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POST UTME VERITAS UNIVERSITY 2020 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 2020 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

Find the derivative of the function ( f(x) = \frac{x^2 + 2x - 3}{x^2 - 4} ) u\sing the quotient rule.

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

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

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

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

Correct Answer: A

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Question 2

A histogram of exam scores is shown below. If the mean score is 60 and the s\tandard deviation is 10, what is the probability that a randomly selected student scored above 70?

A. 0.25

B. 0.5

Correct C. 0.75

D. 0.9

Correct Answer: C

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Question 3

Simplify the expression \( \sqrt[3]{64x^6y^3} \).

Correct A. \( 4x^2y \)

B. \( 2x^2y \)

C. \( 8x^2y \)

D. \( 16x^2y \)

Correct Answer: A

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Question 4

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

Correct A. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 )

B. \( x - 3 \ \)^2 + \( y - 2 \)^2 = 16 )

C. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 9 )

D. \( x - 3 \ \)^2 + \( y - 2 \)^2 = 9 )

Correct Answer: A

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Question 5

A polynomial function is defined as ( f(x) = x^3 - 2x^2 + 5x - 1 ). Find the value of \( f\( -1 \ \) ).

A. 3

Correct B. -3

C. 5

D. -5

Correct Answer: B

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Question 6

Determine the mean of the following data set: 2, 4, 6, 8, 10. If the mean is increased by 2, what is the new mean?

A. 10

Correct B. 12

C. 14

D. 16

Correct Answer: B

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Question 7

Solve for x in the equation: \( \sin^2\( x \ \) + \cos^2(x) = 1 ).

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

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

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

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

Correct Answer: A

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Question 8

Find the area under the curve of the function ( f(x) = 2x^2 + 3x - 1 ) from x = 0 to x = 2.

A. 10

B. 12

Correct C. 14

D. 16

Correct Answer: C

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Question 9

Determine the value of the infinite geometric series: \( \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + cdots \).

A. 1

Correct B. \frac{1}{2}

C. \frac{1}{4}

D. \frac{1}{8}

Correct Answer: B

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Question 10

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

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

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

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

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

Correct Answer: A

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Question 11

Let \( mathbf{a} = egin{pmatrix} 1 \ 2 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} 3 \ 4 \end{pmatrix} \). Find the projection of ( mathbf{b} ) onto ( mathbf{a} ).

Correct A. \( egin{pmatrix} 1.5 \ 3 \end{pmatrix} \)

B. \( egin{pmatrix} 2 \ 4 \end{pmatrix} \)

C. \( egin{pmatrix} 3 \ 6 \end{pmatrix} \)

D. \( egin{pmatrix} 4 \ 8 \end{pmatrix} \)

Correct Answer: A

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Question 12

Evaluate the definite integral: \( int_{0}^{1} x^2 \sin x , dx \).

Correct A. \( -\cos x + \frac{1}{3} \sin x \)

B. \( \cos x + \frac{1}{3} \sin x \)

C. \( -\cos x - \frac{1}{3} \sin x \)

D. \( \cos x - \frac{1}{3} \sin x \)

Correct Answer: A

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Question 13

Solve the equation: \( x^3 - 6x^2 + 11x - 6 = 0 \).

Correct A. \( x = 1, 2, 3 \)

B. \( x = 1, 3, 6 \)

C. \( x = 2, 3, 6 \)

D. \( x = 1, 2, 6 \)

Correct Answer: A

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Question 14

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

A. \( -\frac{1}{3} pi^3 \)

Correct B. \( \frac{1}{3} pi^3 \)

C. \( -\frac{1}{2} pi^3 \)

D. \( \frac{1}{2} pi^3 \)

Correct Answer: B

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Question 15

Determine the value of ( x ) in the equation: \( \log_{10} \( x^2 \ \) = 4 ).

A. \( x = 10^2 \)

Correct B. \( x = 10^4 \)

C. \( x = 10^{-2} \)

D. \( x = 10^{-4} \)

Correct Answer: B

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Question 16

Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.

Correct A. 3,261

B. 3,261.5

C. 3,262

D. 3,262.5

Correct Answer: A

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Question 17

Solve the system of linear equations u\sing matrices: \begin{align*} x + 2y - z &= 3 \ 2x - 3y + 4z &= 2 \ -x + y + 2z &= -1 \end{align*}

Correct A. \begin{pmatrix} 1 \ -2 \ 3 \end{pmatrix}

B. \begin{pmatrix} 2 \ -1 \ 4 \end{pmatrix}

C. \begin{pmatrix} 3 \ 2 \ -1 \end{pmatrix}

D. \begin{pmatrix} 4 \ 3 \ 2 \end{pmatrix}

Correct Answer: A

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Question 18

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

Correct A. y = 2x - 1

B. y = 2x + 1

C. y = -2x + 1

D. y = -2x - 1

Correct Answer: A

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Question 19

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

Correct A. \\begin{pmatrix} -2 \\ 2 \\end{pmatrix}

B. \\begin{pmatrix} -1 \\ 1 \\end{pmatrix}

C. \\begin{pmatrix} 1 \\ -1 \\end{pmatrix}

D. \\begin{pmatrix} 2 \\ -2 \\end{pmatrix}

Correct Answer: A

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Question 20

Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 4).

Correct A. 6

B. 12

C. 18

D. 24

Correct Answer: A

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Question 21

Solve the system of linear equations u\sing substitution: \begin{align*} x + y &= 3 \ 2x - y &= 1 \end{align*}

Correct A. \\begin{pmatrix} 2 \\ 1 \\end{pmatrix}

B. \\begin{pmatrix} 1 \\ 2 \\end{pmatrix}

C. \\begin{pmatrix} 3 \\ 0 \\end{pmatrix}

D. \\begin{pmatrix} 0 \\ 3 \\end{pmatrix}

Correct Answer: A

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Question 22

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 = 32

C. \( x - 2 \)^2 + \( y - 3 \)^2 = 64

D. \( x - 2 \)^2 + \( y - 3 \)^2 = 128

Correct Answer: VIEW ANSWER

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Question 23

Determine the surface area of the given solid formed by revolving the region bounded by the parabola \( y = x^2 \) and the line \( y = 4 \) about the x-axis.

A. (16pi)

B. (32pi)

Correct C. (64pi)

D. (128pi)

Correct Answer: C

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Question 24

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 between 50 and 70?

A. 0.135

B. 0.341

C. 0.674

Correct D. 0.841

Correct Answer: D

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Question 25

Find the equation of the \tangent line to the curve \( y = \frac{1}{x} \) at the point where \( x = 2 \).

Correct A. \( y = -\frac{1}{2}x + 1 \)

B. \( y = \frac{1}{2}x - 1 \)

C. \( y = -\frac{1}{2}x - 1 \)

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

Correct Answer: A

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