. 0.36

Correct Answer: B

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Question 4

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

Correct A. \( x = -2 \)

B. \( x = -1 \)

C. \( x = 1 \)

D. \( x = 2 \)

Correct Answer: A

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Question 5

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 6

Solve the inequality \( \frac{x}{x+2} > 0 \) for \( x in \( -infty, infty \ \) ).

A. \( -2, ∞ \)

Correct B. \( -∞, -2 \) cup (0, ∞)

C. \( -∞, -2 \) cup (2, ∞)

D. \( -∞, 0 \) cup (2, ∞)

Correct Answer: B

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Question 7

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

A. \frac{\pi^3}{3}

Correct B. \frac{\pi^3}{6}

C. \frac{\pi^3}{12}

D. \frac{\pi^3}{24}

Correct Answer: B

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Question 8

Solve the system of equations \( x^2 + y^2 = 4 \) and \( xy = 2 \).

Correct A. \left\{(2, 1), (-2, -1)\right\}

B. \left\{(1, 2), (-1, -2)\right\}

C. \left\{\( 2, -1 \), (-2, 1)\right\}

D. \left\{\( 1, -2 \), (-1, 2)\right\}

Correct Answer: A

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Question 9

Find the value of ( x ) in the equation \( x^3 - 6x^2 + 11x - 6 = 0 \).

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 10

Solve the inequality \( x^2 - 4x + 3 > 0 \).

Correct A. \( -∞, 1 \) cup (3, ∞)

B. \( -∞, 3 \) cup (1, ∞)

C. \( -∞, ∞ \) \setminus \{1, 3\}

D. \( -∞, ∞ \)

Correct Answer: A

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Question 11

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

A. 64

B. 80

Correct C. 96

D. 112

Correct Answer: C

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Question 12

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

Correct A. x = 1, y = 2

B. x = 2, y = 1

C. x = 3, y = 4

D. x = 4, y = 3

Correct Answer: A

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Question 13

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

A. 14

B. 16

Correct C. 18

D. 20

Correct Answer: C

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Question 14

A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?

A. 1/6

B. 1/3

C. 1/2

Correct D. 2/3

Correct Answer: D

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Question 15

Find the derivative of the function ( f(x) = 3x^2 + 2x - 5 ) u\sing the power rule.

Correct A. 6x + 2

B. 6x - 2

C. 3x^2 + 2

D. 3x^2 - 2

Correct Answer: A

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Question 16

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 the probability that X + Y < 1.

Correct A. 1/4

B. 1/2

C. 3/4

D. 1

Correct Answer: A

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Question 17

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

Correct A. -2

B. -1

C. 1

D. 2

Correct Answer: A

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Question 18

Find the mean and s\tandard deviation of the data set: 2, 4, 6, 8, 10.

Correct A. 4, 2

B. 6, 3

C. 8, 4

D. 10, 5

Correct Answer: A

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Question 19

Let A = [2, 4, 6] and B = [1, 3, 5]. Find the dot product of A and B.

Correct A. 32

B. 36

C. 40

D. 44

Correct Answer: A

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Question 20

Solve the polynomial equation x^3 - 6x^2 + 11x - 6 = 0.

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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Question 21

Solve the inequality \( \frac{x^2 - 4}{x + 2} > 0 \) for \( x in \( -infty, -2 \ \) cup \( -2, infty \) ).

Correct A. \( -2, -1 \) ∪ (1, ∞)

B. \( -∞, -2 \) ∪ (2, ∞)

C. \( -∞, -1 \) ∪ (1, ∞)

D. \( -∞, -2 \) ∪ \( -1, ∞ \)

Correct Answer: A

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Question 22

Find the sum of the first 10 terms of the arithmetic sequence with first term \( a = 3 \) and common difference \( d = 2 \).

Correct A. 60

B. 70

C. 80

D. 90

Correct Answer: A

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Question 23

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

A. 0

Correct B. -2

C. 1

D. -1

Correct Answer: B

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Question 24

Find the equation of the circle with center \( C\( -2, 3 \ \) ) and radius \( r = 4 \).

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 25

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

Correct A. 0, \frac{pi}{2}, \pi, \frac{3pi}{2}

B. 0, \pi, 2pi

C. \frac{pi}{2}, \pi, \frac{3pi}{2}

D. 0, \frac{pi}{2}, \pi, \frac{3pi}{2}

Correct Answer: A

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