Exam Body

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POST UTME LAUTECH 2019 Mathematics | Objective

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Question 1

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

A. 4

B. 6

Correct C. 8

D. 10

Correct Answer: C

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Question 2

Solve the inequality \( x^2 - 4x + 4 geq 0 \).

A. x \leq 2

Correct B. x \geq 2

C. x < 2

D. x > 2

Correct Answer: B

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Question 3

Find the determinant of the matrix \( \begin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 3 & 1 & 2 \end{bmatrix} \).

Correct A. 0

B. 1

C. 2

D. 3

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 = 16

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

Correct Answer: A

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Question 5

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

A. 6

B. 8

Correct C. 10

D. 12

Correct Answer: C

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Question 6

A random experiment consists of rolling a fair six-sided die and then tos\sing a fair coin. If the number on the die is even, the coin is tossed twice. Otherwise, the coin is tossed only once. What is the probability that the number of heads obtained is odd?

A. \frac{1}{4}

B. \frac{1}{2}

C. \frac{3}{4}

Correct D. \frac{5}{8}

Correct Answer: D

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Question 7

Find the volume of the solid formed by revolving the region bounded by the parabola y = x^2, the x-axis, and the line x = 2 about the x-axis.

A. \frac{32\pi}{5}

B. \frac{64\pi}{5}

Correct C. \frac{128\pi}{5}

D. \frac{256\pi}{5}

Correct Answer: C

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Question 8

Solve the system of equations: \begin{align*} x + y + z &= 3 \ x + 2y + 3z &= 6 \ x + 3y + 5z &= 10 \end{align*}

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

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

C. \begin{pmatrix} 3 \ 4 \ 5 \end{pmatrix}

D. \begin{pmatrix} 4 \ 5 \ 6 \end{pmatrix}

Correct Answer: A

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Question 9

Find the area under the curve y = x^3 - 6x^2 + 9x + 2 from x = 0 to x = 2.

A. \frac{28}{3}

Correct B. \frac{32}{3}

C. \frac{36}{3}

D. \frac{40}{3}

Correct Answer: B

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Question 10

A matrix A is given by \begin{pmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{pmatrix}. Find the determinant of A.

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 11

Find the value of x in the equation \( \frac{1}{x} + \frac{1}{2} = \frac{3}{4} \).

A. 4

Correct B. 6

C. 8

D. 10

Correct Answer: B

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Question 12

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

Correct A. \( -∞, -1 \) ∪ (3, ∞)

B. \( -∞, 1 \) ∪ (3, ∞)

C. \( -∞, -1 \) ∪ (1, ∞)

D. \( -∞, 3 \) ∪ (1, ∞)

Correct Answer: A

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Question 13

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

A. 62

Correct B. 64

C. 66

D. 68

Correct Answer: B

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Question 14

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

A. 4

Correct B. 10

C. 20

D. 40

Correct Answer: B

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Question 15

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

A. 0

Correct B. -2

C. -4

D. -6

Correct Answer: B

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Question 16

Solve the inequality \( x^2 - 6x + 8 < 0 \).

Correct A. (2, 4)

B. (2, 6)

C. (4, 6)

D. (6, 8)

Correct Answer: A

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Question 17

Find the sum of the first 8 terms of the arithmetic progression 1, 3, 5, ...

A. 32

B. 34

Correct C. 36

D. 38

Correct Answer: C

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Question 18

Solve the equation \( \frac{1}{x} - \frac{1}{2} = \frac{3}{4} \).

A. 4

Correct B. 6

C. 8

D. 10

Correct Answer: B

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Question 19

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

Correct A. 1

B. -1

C. 3

D. -3

Correct Answer: A

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Question 20

Solve the inequality \( x^2 + 4x - 5 > 0 \).

A. \( -∞, -5 \) ∪ (1, ∞)

B. \( -∞, -1 \) ∪ (5, ∞)

C. \( -∞, 1 \) ∪ (5, ∞)

D. \( -∞, 5 \) ∪ (1, ∞)

Correct Answer: VIEW ANSWER

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Question 21

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

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

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

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

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

Correct Answer: B

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Question 22

A circle has a radius of 5 cm. Find the area of the circle.

Correct A. \pi (5)^2

B. 2\pi (5)

C. \pi (5)^3

D. 10\pi (5)

Correct Answer: A

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Question 23

A water \tank has a height of 10 m and a base radius of 4 m. Find the volume of water in the \tank.

Correct A. \frac{1}{3} \pi (4)^2 (10)

B. \frac{1}{3} \pi (4)^3 (10)

C. \frac{1}{3} \pi (4)^2 (5)

D. \frac{1}{3} \pi (4)^3 (5)

Correct Answer: A

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Question 24

Solve the equation \( 2x^2 + 5x - 3 = 0 \) u\sing the quadratic formula.

Correct A. \\frac{-5 \\pm \\sqrt{25 + 24}}{4}

B. \\frac{-5 \\pm \\sqrt{25 - 24}}{4}

C. \\frac{-5 \\pm \\sqrt{25 + 24}}{2}

D. \\frac{-5 \\pm \\sqrt{25 - 24}}{2}

Correct Answer: A

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Question 25

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

Correct A. 3x^2 - 4x + 1

B. 3x^2 - 4x - 1

C. 3x^2 + 4x + 1

D. 3x^2 + 4x - 1

Correct Answer: A

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