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POST UTME COVENANT UNIVERSITY 2022 Mathematics | Objective

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Question 1 View Details

Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 32\pi

Correct B. 48\pi

C. 64\pi

D. 80\pi

Correct Answer: B

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Question 2 View Details

If \(f(x) = 3x^2 + 2x - 5\) and \(g(x) = 2x^2 - 3x + 1\), find the derivative of \(f(g(x))\) using the chain rule.

Correct A. \(6x^3 + 10x^2 - 13x + 3\)

B. \(6x^3 + 10x^2 - 13x - 3\)

C. \(6x^3 + 10x^2 + 13x + 3\)

D. \(6x^3 + 10x^2 - 13x - 1\)

Correct Answer: A

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Question 3 View Details

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

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

B. \begin{bmatrix} 2 \ 1 \end{bmatrix}

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

D. \begin{bmatrix} 4 \ 3 \end{bmatrix}

Correct Answer: A

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Question 4 View Details

A fair six-sided die is rolled twice. What is the probability that the sum of the two rolls is 7?

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

B. \(\frac{1}{12}\)\)

Correct C. \(\frac{1}{36}\)\)

D. \(\frac{1}{18}\)\)

Correct Answer: C

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Question 5 View Details

Convert the decimal number 0.375 to a \fraction in its simplest form.

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

B. \(\frac{1}{8}\)\)

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

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

Correct Answer: C

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Question 6 View Details

Find the equation of the line passing through the points ( P(2,3) ) and ( Q(4,5) ).

A. \(y = x + 1\)

B. \(y = x - 1\)

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

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

Correct Answer: C

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Question 7 View Details

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

Correct A. \(x < -1\) or \(x > 3\)

B. \(x < 1\) or \(x > 3\)

C. \(x < -1\) or \(x < 3\)

D. \(x > 1\) or \(x > 3\)

Correct Answer: A

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Question 8 View Details

Find the derivative of the function ( f(x) = \(3x^2 - 2x + 1\) ) using the chain rule.

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

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

C. ( f'\((x) =\)\(6x^2 - 2\) )

D. ( f'\((x) =\)\(6x^2 + 2\) )

Correct Answer: A

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Question 9 View Details

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

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

B. \(x = 2, y = 6\)

C. \(x = 6, y = 2\)

D. \(x = 6, y = 6\)

Correct Answer: A

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Question 10 View Details

Find the equation of the circle with center ( C(2,3) ) and radius \(r = 4\).

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

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

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

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

Correct Answer: A

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Question 11 View Details

In the diagram below, the vector µ\(A = 2i + 3j\) and vector µ\(B = i - 2j\). What is the magnitude of the resultant vector µA + µB?

A. 1.0

B. 3.0

Correct C. 5.0

D. 7.0

Correct Answer: C

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Question 12 View Details

If the equation of a circle is \(x^2\) + \\((y^2 + 4x - 6y - 12\)\(= 0\)\), find the radius of the circle.

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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Question 13 View Details

A rectangular prism has a length of 6 cm, a width of 4 cm, and a height of 3 cm. What is the volume of the prism?

Correct A. 72

B. 80

C. 88

D. 96

Correct Answer: A

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Question 14 View Details

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

A. \(x < -1\)

B. \(x > -1\)

Correct C. \(x < 1\)

D. \(x > 1\)

Correct Answer: C

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Question 15 View Details

Find the equation of the line passing through the points (2, 3) and (4, 5).

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

Correct B. \(y = 2x + 1\)

C. \(y = x - 1\)

D. \(y = x + 1\)

Correct Answer: B

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Question 16 View Details

In the polynomial (p(x) = \(3x^4 - 2x^3 + 5x^2 - x + 1\)\), find the value of \(p -1\\((p(x) = 3x^4 - 2x^3 + 5x^2 - x + 1), find the value of\)\) using the Remainder Theorem.

Correct A. 11

B. 13

C. 15

D. 17

Correct Answer: A

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Question 17 View Details

A circle has equation \(x^2 + y^2 + 4x - 6y - 12 = 0\). Find the coordinates of the center of the circle.

Correct A. \(2, -3\)

B. \(-2, 3\)

C. (3, 2)

D. \(-3, -2\)

Correct Answer: A

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Question 18 View Details

Two events, A and B, are independent. If P(A) = 0.4 and P(B) = 0.6, find P(\(A \cap B\)).

Correct A. 0.24

B. 0.36

C. 0.48

D. 0.60

Correct Answer: A

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Question 19 View Details

A number is represented in base 8 as 1234. What is the value of this number in base 10?

A. 512

B. 768

Correct C. 1024

D. 1280

Correct Answer: C

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Question 20 View Details

A rectangular prism has dimensions 5 cm, 6 cm, and 7 cm. Find the volume of the prism.

Correct A. 210

B. 240

C. 270

D. 300

Correct Answer: A

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Question 21 View Details

Determine the value of \(\frac{1}{2} \log_{10} x^2\)\(= 4\)\).

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 22 View Details

Solve for (x\) in the equation \(\\((x) in the equation \begin{vmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{vmatrix} = 0\).

Correct A. -1

B. 1

C. 2

D. 3

Correct Answer: A

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Question 23 View Details

Find the equation of the line passing through the points \((2,3)\) and \((4,5)\).

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

Correct B. \(y = 2x + 1\)

C. \(y = x + 1\)

D. \(y = x - 1\)

Correct Answer: B

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Question 24 View Details

Solve the inequality \(|x-2| > 3\).

Correct A. \(-∞, -1\) ∪ (5, ∞)

B. \(-∞, 1\) ∪ (5, ∞)

C. \(-∞, -1\) ∪ (2, 5)

D. \(-∞, 1\) ∪ (2, 5)

Correct Answer: A

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Question 25 View Details

Find the value of (\sin(2x)\) given that \\((sin(2x)\(\sin(x) = \frac{3}{5}\) and \(\cos(x) = \frac{4}{5}\).

Correct A. \(\frac{24}{25}\)\)

B. \(\frac{24}{25}\)\)

C. \(\frac{24}{25}\)\)

D. \(\frac{24}{25}\)\)

Correct Answer: A

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