Exam Body

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Subject

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POST UTME LAUTECH 2021 Mathematics | Objective

Are you preparing for POST UTME LAUTECH 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.

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Question 1

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

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

B. \( \frac{1}{3} \)

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

D. \( \frac{1}{5} \)

Correct Answer: A

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Question 2

In the diagram below, identify the part labeled A.

Correct A. Beaker

B. Burette

C. Test Tube

D. Cell

Correct Answer: A

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Question 3

Solve for ( 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 4

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

A. \( \frac{32}{3} pi \)

Correct B. \( \frac{64}{3} pi \)

C. \( \frac{128}{3} pi \)

D. \( \frac{256}{3} pi \)

Correct Answer: B

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Question 5

In the diagram below, identify the part labeled B.

Correct A. Plant

B. Animal

C. Cell

D. Graph

Correct Answer: A

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Question 6

Find the area under the curve y = x^2 + 2x + 1 from x = 0 to x = 3.

Correct A. 27

B. 30

C. 33

D. 36

Correct Answer: A

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Question 7

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

A. x = 2

Correct B. x = 3

C. x = 4

D. x = 5

Correct Answer: B

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Question 8

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

A. 3

Correct B. 4

C. 5

D. 6

Correct Answer: B

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Question 9

Solve the matrix equation \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 5 \ 6 \end{bmatrix}

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

B. \begin{bmatrix} 2 \ 3 \end{bmatrix}

C. \begin{bmatrix} 3 \ 4 \end{bmatrix}

D. \begin{bmatrix} 4 \ 5 \end{bmatrix}

Correct Answer: A

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Question 10

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

A. 104

B. 105

Correct C. 106

D. 107

Correct Answer: C

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Question 11

If P(A) = 0.4, P(B) = 0.5, and P(A ∩ B) = 0.15, find P\( A|B \).

A. 0.3

Correct B. 0.6

C. 0.8

D. 1.0

Correct Answer: B

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Question 12

Solve the equation: \( \frac{1}{2} \sin^2 x + \frac{1}{4} \cos^2 x = \frac{1}{4} \)

Correct A. x = \frac{\pi}{6}

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

C. x = \frac{\pi}{3}

D. x = \frac{\pi}{2}

Correct Answer: A

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Question 13

Find the area under the curve y = 2x^2 + 3x - 1 from x = 0 to x = 2.

A. 13

B. 14

Correct C. 15

D. 16

Correct Answer: C

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Question 14

If f(x) = 2x^2 + 3x - 1, find f'(x).

Correct A. 4x + 3

B. 2x^2 + 3

C. 2x + 3

D. 4x - 3

Correct Answer: A

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Question 15

Find the sum of the first 5 terms of the geometric series 2, 6, 18, ...

A. 62

B. 64

Correct C. 66

D. 68

Correct Answer: C

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Question 16

Solve the inequality \( \frac{x^2 - 4}{x + 2} > 0 \) for ( x in mathbb{R} ).

Correct A. \( -∞, -2 \) ∪ (2, ∞)

B. \( -∞, -2 \) ∪ \( -2, 2 \) ∪ (2, ∞)

C. \( -∞, -2 \) ∩ (2, ∞)

D. \( -∞, 2 \) ∪ (2, ∞)

Correct Answer: A

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Question 17

Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \).

Correct A. 64

B. 32

C. 16

D. 8

Correct Answer: A

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Question 18

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

Correct A. x = 0, \pi/2, \pi, 3\pi/2

B. x = 0, \pi/2, \pi, 3\pi/2, 2\pi

C. x = 0, \pi/2, \pi, 3\pi/2, 5\pi/2

D. x = 0, \pi/2, \pi, 3\pi/2, 4\pi

Correct Answer: A

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Question 19

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 = 16

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

Correct Answer: A

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Question 20

Solve the system of equations \( x + y = 3 \) and \( x - y = 1 \).

Correct A. x = 2, y = 1

B. x = 1, y = 2

C. x = 2, y = 2

D. x = 1, y = 1

Correct Answer: A

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Question 21

Determine the value of x in the equation \( \sin^2\( x \ \) + \cos^2(x) = 1 ) if \( \tan\( x \ \) = \frac{3}{4} ).

Correct A. \( \frac{pi}{4} \)

B. \( \frac{3pi}{4} \)

C. \( \frac{5pi}{4} \)

D. \( \frac{7pi}{4} \)

Correct Answer: A

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Question 22

Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \) u\sing the definite integral.

A. \( \frac{64}{3} \)

B. \( \frac{128}{3} \)

Correct C. \( \frac{256}{3} \)

D. \( \frac{512}{3} \)

Correct Answer: C

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Question 23

Solve the equation \( x^3 - 6x^2 + 11x - 6 = 0 \) u\sing the factor theorem.

A. \( x = 1 \)

B. \( x = 2 \)

Correct C. \( x = 3 \)

D. \( x = 6 \)

Correct Answer: C

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Question 24

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 25

A particle moves in a straight line with an initial velocity of \( 5 , \text{m/s} \) and an acceleration of \( 2 , \text{m/s}^2 \). Find its velocity after ( 3 ) seconds.

A. \( 13 , \text{m/s} \)

B. \( 15 , \text{m/s} \)

Correct C. \( 17 , \text{m/s} \)

D. \( 19 , \text{m/s} \)

Correct Answer: C

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