Exam Body

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Subject

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POST UTME UI 2018 Mathematics | Objective

Are you preparing for POST UTME UI 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.

Practice these randomly selected questions to test your readiness.

Question 1

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

Correct A. ( f'(x) = \frac{-x}{\( x^2 + 1 \)^{3/2}} )

B. ( f'(x) = \frac{x}{\( x^2 + 1 \)^{3/2}} )

C. ( f'(x) = \frac{1}{\( x^2 + 1 \)^{3/2}} )

D. ( f'(x) = \frac{-1}{\( x^2 + 1 \)^{3/2}} )

Correct Answer: A

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Question 2

Solve the system of equations u\sing matrices:\( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix} \).

Correct A. \( egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 1 \ 2 \end{bmatrix} \)

B. \( egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 2 \ 1 \end{bmatrix} \)

C. \( egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 3 \ 4 \end{bmatrix} \)

D. \( egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 4 \ 3 \end{bmatrix} \)

Correct Answer: A

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Question 3

Find the area under the curve \( y = \sin\( x \ \) ) from \( x = 0 \) to \( x = \frac{pi}{2} \).

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

B. \( \frac{pi}{2} \)

C. \( \frac{pi}{4} \)

D. \( \frac{1}{4} \)

Correct Answer: A

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Question 4

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

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

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

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

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

Correct Answer: A

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Question 5

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

A. ( f'(x) = \frac{-2}{x^3} )

Correct B. ( f'(x) = \frac{2}{x^3} )

C. ( f'(x) = \frac{-1}{x^3} )

D. ( f'(x) = \frac{1}{x^3} )

Correct Answer: B

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Question 6

Find the equation of the circle pas\sing through the points (2, 3), (4, 1), and \( -1, 2 \).

Correct A. x^2 + y^2 - 6x - 4y + 12 = 0

B. x^2 + y^2 - 8x - 2y + 16 = 0

C. x^2 + y^2 - 4x - 6y + 20 = 0

D. x^2 + y^2 - 2x - 4y + 8 = 0

Correct Answer: A

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Question 7

Evaluate the integral \int_0^1 x^2 \ln x \, dx.

Correct A. \frac{1}{3} - \frac{1}{4}

B. \frac{1}{2} - \frac{1}{3}

C. \frac{1}{3} + \frac{1}{4}

D. \frac{1}{2} + \frac{1}{3}

Correct Answer: A

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Question 8

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

A. \frac{1}{2}

B. \frac{2}{3}

Correct C. \frac{5}{8}

D. \frac{3}{4}

Correct Answer: C

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Question 9

Find the sum of the first 10 terms of the geometric series 2, 6, 18, ...

A. 3120

B. 3240

Correct C. 3360

D. 3480

Correct Answer: C

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Question 10

Find the determinant of the matrix \begin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix}

Correct A. 0

B. 1

C. -1

D. 2

Correct Answer: A

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Question 11

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

A. 64π cm³

Correct B. 128π cm³

C. 256π cm³

D. 512π cm³

Correct Answer: B

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Question 12

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 13

Find the area of the region bounded by the parabola \( y = x^2 + 1 \) and the line \( y = 2x + 1 \).

A. 3/2

B. 5/2

Correct C. 7/2

D. 9/2

Correct Answer: C

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Question 14

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

A. \( -3, 2 \)

Correct B. \( -2, 3 \)

C. \( 1, -2 \)

D. \( -1, 2 \)

Correct Answer: B

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Question 15

Find the value of (x) in the equation \( 2^x + 2^x = 64 \).

A. 4

Correct B. 5

C. 6

D. 7

Correct Answer: B

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Question 16

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

Correct A. \( \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ \) )

B. \( \frac{1}{2} left\( \frac{0^3}{3} + 3 cdot 0^2 - 2 cdot 0 \right \ \) )

C. \( \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ \) + \frac{1}{2} left\( \frac{0^3}{3} + 3 cdot 0^2 - 2 cdot 0 \right \) )

D. \( \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ \) - \frac{1}{2} left\( \frac{0^3}{3} + 3 cdot 0^2 - 2 cdot 0 \right \) )

Correct Answer: A

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Question 17

A rec\tangular box has dimensions ( x ) cm by ( 2x ) cm by ( 3x ) cm. If its surface area is 264 cm², find the value of ( x ).

A. \( x = 4 \)

Correct B. \( x = 6 \)

C. \( x = 8 \)

D. \( x = 10 \)

Correct Answer: B

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Question 18

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

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

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

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

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

Correct Answer: C

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Question 19

A circle has a diameter of 10 cm. Find the area of the sector formed by a central angle of 60°.

Correct A. \( \frac{1}{6} pi cdot 5^2 \)

B. \( \frac{1}{6} pi cdot 10^2 \)

C. \( \frac{1}{6} pi cdot 5^2 cdot \frac{3}{2} \)

D. \( \frac{1}{6} pi cdot 10^2 cdot \frac{3}{2} \)

Correct Answer: A

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Question 20

Find the value of \( int_{0}^{1} x^2 , dx \).

Correct A. \( \frac{1}{3} \)

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

C. \( \frac{2}{3} \)

D. ( 1 )

Correct Answer: A

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Question 21

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

Correct A. 16

B. 32

C. 64

D. 128

Correct Answer: A

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Question 22

Find the volume of the sphere \( V = \frac{4}{3} pi r^3 \) if the radius is 6 cm.

Correct A. 904.778

B. 904.779

C. 904.780

D. 904.781

Correct Answer: A

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Question 23

Solve the quadratic equation \( x^2 + 5x + 6 = 0 \) u\sing the quadratic formula.

A. -2

Correct B. -3

C. -4

D. -5

Correct Answer: B

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Question 24

Find the equation of the circle with center ( (3, 4) ) and radius 5.

Correct A. \( x - 3 \)^2 + \( y - 4 \)^2 = 25

B. \( x - 4 \)^2 + \( y - 3 \)^2 = 25

C. \( x - 3 \)^2 + \( y - 4 \)^2 = 30

D. \( x - 4 \)^2 + \( y - 3 \)^2 = 30

Correct Answer: A

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Question 25

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

Correct A. \( -∞, -1 \) ∪ (3, ∞)

B. \( -∞, -3 \) ∪ (1, ∞)

C. \( -∞, -2 \) ∪ (2, ∞)

D. \( -∞, -4 \) ∪ (4, ∞)

Correct Answer: A

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