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POST UTME LEAD CITY UNIVERSITY 2017 Mathematics | Objective

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Question 1 View Details

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

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

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

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

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

Correct Answer: C

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Question 2 View Details

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

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

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

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

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

Correct Answer: A

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Question 3 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 - 2 \\)^2 + \(y - 3\)^\(2 = 25\) )

D. \(x - 3 \\)^2 + \(y - 2\)^\(2 = 25\) )

Correct Answer: A

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Question 4 View Details

A card is drawn from a standard deck of 52 cards. What is the probability that the card is a heart or a diamond?

A. \(\frac{13}{52}\)

Correct B. \(\frac{26}{52}\)

C. \(\frac{39}{52}\)

D. \(\frac{52}{52}\)

Correct Answer: B

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Question 5 View Details

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

Correct A. \(\frac{8\pi}{3}\)

B. \(\frac{16\pi}{3}\)

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

D. \(\frac{64\pi}{3}\)

Correct Answer: A

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Question 6 View Details

Solve the quadratic equation \(x^2 + 4x + 4 = 0\) using the quadratic formula. What is the value of ( x )?

A. 0

Correct B. -2

C. 2

D. -1

Correct Answer: B

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Question 7 View Details

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

Correct A. 6x + 2

B. 6x - 2

C. \(3x^2 + 2\)

D. \(3x^2 - 2\)

Correct Answer: A

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Question 8 View Details

Solve the system of linear equations using matrices. Find the values of ( x ) and ( y ) in the system \(\begin{bmatrix} 2 & 1 \ 1 & 2 \ \end{bmatrix} \begin{bmatrix} x \ y \ \end{bmatrix} = \begin{bmatrix} 3 \ 4 \ \end{bmatrix} \\).

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

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

C. \(x = 3\), \(y = 4\)

D. \(x = 4\), \(y = 3\)

Correct Answer: A

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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. \(x - 2\)^2 + \(y - 3\)^\(2 = 9\) \)

D. \(x - 3\)^2 + \(y - 2\)^\(2 = 9\) \)

Correct Answer: A

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Question 10 View Details

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

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

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

C. \(-\frac{1}{x^3}\)

D. \(\frac{1}{x^3}\)

Correct Answer: A

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Question 11 View Details

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

A. 0

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

C. \(\frac{\pi}{2}\)\)

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

Correct Answer: B

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Question 12 View Details

A set (A\) is defined as A = \{x \\((A) is defined as A = \in \mathbb{R} : \\((x^2 + 2x + 1\)\(> 0)\)\}. Find the value of \(\\()}. Find the value of \cup A\).

Correct A. \mathbb{R}

B. \(-\infty, 0\)

C. \(0, \infty\)

D. \(-1, 1\)

Correct Answer: A

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Question 13 View Details

Find the value of \(\sum_{n = 1}^{\infty} \frac{1}{n^2}\).

Correct A. 1

B. \(\frac{1}{2}\)\)

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

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

Correct Answer: A

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Question 14 View Details

A sequence (a_n\) is defined as \(a_\(n =\)\\((a_n) is defined as \(\frac{1}{n}\)). Find the value of \lim_{n \to \\(). Find the value of lim_{n \infty} a_n.

Correct A. 0

B. 1

C. \(\frac{1}{2}\)\)

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

Correct Answer: A

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Question 15 View Details

A probability experiment consists of rolling a fair six-sided die. Find the probability that the number rolled is greater than 4.

A. \(\frac{1}{6}\)\)

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

C. \(\frac{1}{2}\)\)

Correct D. \(\frac{2}{3}\)\)

Correct Answer: D

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Question 16 View Details

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

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 17 View Details

Solve the inequality \(\frac{1}{x-2} + \frac{1}{x+2} \leq \frac{1}{2}\).

A. x \in \(-\infty, -2\) \cup \(2, \infty\)

B. x \in \(-\infty, -2\) \cup (2, 4]

Correct C. x \in \(-\infty, -2\) \cup (2, \infty]

D. x \in \(-\infty, -2] \cup 2, \infty \\)

Correct Answer: C

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Question 18 View Details

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

A. 10

Correct B. 12

C. 14

D. 16

Correct Answer: B

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Question 19 View Details

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

A. \(x = -1\)

Correct B. \(x = 1\)

C. \(x = -2\)

D. \(x = 2\)

Correct Answer: B

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Question 20 View Details

Find the value of (x\) in the equation \(\\((x) in the equation \log_{10} x^2\)\(= 4\)\).

A. 2

Correct B. 4

C. 8

D. 16

Correct Answer: B

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Question 21 View Details

Find the determinant of the matrix [ egin{array}{ccc} 2 & 3 & 1 \ 4 & 5 & 2 \ 1 & 2 & 3 \end{array} ].

Correct A. -3

B. 3

C. -1

D. 1

Correct Answer: A

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Question 22 View Details

A sequence is defined by the recurrence relation [ a_\(n = 2a\)_{n-1} + 3 ] with initial term [ \(a_1 = 2\) ]. Find the sum of the first five terms of the sequence.

A. 55

Correct B. 65

C. 75

D. 85

Correct Answer: B

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Question 23 View Details

The mean of a set of five numbers is 15. If one of the numbers is 10, find the sum of the remaining four numbers.

Correct A. 50

B. 60

C. 70

D. 80

Correct Answer: A

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Question 24 View Details

Solve the equation [ \\((2x^2 + 3x - 1\)\(= 0\)\) ].

A. \(x =\)\(-1/2\)

Correct B. \(x = 1/2\)\)

C. \(x = -1\)

D. \(x = 1\)

Correct Answer: B

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Question 25 View Details

Find the vector [ mathbf{a} ] such that [ mathbf{a} cdot mathbf{b}\(= 10\)] and [ mathbf{a} cdot mathbf{c}\(= 5\)], where [ mathbf{b} = egin{pmatrix} 2 \ 3 \end{pmatrix} ] and [ mathbf{c} = egin{pmatrix} 1 \ 2 \end{pmatrix} ].

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

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

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

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

Correct Answer: A

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