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POST UTME VERITAS UNIVERSITY 2024 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 2024 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

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

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

B. ( 3 )

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

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

Correct Answer: D

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Question 2

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

Correct A. \( x < -1 \) or \( x > \frac{3}{2} \)

B. \( x < -1 \) or \( x < \frac{3}{2} \)

C. \( x > -1 \) or \( x < \frac{3}{2} \)

D. \( x > -1 \) or \( x > \frac{3}{2} \)

Correct Answer: A

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Question 3

Find the determinant of the matrix \( egin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 1 & 3 & 2 \end{bmatrix} \).

A. ( 2 )

Correct B. \( -1 \)

C. ( 1 )

D. ( 0 )

Correct Answer: B

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Question 4

In the circuit below, find the current flowing through the 5 ohm resistor.

Correct A. ( 1 ) A

B. ( 2 ) A

C. ( 3 ) A

D. ( 4 ) A

Correct Answer: A

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Question 5

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

A. \( x = \frac{pi}{2} \)

Correct B. \( x = \frac{pi}{4} \)

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

D. \( x = \frac{5pi}{4} \)

Correct Answer: B

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Question 6

Find the volume of the solid formed by revolving the region bounded by the curve \( y = \frac{1}{2}x^2 \) about the x-axis, from \( x = 0 \) to \( x = 2 \).

Correct A. π/3

B. π/2

C. 2π/3

D. π

Correct Answer: A

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Question 7

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

Correct A. \( -∞, -1 \) ∪ (3, ∞)

B. \( -∞, -3 \) ∪ (1, ∞)

C. \( -∞, 1 \) ∪ (3, ∞)

D. \( -∞, -3 \) ∪ (1, ∞)

Correct Answer: A

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Question 8

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

Correct A. 11/3

B. 13/3

C. 15/3

D. 17/3

Correct Answer: A

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Question 9

Find the sum of the first 5 terms of the arithmetic progression 3, 6, 9, ...

Correct A. 45

B. 50

C. 55

D. 60

Correct Answer: A

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Question 10

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

Correct A. \( -3, 2 \)

B. \( -2, 3 \)

C. \( -3, 3 \)

D. \( -2, 2 \)

Correct Answer: A

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Question 11

Let ( f(x) = x^3 - 6x^2 + 11x - 6 ). Find the value of ( f(2) ).

Correct A. 10

B. 12

C. 14

D. 16

Correct Answer: A

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Question 12

A set ( A ) contains the elements ( 1, 2, 3, 4, 5 ). Find the number of subsets of ( A ) that contain exactly two elements.

A. 10

B. 12

Correct C. 15

D. 20

Correct Answer: C

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Question 13

Find the sum of the infinite geometric series \( 1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \cdots \ \)

Correct A. 2

B. 4

C. 8

D. 16

Correct Answer: A

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Question 14

In the diagram below, ( ABC ) is a right-angled triangle with \( AB = 3 \) and \( BC = 4 \). Find the length of ( AC ).

A. 5

B. 6

Correct C. 7

D. 8

Correct Answer: C

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Question 15

A bag contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?

A. \frac{1}{4}

B. \frac{1}{2}

Correct C. \frac{3}{8}

D. \frac{5}{8}

Correct Answer: C

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Question 16

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

Correct A. x^2 + y^2 + 4x - 6y + 4 = 0

B. x^2 + y^2 - 4x + 6y + 4 = 0

C. x^2 + y^2 + 2x - 3y + 4 = 0

D. x^2 + y^2 - 2x + 3y + 4 = 0

Correct Answer: A

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Question 17

Solve for x in the equation: \[ \begin{array}{rcl} 2x + 5 &=& 11 \ 3x - 2 &=& 7 \ \hline \end{array} \]

A. x = 2

Correct B. x = 3

C. x = 4

D. x = 5

Correct Answer: B

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Question 18

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

A. 5

B. 6

Correct C. 7

D. 8

Correct Answer: C

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Question 19

Solve the matrix equation: \[ \begin{array}{ccc} 2 & -1 & 3 \ 4 & 2 & -5 \ 1 & 3 & 2 \ \end{array} \] \begin{array}{c} x \ y \ z \ \end{array} = \begin{array}{c} 10 \ 15 \ 20 \ \end{array} \]

Correct A. x = 2, y = 3, z = 4

B. x = 3, y = 4, z = 5

C. x = 4, y = 5, z = 6

D. x = 5, y = 6, z = 7

Correct Answer: A

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Question 20

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

A. y = 2x - 1

Correct B. y = 2x + 1

C. y = -2x + 1

D. y = -2x - 1

Correct Answer: B

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Question 21

A right circular cone has a height of 8 cm and a base radius of 4 cm. Find the volume of the cone in cubic centimeters.

A. 256\pi

B. 512\pi

Correct C. 1024\pi

D. 2048\pi

Correct Answer: C

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Question 22

Solve the inequality \frac{x+2}{x-1} > 0.

Correct A. x < -2 or x > 1

B. x < -2 or x < 1

C. x > -2 or x > 1

D. x < -2 or x = 1

Correct Answer: A

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Question 23

A die is rolled twice. Find the probability that the sum of the numbers shown on the two dice is 7.

Correct A. \frac{1}{6}

B. \frac{1}{12}

C. \frac{1}{18}

D. \frac{1}{36}

Correct Answer: A

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Question 24

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 25

Find the value of x in the equation 2^x + 5^x = 7^x.

A. x = 2

Correct B. x = 3

C. x = 4

D. x = 5

Correct Answer: B

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