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POST UTME COVENANT UNIVERSITY 2018 Mathematics | Objective

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Question 1 View Details

Determine the value of (x\) in the equation [ egin{pmatrix} 2 & 1 \ 3 & 2 \\((x) in the equation [ egin{pmatrix} 2 & 1 \end{pmatrix} egin{pmatrix} x \ 1 \end{pmatrix} = egin{pmatrix} 5 \ 8 \end{pmatrix} ].

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 2 View Details

A set (S\) contains the elements \(\\((S) contains the elements \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}\). If \(T\\(}). If\) is a subset of \(S\) such that \(T\) contains the elements of (S\) that are greater than \(5\\((S) that are greater than\), what is the number of elements in \(T\)?

A. 5

Correct B. 6

C. 7

D. 8

Correct Answer: B

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Question 3 View Details

The sequence \(\{a_n\}\) is defined by (a_\(n = 2n + 1\)\) for \(n = 1, 2, 3, \\((a_n = 2n + 1) for \dots\). Find the sum of the first five terms of the sequence.

A. 30

B. 35

Correct C. 40

D. 45

Correct Answer: C

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Question 4 View Details

Solve the inequality \(\frac{x}{2} + 3 > 7\).

Correct A. \(x > 8\)

B. \(x < 8\)

C. \(x > 2\)

D. \(x < 2\)

Correct Answer: A

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Question 5 View Details

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

A. 2

B. 4

Correct C. 8

D. 16

Correct Answer: C

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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. f'\((x) =\)\(\frac{-x}\){ \(x^2 + 1\) \)^{\(3/2\)}}\)

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

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

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

Correct Answer: A

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Question 7 View Details

Solve the equation \(x^2 + 4x + 4 = 0\) using the quadratic formula.

A. \(\frac{-4 \pm \sqrt{16 - 16}\)}{2}\)

B. \(\frac{-4 \pm \sqrt{16 + 16}\)}{2}\)

Correct C. \(\frac{-4 \pm \sqrt{16 - 4}\)}{2}\)

D. \(\frac{-4 \pm \sqrt{16 + 4}\)}{2}\)

Correct Answer: C

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Question 8 View Details

Find the area under the curve \(y = x^2\) from \(x = 0\) to \(x = 2\) using integration.

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

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

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

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

Correct Answer: A

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Question 9 View Details

Find the equation of the circle with center ( (2, 3) ) and radius ( 4 ) using the standard form.

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

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

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

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

Correct Answer: A

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Question 10 View Details

Find the derivative of the function ( f(x) = \sin\(x^2\) ) using the chain rule.

Correct A. f'\((x) = 2x\)\cos\(x^2\)

B. f'\((x) = -2x\)\cos\(x^2\)

C. f'\((x) =\)\(x^2\) \cos\(x^2\)

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

Correct Answer: A

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Question 11 View Details

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

A. 24

B. 36

Correct C. 48

D. 60

Correct Answer: C

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Question 12 View Details

Solve the system of linear equations using matrices: \(egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 7 \ 10 \end{bmatrix}\).

Correct A. [1, 2]

B. [2, 3]

C. [3, 4]

D. [4, 5]

Correct Answer: A

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Question 13 View Details

Find the probability of drawing two cards from a deck of 52 cards such that the second card drawn is a heart given that the first card drawn is a heart.

Correct A. \(1/3\)

B. \(1/4\)

C. \(1/5\)

D. \(1/6\)

Correct Answer: A

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Question 14 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 15 View Details

Solve the quadratic equation \(x^2 + 4x + 4 = 0\).

Correct A. \(x = -2\)

B. \(x = 2\)

C. \(x = -1\)

D. \(x = 1\)

Correct Answer: A

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Question 16 View Details

Find the volume of the solid formed by revolving the region bounded by the curves \(y = x^2\) and \(y = 4 - x^2\) about the x-axis.

A. 32\pi

B. 64\pi

Correct C. 128\pi

D. 256\pi

Correct Answer: C

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Question 17 View Details

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

A. 10

B. 100

Correct C. 1000

D. 10000

Correct Answer: C

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Question 18 View Details

A particle moves along the curve (y = \(x^3 - 6x^2 + 9x + 2\)\) with a velocity of \(\\((y = x^3 - 6x^2 + 9x + 2) with a velocity of \frac{dy}{dt} = 6x^2 - 12x + 9\). Find the acceleration of the particle at the point where \(x = 1\).

A. 18

B. 36

Correct C. 54

D. 72

Correct Answer: C

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Question 19 View Details

Find the area of the region bounded by the curves \(y = x^2\) and \(y = 4 - x^2\).

A. 16

B. 32

Correct C. 64

D. 128

Correct Answer: C

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Question 20 View Details

Solve the equation \(\frac{dy}{dx} = \frac{x^2 + 1}{x^2 - 1}\) for \(y\).

Correct A. \(y =\)\(\frac{1}{2}\)\) \log \(x^2 - 1\) + C

B. \(y =\)\(\frac{1}{2}\)\) \log \(x^2 + 1\) + C

C. \(y =\)\(\frac{1}{2}\)\) \log \(x^2 - 1\) - C

D. \(y =\)\(\frac{1}{2}\)\) \log \(x^2 + 1\) - C

Correct Answer: A

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Question 21 View Details

Let A be a 3x3 matrix with determinant 6. If A is multiplied by a scalar k, what is the determinant of kA?

Correct A. \(6k^3\)

B. 6k

C. 6

D. \(6k^2\)

Correct Answer: A

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Question 22 View Details

A polynomial P(x) has roots at x = -2, \(x = 1\), and \(x = 3\). What is the polynomial P(x) in factored form?

Correct A. \(x + 2\), x - 1\)\(x - 3\)

B. \(x - 2\), x + 1\)\(x - 3\)

C. \(x + 2\), x + 1\)\(x - 3\)

D. \(x - 2\), x - 1\)\(x + 3\)

Correct Answer: A

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Question 23 View Details

A set A contains the elements {1, 2, 3, 4, 5}. What is the number of subsets of A that contain exactly 3 elements?

Correct A. 10

B. 20

C. 30

D. 40

Correct Answer: A

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Question 24 View Details

A sequence is defined by the formula \(a_n = 2n + 1\). What is the sum of the first 5 terms of the sequence?

Correct A. 15

B. 20

C. 25

D. 30

Correct Answer: A

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Question 25 View Details

A histogram is shown below. What is the mean of the data represented by the histogram?

A. 20

Correct B. 25

C. 30

D. 35

Correct Answer: B

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