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POST UTME COVENANT UNIVERSITY 2023 Mathematics | Objective

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Question 1 View Details

Determine the value of \(\mathbf{a} \cdot \mathbf{b} \times \mathbf{c}\) ) given that \(\mathbf{a} = egin{pmatrix} 1 \\() ) given that (\ 2 \ 3 \end{pmatrix}\), mathbf{b} = egin{pmatrix} 4 \ 5 \ 6 \end{pmatrix}\), and \(\mathbf{c} = egin{pmatrix} 7 \ 8 \ 9 \end{pmatrix}\).

A. -18

B. 18

Correct C. 0

D. 36

Correct Answer: C

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Question 2 View Details

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

A. \(x = \frac{\pi}{2}\)

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

C. \(x = \frac{3\pi}{4}\)

D. \(x = \frac{5\pi}{4}\)

Correct Answer: B

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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. \(y = \frac{1}{2}x + \frac{1}{2}\)

B. \(y = \frac{1}{2}x - \frac{1}{2}\)

C. \(y = 2x - 1\)

D. \(y = 2x + 1\)

Correct Answer: A

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Question 4 View Details

A cylindrical \tank with a radius of 4 meters and a height of 10 meters is filled with water. Find the volume of water in the \tank.

A. 160π

B. 320π

Correct C. 640π

D. 1280π

Correct Answer: C

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Question 5 View Details

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

A. -2

Correct B. 2

C. 4

D. 6

Correct Answer: B

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Question 6 View Details

Let \(A = egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix}\) and \(B = egin{bmatrix} 5 & 6 \ 7 & 8 \end{bmatrix}\). Find ( AB ) if it exists.

Correct A. \begin{bmatrix} 19 & 22 \\ 43 & 50 \end{bmatrix}

B. \begin{bmatrix} 11 & 14 \\ 23 & 28 \end{bmatrix}

C. \begin{bmatrix} 17 & 20 \\ 37 & 44 \end{bmatrix}

D. \begin{bmatrix} 13 & 16 \\ 29 & 36 \end{bmatrix}

Correct Answer: A

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Question 7 View Details

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

Correct A. \(x =\)\(\frac{\pi}{4}\)\)

B. \(x =\)\(\frac{\pi}{2}\)\)

C. \(x =\)\(\frac{\pi}{6}\)\)

D. \(x =\)\(\frac{\pi}{3}\)\)

Correct Answer: A

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Question 8 View Details

Find the sum of the first 10 terms of the arithmetic progression \(2, 5, 8, \ldots\).

Correct A. 55

B. 60

C. 65

D. 70

Correct Answer: A

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Question 9 View Details

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

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

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

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

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

Correct Answer: A

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Question 10 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 + \(y - 3\)^\(2 = 25\)

C. \(x - 2\)^2 + \(y - 3\)^\(2 = 36\)

D. \(x - 2\)^2 + \(y - 3\)^\(2 = 49\)

Correct Answer: A

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Question 11 View Details

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

A. 2.999999999

Correct B. 3.000000001

C. 3.000000002

D. 3.000000003

Correct Answer: B

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Question 12 View Details

Solve for x in the equation \(\begin{array}{c} 2x + 5y = 11 \ 3x - 2y = -7 \end{array}\) using matrices.

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

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

Correct Answer: A

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Question 14 View Details

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

Correct A. \(x =\)\(\frac{\pi}{4}\)\)

B. \(x =\)\(\frac{\pi}{2}\)\)

C. \(x =\)\(\frac{3\pi}{4}\)\)

D. \(x =\)\(\frac{5\pi}{4}\)\)

Correct Answer: A

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Question 15 View Details

Find the determinant of the matrix \(\begin{array}{ccc} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{array}\).

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 16 View Details

Solve the inequality \(\frac{x-2}{x+1} \geq 0\) for ( x in mathbb{R} ).

Correct A. \(x \leq -1\) or ( x geq 2 )

B. \(x < -1\) or \(x > 2\)

C. \(x \leq -1\) or \(x > 2\)

D. \(x < -1\) or ( x leq 2 )

Correct Answer: A

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Question 17 View Details

Find the mean of the data set ( { 2, 4, 6, 8, 10 } ).

Correct A. 6

B. 8

C. 10

D. 12

Correct Answer: A

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Question 18 View Details

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

Correct A. \(x = -2\)

B. \(x = -1\)

C. \(x = 0\)

D. \(x = 1\)

Correct Answer: A

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Question 19 View Details

Find the sum of the first 5 terms of the arithmetic progression ( 2, 5, 8, 11, ldots ).

Correct A. 30

B. 40

C. 50

D. 60

Correct Answer: A

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Question 20 View Details

Solve the inequality \(\log_{10} x^2 \\)\(> 4 ).\)

Correct A. \(x > 10\)

B. \(x < -10\)

C. \(x > 100\)

D. \(x < -100\)

Correct Answer: A

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Question 21 View Details

Find the derivative of the function ( f(x) = \(\frac{x^2 + 2x - 3}{x^2 - 4}\)\)\) ) using the quotient rule.

A. \(\frac{2x x^2 - 4 - x^2 + 2x - 3\) (2x)}{ \(x^2 - 4\) ^2}\)\)

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

Correct C. \(\frac{2x x^2 - 4 - x^2 + 2x - 3\) (2x)}{ \(x^2 - 4\) ^2}\)\)

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

Correct Answer: C

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Question 22 View Details

A fair six-sided die is rolled. What is the probability that the number obtained is greater than 4?

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

B. \(\frac{2}{6}\)\)

C. \(\frac{3}{6}\)\)

Correct D. \(\frac{4}{6}\)\)

Correct Answer: D

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Question 23 View Details

Solve the system of equations using matrices: \begin{align*} 2x + 3y &= 7 \ 4x - 2y &= -3 \end{align*}

Correct A. \begin{pmatrix} x \ y \end{pmatrix} = \begin{pmatrix} 1 \ 2 \end{pmatrix}

B. \begin{pmatrix} x \ y \end{pmatrix} = \begin{pmatrix} 2 \ 1 \end{pmatrix}

C. \begin{pmatrix} x \ y \end{pmatrix} = \begin{pmatrix} 3 \ 4 \end{pmatrix}

D. \begin{pmatrix} x \ y \end{pmatrix} = \begin{pmatrix} 4 \ 3 \end{pmatrix}

Correct Answer: A

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Question 24 View Details

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

A. \(\frac{14}{3}\)\)

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

C. \(\frac{18}{3}\)\)

D. \(\frac{20}{3}\)\)

Correct Answer: B

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Question 25 View Details

A bag contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?

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

B. \(\frac{2}{7}\)\)

C. \(\frac{3}{7}\)\)

Correct D. \(\frac{4}{7}\)\)

Correct Answer: D

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