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

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Question 1

In a random experiment, two events A and B are indep\endent. If P(A) = 0.4 and P(B) = 0.6, what is the probability that both events occur?

Correct A. 0.24

B. 0.48

C. 0.64

D. 0.76

Correct Answer: A

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Question 2

Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 24π cm^3

Correct B. 48π cm^3

C. 64π cm^3

D. 80π cm^3

Correct Answer: B

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Question 3

In the diagram below, the circle with center O passes through points A, B, and C. What is the measure of angle AOC?

A. 60°

B. 90°

Correct C. 120°

D. 150°

Correct Answer: C

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Question 4

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

A. 10^4

Correct B. 10^8

C. 10^12

D. 10^16

Correct Answer: B

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Question 5

A right triangle has a hypotenuse of length 10 cm and one leg of length 6 cm. What is the length of the other leg?

A. 4 cm

B. 6 cm

Correct C. 8 cm

D. 12 cm

Correct Answer: C

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Question 6

Find the volume of the frustum of a cone with height 8 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 256\pi cm^3

B. 512\pi cm^3

Correct C. 768\pi cm^3

D. 1024\pi cm^3

Correct Answer: C

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Question 7

Solve the equation \( x^2 + 2x - 6 = 0 \) u\sing the quadratic formula.

Correct A. x = 2 \pm \sqrt{7}

B. x = -2 \pm \sqrt{7}

C. x = 2 \pm \sqrt{5}

D. x = -2 \pm \sqrt{5}

Correct Answer: A

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Question 8

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

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

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

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

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

Correct Answer: A

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Question 9

Solve the trigonometric equation \( 2\sin^2 x + 3\cos x - 1 = 0 \) for \( 0 \leq x \leq 2\pi \).

Correct A. \frac{\pi}{6}, \frac{\pi}{2}, \frac{5\pi}{6}

B. \frac{\pi}{6}, \frac{\pi}{4}, \frac{5\pi}{4}

C. \frac{\pi}{4}, \frac{\pi}{2}, \frac{3\pi}{4}

D. \frac{\pi}{6}, \frac{\pi}{3}, \frac{\pi}{2}

Correct Answer: A

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Question 10

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 = x - 1

D. y = x + 1

Correct Answer: A

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Question 11

Find the determinant of the matrix [ egin{array}{ccc} 2 & 3 & 1 \ 4 & 5 & 2 \ 1 & 2 & 3 \end{array} ].

Correct A. -1

B. 1

C. 2

D. 3

Correct Answer: A

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Question 12

Solve for x in the equation [ 2^x + 2^{x+1} = 3 \cdot 2^x ].

A. -1

B. 0

Correct C. 1

D. 2

Correct Answer: C

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Question 13

Find the volume of the solid formed by revolving the region bounded by the curve [ y = x^2 \] and the line [ y = 2x \] about the x-axis.

A. 4\pi

B. 8\pi

C. 16\pi

Correct D. 32\pi

Correct Answer: D

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Question 14

A set of 5 points [ A, B, C, D, E \] are chosen at random from the set of points [ (0,0), (1,0), (2,0), (3,0), (4,0), (5,0), (6,0), (7,0), (8,0), (9,0) \]. What is the probability that the points [ A, B, C, D, E \] are in increa\sing order?

A. \frac{1}{252}

B. \frac{1}{126}

Correct C. \frac{1}{63}

D. \frac{1}{32}

Correct Answer: C

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Question 15

Find the surface area of the solid formed by revolving the region bounded by the curve [ y = x^2 \] and the line [ y = 2x \] about the x-axis.

A. 16\pi

B. 32\pi

C. 64\pi

Correct D. 128\pi

Correct Answer: D

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Question 16

Solve the inequality \( \frac{x}{x-1} > 2 \) for \( x > 1 \).

A. x > 3

B. x > 5

C. x > 2

Correct D. x > 4

Correct Answer: D

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Question 17

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

A. 4

B. 6

Correct C. 8

D. 10

Correct Answer: C

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Question 18

A sequence is defined by \( a_n = 2n^2 - 3n + 1 \). Find the sum of the first 5 terms of the sequence.

A. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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Question 19

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

Correct A. x = -2

B. x = 0

C. x = -1

D. x = 1

Correct Answer: A

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Question 20

Find the value of \( \log_{10} \( 1000 \ \) ).

A. 3

Correct B. 4

C. 5

D. 6

Correct Answer: B

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Question 21

Solve the quadratic equation \( x^2 + 4x + 4 = 0 \) u\sing the quadratic formula. What is the value of ( x )?

A. 0

B. -2

Correct C. 2

D. -1

Correct Answer: C

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Question 22

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

A. 1/2

B. 1/3

Correct C. 2/3

D. 1/6

Correct Answer: C

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Question 23

The mean of a set of numbers is 25. If one of the numbers is increased by 5, the mean becomes 26. How many numbers are in the set?

A. 5

Correct B. 10

C. 15

D. 20

Correct Answer: B

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Question 24

Solve for ( x ) in the equation \( 2^x = 16 \).

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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Question 25

A circle has a radius of 4 cm. What is the area of the circle?

A. 16π

Correct B. 32π

C. 64π

D. 128π

Correct Answer: B

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