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POST UTME LASU 2017 Mathematics | Objective

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Question 1 View Details

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

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

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 View Details

Find the equation of the line passing 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 View Details

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

Correct A. The mean score is 60.

B. The median score is 60.

C. The mode score is 60.

D. The standard deviation is 10.

Correct Answer: A

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Question 5 View Details

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 View Details

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 missing data point?

Correct A. 22

B. 20

C. 18

D. 16

Correct Answer: A

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Question 7 View Details

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 View Details

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 \(x = \\((cm^2), what is the value of x in the equation \frac{\pi r^2}{A}\)?

A. 2

B. 3

C. 4

Correct D. 5

Correct Answer: D

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Question 9 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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

A. \(x = 0\)

Correct B. \(x =\)π/2

C. \(x =\)π

D. \(x = 2\)π

Correct Answer: B

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Question 16 View Details

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 View Details

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 View Details

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 View Details

Find the equation of the line passing 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 View Details

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 View Details

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 View Details

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 View Details

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

A rectangular 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 View Details

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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