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POST UTME VERITAS UNIVERSITY 2021 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 2021 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

Find the value of x in the equation $ 2x^2 + 5x - 3 = 0 $ u\sing the quadratic formula.

Correct A. 1

B. -1

C. 2

D. -2

Correct Answer: A

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Question 2

Solve for y in the equation $ y = \log_{10} \( x^2 \ $ = 4 ).

Correct A. 10^4

B. 10^2

C. 10^8

D. 10^6

Correct Answer: A

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Question 3

A circle has an equation of the form $ x - h \ $^2 + $ y - k $^2 = r^2 ). If the center of the circle is at (3, 4) and the radius is 5, find the equation of the circle.

Correct A. $ x - 3 $^2 + $ y - 4 $^2 = 25

B. $ x - 4 $^2 + $ y - 3 $^2 = 25

C. $ x - 3 $^2 + $ y - 4 $^2 = 9

D. $ x - 4 $^2 + $ y - 3 $^2 = 9

Correct Answer: A

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Question 4

Find the value of x in the equation $ x^3 - 6x^2 + 11x - 6 = 0 $ u\sing synthetic division.

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 5

A vector $ \vec{a} $ has a magnitude of 5 and is directed at an angle of 60° to the x-axis. Find the x and y components of the vector.

Correct A. 2.5, 4.33

B. 4.33, 2.5

C. 3.33, 3.33

D. 2.5, 2.5

Correct Answer: A

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Question 6

Find the value of $\tan \left$ \frac{\pi}{4} + \arc\tan 2 \right $$ u\sing the sum identity for \tangent.

A. 2

Correct B. \sqrt{5}

C. -\sqrt{5}

D. -2

Correct Answer: B

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Question 7

Determine the value of $x$ in the equation $\begin{vmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{vmatrix} = 0$.

Correct A. -1

B. 1

C. 2

D. 3

Correct Answer: A

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Question 8

A sequence is defined by $a_n = \frac{2n + 1}{n^2 + 1}$. Find the sum of the first 5 terms of the sequence.

Correct A. \frac{13}{6}

B. \frac{15}{8}

C. \frac{17}{10}

D. \frac{19}{12}

Correct Answer: A

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Question 9

A histogram is shown below. Find the mean of the data set.

A. 10

B. 15

Correct C. 20

D. 25

Correct Answer: C

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Question 10

Solve the inequality $x^2 + 4x - 5 > 0$.

Correct A. $ -\infty, -1 $ \cup $ 5, \infty $

B. $ -\infty, -5 $ \cup $ 1, \infty $

C. $ -\infty, 1 $ \cup $ 5, \infty $

D. $ -\infty, -5 $ \cup $ 1, \infty $

Correct Answer: A

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Question 11

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

A. x \ln $ x^2 + 1 $

B. \frac{x}{x^2 + 1}

Correct C. \frac{1}{2} \frac{2x}{x^2 + 1}

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

Correct Answer: C

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Question 12

Solve the system of equations u\sing matrices: \begin{align*} x + y + z &= 6, \ 2x - y + 3z &= 7, \ x - 2y + z &= -2 \end{align*}.

Correct A. [1, 2, 3]

B. [2, -1, 1]

C. [3, 1, -1]

D. [1, -1, 2]

Correct Answer: A

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Question 13

Find the area under the curve $ y = x^2 $ from $ x = 0 $ to $ x = 4 $ u\sing integration.

Correct A. 64

B. 16

C. 32

D. 48

Correct Answer: A

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Question 14

A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find its volume.

Correct A. 30

B. 50

C. 60

D. 70

Correct Answer: A

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Question 15

Solve the trigonometric equation $ \sin^2 x + \cos^2 x = 1 $ for ( x ) in the interval ( [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}{4}, \frac{3pi}{4}]

Correct Answer: A

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Question 16

In the diagram below, what is the value of x?

Correct A. 4

B. 5

C. 6

D. 7

Correct Answer: A

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Question 17

Solve for x in the equation $ \log_{10} \( x^2 \ $ = 4 ).

A. 2

B. 4

C. 8

Correct D. 16

Correct Answer: D

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Question 18

Find the surface area of the sphere with radius 5 cm.

Correct A. 314.16

B. 314.16

C. 314.16

D. 314.16

Correct Answer: A

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Question 19

A sequence is defined by the formula $ a_n = 2n + 1 $. Find the 10th term of the sequence.

A. 21

B. 22

Correct C. 23

D. 24

Correct Answer: C

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Question 20

A histogram shows the distribution of exam scores. What is the mean of the scores?

A. 50

B. 60

Correct C. 70

D. 80

Correct Answer: C

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Question 21

Find the volume of the frustum of a cone with height 10 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 100π cm³

B. 200π cm³

Correct C. 300π cm³

D. 400π cm³

Correct Answer: C

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Question 22

A set of 5 numbers has an average of 10. If 5 is added to each number, what is the new average?

A. 8

B. 10

Correct C. 12

D. 15

Correct Answer: C

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Question 23

Solve for x in the equation: $ \frac{1}{x} + \frac{1}{2x} = \frac{3}{4x} $.

A. 4

Correct B. 8

C. 16

D. 32

Correct Answer: B

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Question 24

Find the surface area of the sphere with radius 6 cm.

Correct A. 288π cm²

B. 288π cm²

C. 288π cm²

D. 288π cm²

Correct Answer: A

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Question 25

A matrix A has elements a11 = 2, a12 = 3, a21 = 4, a22 = 5. Find the determinant of A.

A. -1

B. 1

Correct C. 3

D. 5

Correct Answer: C

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