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POST UTME LAUTECH 2017 Mathematics | Objective

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Question 1 View Details

Determine the value of x in the equation \(\frac{1}{2}x^2 + 5x - 3 = 17\).

Correct A. 4

B. -4

C. 6

D. -6

Correct Answer: A

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Question 2 View Details

A histogram of exam scores is shown below. What is the mean of the scores?

A. 60

B. 70

Correct C. 80

D. 90

Correct Answer: C

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Question 3 View Details

Solve the system of equations \(egin{cases} x + y = 4 \ 2x - 3y = 5 \end{cases}\).

Correct A. (2, 2)

B. (3, 1)

C. (4, 0)

D. \(5, -1\)

Correct Answer: A

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Question 4 View Details

Find the sum of the first 10 terms of the geometric series \(2 + 6 + 18 + ldots\).

A. 1950

B. 2050

Correct C. 2150

D. 2250

Correct Answer: C

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Question 5 View Details

A matrix A is given by \(A = \begin{bmatrix} 2 & 1 \ 4 & 3 \end{bmatrix}\). Find the determinant of A.

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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Question 6 View Details

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

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

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

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

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

Correct Answer: A

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Question 7 View Details

A histogram of exam scores is shown below. Find the mean and standard deviation of the scores.

A. Mean: 75, Standard Deviation: 10

Correct B. Mean: 80, Standard Deviation: 15

C. Mean: 85, Standard Deviation: 20

D. Mean: 90, Standard Deviation: 25

Correct Answer: B

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Question 8 View Details

Solve for ( x ) in the equation \(2^x + 3^x = 5^x\).

A. \(x = 2\)

B. \(x = 3\)

Correct C. \(x = 4\)

D. \(x = 5\)

Correct Answer: C

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Question 9 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 - 3 \\)^2 + \(y - 2\)^\(2 = 16\) )

C. \(x - 4 \\)^2 + \(y - 3\)^\(2 = 16\) )

D. \(x - 3 \\)^2 + \(y - 4\)^\(2 = 16\) )

Correct Answer: A

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Question 10 View Details

A population of bacteria is growing at a rate of ( 20% ) per hour. If the initial population is ( 1000 ), find the population after ( 3 ) hours.

Correct A. ( 1000(1.\(2)^3\) )

B. ( 1000(1.\(2)^2\) )

C. ( 1000(1.\(2)^1\) )

D. ( 1000(1.\(2)^0\) )

Correct Answer: A

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Question 11 View Details

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

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

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

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

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

Correct Answer: A

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Question 12 View Details

A circle has a radius of 5 cm. Find the area of the circle using the formula \(A = \pi r^2\).

A. ( 50pi ) \(cm^2\)

Correct B. ( 25pi ) \(cm^2\)

C. ( 75pi ) \(cm^2\)

D. ( 100pi ) \(cm^2\)

Correct Answer: B

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Question 13 View Details

Find the volume of the frustum of a cone with a height of 10 cm, a base radius of 5 cm, and a top radius of 3 cm.

A. ( 100pi ) \(cm^3\)

B. ( 150pi ) \(cm^3\)

Correct C. ( 200pi ) \(cm^3\)

D. ( 250pi ) \(cm^3\)

Correct Answer: C

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Question 14 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. \(x < -\frac{1}{2}\) or \(x < \frac{3}{2}\)

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

Correct Answer: A

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Question 15 View Details

A binary operation ( odot ) is defined as \(a odot b = ab + 2\). Find the value of ( 3 odot 4 ).

A. ( 14 )

B. ( 16 )

Correct C. ( 18 )

D. ( 20 )

Correct Answer: C

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Question 16 View Details

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

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

B. \(\frac{1}{2} \times 4^2 + 3 \times 4 - 2\)

C. \(\frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4^2\)

D. \(\frac{1}{2} \times 4^2 + 3 \times 4 - 2 \times 4\)

Correct Answer: A

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Question 17 View Details

Solve the system of equations \(2x + 3y = 7\) and \(x - 2y = -3\).

Correct A. \(x = 1, y = 2\)

B. \(x = 2, y = 1\)

C. \(x = 1, y = -1\)

D. \(x = -1, y = 1\)

Correct Answer: A

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Question 18 View Details

A histogram of exam scores is shown below. What is the mean score?

A. ( 50 )

Correct B. ( 60 )

C. ( 70 )

D. ( 80 )

Correct Answer: B

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Question 19 View Details

Find the derivative of the function ( f(x) = \(3x^2 + 2x - 5\) ).

Correct A. ( f'\((x) = 6x + 2 )\)

B. ( f'\((x) = 6x - 2 )\)

C. ( f'\((x) =\)\(3x^2 + 2x - 5\) )

D. ( f'\((x) =\)\(3x^2 - 2x - 5\) )

Correct Answer: A

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Question 20 View Details

A binary operation ( oplus ) is defined as \(a oplus b = a + b - ab\). Find the value of ( 2 oplus 3 ).

A. ( 5 )

Correct B. ( 7 )

C. ( 9 )

D. ( 11 )

Correct Answer: B

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Question 21 View Details

A vector ( mathbf{a} ) is given by \(\mathbf{a} = 2\mathbf{i} + 3\mathbf{j}\). Find the magnitude of ( mathbf{a} ).

Correct A. \(\sqrt{13}\)

B. \(\sqrt{15}\)

C. \(\sqrt{17}\)

D. \(\sqrt{19}\)

Correct Answer: A

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Question 22 View Details

A probability distribution is given by ( P(x) = \(\frac{1}{2}\)\\()x^2\) ) for ( 0 leq x leq 2 ). Find the expected value of ( X ).

A. ( 1 )

Correct B. ( 2 )

C. ( 3 )

D. ( 4 )

Correct Answer: B

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Question 23 View Details

A polynomial ( f(x) = \(x^3 - 2x^2 + x - 1\) ) has a root at \(x = 1\). Find the other two roots.

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

B. \(x = 1, x = 2\)

C. \(x = 1, x = 3\)

D. \(x = 2, x = 4\)

Correct Answer: A

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Question 24 View Details

A \fraction \(\frac{1}{2}\) is written in base 8. What is its decimal equivalent?

A. ( 0.5 )

B. ( 0.6 )

C. ( 0.7 )

D. ( 0.8 )

Correct Answer: VIEW ANSWER

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Question 25 View Details

Find the value of \(\int_{0}^{\pi} \frac{1}{1+\sin^2x} dx\).

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

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

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

D. \(\frac{\pi}{6}\)\)

Correct Answer: A

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