Exam Body

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Subject

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POST UTME SUMMIT UNIVERSITY 2019 Mathematics | Objective

Are you preparing for POST UTME SUMMIT 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.

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Question 1

In the number system with base 8, what is the value of the expression \( 5 \times 8^2 + 3 \times 8^1 + 2 \times 8^0 \)?

Correct A. 42

B. 48

C. 52

D. 58

Correct Answer: A

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Question 2

Find the area under the curve \( y = \frac{1}{x} \) from \( x = 1 \) to \( x = 2 \).

Correct A. 0.5

B. 1

C. 1.5

D. 2

Correct Answer: A

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Question 3

Given the vectors \( mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} 4 \ 5 \end{pmatrix} \), find the magnitude of the vector \( mathbf{a} + mathbf{b} \).

A. 5

B. 6

Correct C. 7

D. 8

Correct Answer: C

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Question 4

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

Correct A. x = -2

B. x = -1

C. x = 0

D. x = 1

Correct Answer: A

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Question 5

Find the value of \( \sin\( 2\theta \ \) ) given that \( \sin\( \theta \ \) = \frac{3}{5} ) and \( \cos\( \theta \ \) = \frac{4}{5} ).

Correct A. \frac{24}{25}

B. \frac{16}{25}

C. \frac{20}{25}

D. \frac{12}{25}

Correct Answer: A

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Question 6

Let \( S = {1, 2, 3, 4, 5} \) and \( T = {2, 3, 5, 7, 11} \). Find the symmetric difference of sets S and T.

A. S \cup T

B. S \cap T

Correct C. S \triangle T

D. S \oplus T

Correct Answer: C

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Question 7

Find the sum of the first 10 terms of the geometric series \( 2x + 3x^2 + 4x^3 + ldots \).

A. 2x + 3x^2 + 4x^3 + ldots + 20x^{10}

Correct B. 2x + 3x^2 + 4x^3 + ldots + 21x^{10}

C. 2x + 3x^2 + 4x^3 + ldots + 22x^{10}

D. 2x + 3x^2 + 4x^3 + ldots + 23x^{10}

Correct Answer: B

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Question 8

Let \( vec{a} = egin{pmatrix} 2 \ 3 \ -1 \end{pmatrix} \) and \( vec{b} = egin{pmatrix} 1 \ -2 \ 4 \end{pmatrix} \). Find the cross product of vectors ( vec{a} ) and ( vec{b} ).

Correct A. \( egin{pmatrix} 11 \ -14 \ 8 \end{pmatrix} \)

B. \( egin{pmatrix} 10 \ -13 \ 7 \end{pmatrix} \)

C. \( egin{pmatrix} 9 \ -12 \ 6 \end{pmatrix} \)

D. \( egin{pmatrix} 8 \ -11 \ 5 \end{pmatrix} \)

Correct Answer: A

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Question 9

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

A. \( x = 0, pi, 2pi \)

B. \( x = \frac{pi}{2}, \frac{3pi}{2} \)

Correct C. \( x = \frac{pi}{4}, \frac{3pi}{4}, \frac{5pi}{4}, \frac{7pi}{4} \)

D. \( x = \frac{pi}{6}, \frac{5pi}{6}, \frac{7pi}{6}, \frac{11pi}{6} \)

Correct Answer: C

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Question 10

Find the derivative of the function ( f(x) = x^3 - 2x^2 + 3x - 1 ) u\sing the power rule.

Correct A. ( f'(x) = 3x^2 - 4x + 3 )

B. ( f'(x) = x^2 - 2x + 1 )

C. ( f'(x) = 3x^2 - 4x + 2 )

D. ( f'(x) = x^2 - 2x - 1 )

Correct Answer: A

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Question 11

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

Correct A. x = -2π/3, x = π/3

B. x = 2π/3, x = -π/3

C. x = π/3, x = -π/3

D. x = 2π/3, x = π/3

Correct Answer: A

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Question 12

Find the value of y in the equation \( y = \frac{1}{2} left\( x + \frac{1}{x} \right \ \) ) when x = 2.

Correct A. 3/2

B. 5/2

C. 7/2

D. 9/2

Correct Answer: A

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Question 13

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

Correct A. x < -3/2 or x > 1

B. x < -1 or x > 3

C. x < 1 or x > 3

D. x < -3/2 or x < 1

Correct Answer: A

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Question 14

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

Correct A. x = 1

B. x = 2

C. x = 3

D. x = 4

Correct Answer: A

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Question 15

Find the value of x in the equation \( x^2 + 4x + 4 = 0 \).

Correct A. x = -2

B. x = -1

C. x = 0

D. x = 1

Correct Answer: A

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Question 16

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 \text{ cm}^3

B. 512\pi \text{ cm}^3

Correct C. 768\pi \text{ cm}^3

D. 1024\pi \text{ cm}^3

Correct Answer: C

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Question 17

A fair six-sided die is rolled. What is the probability that the number obtained is a multiple of 3?

Correct A. \frac{1}{3}

B. \frac{1}{2}

C. \frac{2}{3}

D. \frac{4}{5}

Correct Answer: A

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Question 18

Find the area under the curve y = x^2 + 2x - 3 from x = 1 to x = 4.

A. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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Question 19

Solve for x in the equation \frac{1}{x + 2} + \frac{1}{x - 1} = \frac{3}{2}

A. x = -3

B. x = 2

Correct C. x = 4

D. x = 5

Correct Answer: C

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Question 20

Find the value of \sin 75^\circ in terms of \sin 15^\circ and \cos 15^\circ.

Correct A. \sin 15^\circ + \cos 15^\circ

B. \sin 15^\circ - \cos 15^\circ

C. \sin 15^\circ \cos 15^\circ

D. \cos 15^\circ - \sin 15^\circ

Correct Answer: A

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Question 21

Find the volume of the solid formed by rotating the region bounded by the curves y = x^2 and y = 4 - x^2 about the x-axis.

A. 16\pi

B. 32\pi

Correct C. 64\pi

D. 128\pi

Correct Answer: C

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Question 22

If f(x) = 3x^2 + 2x - 5, find the derivative of f(x) u\sing the chain rule.

Correct A. 6x + 2

B. 6x - 2

C. 3x^2 + 2x - 5

D. 9x^2 + 4x - 10

Correct Answer: A

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Question 23

Solve the equation \tan x = \sqrt{3} u\sing the unit circle.

A. \frac{\pi}{3}

Correct B. \frac{2\pi}{3}

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

D. \frac{5\pi}{3}

Correct Answer: B

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Question 24

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

A. 6

B. 8

Correct C. 10

D. 12

Correct Answer: C

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Question 25

Evaluate the definite integral \int_{0}^{1} x^2 dx.

Correct A. \frac{1}{3}

B. \frac{1}{2}

C. \frac{2}{3}

D. \frac{3}{4}

Correct Answer: A

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