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POST UTME LASU 2017 Mathematics | Objective

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Question 1

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{2}{\( x^2 + 1 \ \)^2} )

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

Correct Answer: A

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Question 2

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

Correct A. \( x = 2, y = 3 \)

B. \( x = 3, y = 2 \)

C. \( x = 4, y = 5 \)

D. \( x = 5, y = 4 \)

Correct Answer: A

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Question 3

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. \( y = 3x - 2 \)

D. \( y = 3x + 2 \)

Correct Answer: A

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Question 4

A histogram of exam scores is shown below:\n\n[Diagram Spec]

Correct A. The mean score is 60.

B. The median score is 60.

C. The mode score is 60.

D. The s\tandard deviation is 10.

Correct Answer: A

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Question 5

Find the area of the circle with radius \( r = 4 \) cm.

Correct A. ( 16pi ) cm^2

B. ( 32pi ) cm^2

C. ( 64pi ) cm^2

D. ( 128pi ) cm^2

Correct Answer: A

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Question 6

Determine the mean of the following data set: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20. If the mean is 12, what is the value of the mis\sing data point?

Correct A. 22

B. 20

C. 18

D. 16

Correct Answer: A

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Question 7

Solve for x in the equation \( \frac{1}{x} + 2 = \frac{3}{x} \).

A. -1

Correct B. 1

C. 2

D. 3

Correct Answer: B

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Question 8

A circle has a radius of 4 cm. If the area of the circle is 50.24 cm^2, what is the value of x in the equation \( x = \frac{\pi r^2}{A} \)?

A. 2

B. 3

C. 4

Correct D. 5

Correct Answer: D

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Question 9

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

A. 15

B. 20

Correct C. 25

D. 30

Correct Answer: C

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Question 10

A set of numbers is defined as \( S = \{ 1, 2, 3, 4, 5 \} \). Find the number of subsets of S.

A. 5

Correct B. 6

C. 7

D. 8

Correct Answer: B

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Question 11

Find the value of x in the equation \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ 1 \end{bmatrix} = egin{bmatrix} 7 \ 11 \end{bmatrix} \).

A. 5

B. 6

Correct C. 7

D. 8

Correct Answer: C

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Question 12

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

Correct A. \( -∞, -1 \) ∪ (3, ∞)

B. \( -∞, -3 \) ∪ (1, ∞)

C. \( -∞, -1 \) ∪ (1, ∞)

D. \( -∞, 1 \) ∪ (3, ∞)

Correct Answer: A

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Question 13

Find the equation of the circle with center \( -2, 3 \) and radius 4.

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

B. \( x - 2 \)^2 + \( y + 3 \)^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 14

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

A. -2x/\( x^2 + 1 \)^2

Correct B. 2x/\( x^2 + 1 \)^2

C. -2/\( x^2 + 1 \)^2

D. 2/\( x^2 + 1 \)^2

Correct Answer: B

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Question 15

Solve the trigonometric equation \( \sin^2 x + \cos^2 x = 1 \).

A. x = 0

Correct B. x = π/2

C. x = π

D. x = 2π

Correct Answer: B

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Question 16

Find the determinant of the matrix [ egin{pmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{pmatrix} ].

Correct A. -120

B. 120

C. -60

D. 60

Correct Answer: A

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Question 17

If [ f(x) = \frac{x^2 - 4}{x + 2} ], find [ f'(x) ].

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

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

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

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

Correct Answer: A

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Question 18

Solve the system of linear equations [ egin{cases} x + y + z = 6 \\ x + 2y + 3z = 13 \\ x + 3y + 5z = 20 \end{cases} ].

Correct A. (1, 2, 3)

B. (2, 3, 1)

C. (3, 1, 2)

D. (1, 3, 2)

Correct Answer: A

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Question 19

Find the equation of the line pas\sing through the points (2, 3) and (4, 5).

Correct A. y - 3 = \frac{2}{2}\( x - 2 \)

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

C. y - 5 = \frac{2}{2}\( x - 4 \)

D. y - 5 = \frac{2}{2}\( x - 4 \)

Correct Answer: A

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Question 20

Solve the inequality [ 2x^2 + 5x - 3 > 0 ].

Correct A. \( -\infty, -1 \) \cup \( 3, \infty \)

B. \( -\infty, -3 \) \cup \( 1, \infty \)

C. \( -\infty, -1 \) \cup \( 1, \infty \)

D. \( -\infty, -3 \) \cup \( 3, \infty \)

Correct Answer: A

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Question 21

Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.

Correct A. \( 2\( 3^{10}-1 \ \)/\( 3-1 \) )

B. \( 2\( 3^{10}+1 \ \)/\( 3+1 \) )

C. \( 2\( 3^{10}-1 \ \)/\( 3+1 \) )

D. \( 2\( 3^{10}+1 \ \)/\( 3-1 \) )

Correct Answer: A

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Question 22

Solve the matrix equation \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix} \).

Correct A. \( egin{bmatrix} 3 \ 7 \end{bmatrix} \)

B. \( egin{bmatrix} 7 \ 3 \end{bmatrix} \)

C. \( egin{bmatrix} 5 \ 4 \end{bmatrix} \)

D. \( egin{bmatrix} 4 \ 5 \end{bmatrix} \)

Correct Answer: A

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Question 23

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{2}{\( x^2+1 \ \)^2} )

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

Correct Answer: A

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Question 24

A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find its volume.

Correct A. ( 30 ) cm³

B. ( 50 ) cm³

C. ( 70 ) cm³

D. ( 90 ) cm³

Correct Answer: A

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Question 25

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

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

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

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

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

Correct Answer: A

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