POST UTME BABCOCK UNIVERSITY 2022 Mathematics | Objective

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Question 1 View Details
Find the derivative of ( f(x) = \(\frac{1}\){\(\sqrt{x}\)}\) ) using the chain rule.
Correct A. ( f'\((x) = -\)\(\frac{1}{2}\)\\()x^{-\)\(\frac{3}{2}\)\)} )
B. ( f'\((x) =\)\(\frac{1}{2}\)\\()x^{-\)\(\frac{3}{2}\)\)} )
C. ( f'\((x) = -\)\(\frac{1}{2}\)\\()x^{-\)\(\frac{1}{2}\)\)} )
D. ( f'\((x) =\)\(\frac{1}{2}\)\\()x^{-\)\(\frac{1}{2}\)\)} )

Correct Answer: A

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Question 2 View Details
Solve the system of equations using matrices: \(egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix}\).
Correct A. \(egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 1 \ 2 \end{bmatrix}\)
B. \(egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 2 \ 1 \end{bmatrix}\)
C. \(egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 3 \ 4 \end{bmatrix}\)
D. \(egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 4 \ 3 \end{bmatrix}\)

Correct Answer: A

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Question 3 View Details
Find the determinant of the matrix \(egin{bmatrix} 2 & 3 & 1 \ 4 & 5 & 2 \ 1 & 2 & 3 \end{bmatrix}\).
Correct A. ( 20 )
B. ( 30 )
C. ( 40 )
D. ( 50 )

Correct Answer: A

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Question 4 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 5 View Details
Find the derivative of ( f(x) = \\(\sin^2(x)\) ) using the chain rule.
Correct A. ( f'\((x) = 2\)\sin\(x)\cos(x\) )
B. ( f'\((x) =\)\sin(x) )
C. ( f'\((x) =\)\cos(x) )
D. ( f'\((x) =\)\tan(x) )

Correct Answer: A

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Question 6 View Details
Find the volume of the solid formed by revolving the region bounded by the curve (y = \(\frac{1}{2}\\()x^2\)\), the x-axis, and the line \\((y = frac{1}{2}x^2\(x = 2\) about the x-axis.
Correct A. \(\frac{16\pi}{3}\)
B. \(\frac{32\pi}{3}\)
C. \(\frac{64\pi}{3}\)
D. \(\frac{128\pi}{3}\)

Correct Answer: A

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Question 7 View Details
Solve the inequality \(\log_{10} x^2 - 4 \\)\(> 2 ).\)
A. \(x > 2\)
Correct B. \(x < 2\)
C. \(x > 4\)
D. \(x < 4\)

Correct Answer: B

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Question 8 View Details
Find the equation of the circle passing through the points ( (2, 3) ) and ( (4, 5) ).
A. \(x^2 + y^2 - 6x - 4y + 4 = 0\)
Correct B. \(x^2 + y^2 - 8x - 6y + 9 = 0\)
C. \(x^2 + y^2 - 10x - 8y + 16 = 0\)
D. \(x^2 + y^2 - 12x - 10y + 25 = 0\)

Correct Answer: B

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Question 9 View Details
Find the area under the curve \(y = \frac{1}{x^2 + 1}\) from \(x = 0\) to \(x = 1\).
Correct A. \(\frac{\pi}{2} - 1\)
B. \(\frac{\pi}{2} + 1\)
C. \(\frac{\pi}{2} - \frac{1}{2}\)
D. \(\frac{\pi}{2} + \frac{1}{2}\)

Correct Answer: A

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Question 10 View Details
Solve the equation \(x^3 - 6x^2 + 11x - 6 = 0\).
Correct A. \(x = 1, 2, 3\)
B. \(x = 1, 3, 4\)
C. \(x = 2, 3, 4\)
D. \(x = 1, 2, 5\)

Correct Answer: A

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