POST UTME BABCOCK UNIVERSITY 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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 \( x = 2 \) about the x-axis.
A. \( \frac{16pi}{3} \)
B. \( \frac{32pi}{3} \)
C. \( \frac{64pi}{3} \)
D. \( \frac{128pi}{3} \)
Question 2
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).
A. \( x = -2 \)
B. \( x = 2 \)
C. \( x = -1 \)
D. \( x = 1 \)
Question 3
Find the equation of the circle pas\sing through the points ( (2, 3) ) and ( (4, 5) ).
A. \( x^2 + y^2 - 6x - 4y + 4 = 0 \)
B. \( x^2 + y^2 - 8x - 6y + 9 = 0 \)
C. \( x^2 + y^2 - 10x - 8y + 16 = 0 \)
D. \( x^2 + y^2 - 12x - 10y + 25 = 0 \)
Question 4
Solve the equation \( x^3 - 6x^2 + 11x - 6 = 0 \).
A. \( x = 1, 2, 3 \)
B. \( x = 1, 3, 4 \)
C. \( x = 2, 3, 4 \)
D. \( x = 1, 2, 5 \)
Question 5
Find the area under the curve \( y = \frac{1}{x^2 + 1} \) from \( x = 0 \) to \( x = 1 \).
A. \( \frac{pi}{2} - 1 \)
B. \( \frac{pi}{2} + 1 \)
C. \( \frac{pi}{2} - \frac{1}{2} \)
D. \( \frac{pi}{2} + \frac{1}{2} \)
Question 6
Find the derivative of ( f(x) = \frac{1}{\sqrt{x}} ) u\sing the chain rule.
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}} )
Question 7
Find the determinant of the matrix \( egin{bmatrix} 2 & 3 & 1 \ 4 & 5 & 2 \ 1 & 2 & 3 \end{bmatrix} \).
A. ( 20 )
B. ( 30 )
C. ( 40 )
D. ( 50 )
Question 8
Find the derivative of ( f(x) = \sin^2(x) ) u\sing the chain rule.
A. ( f'(x) = 2\sin\( x)\cos(x \) )
B. ( f'(x) = \sin(x) )
C. ( f'(x) = \cos(x) )
D. ( f'(x) = \tan(x) )
Question 9
Solve the inequality \( \log_{10} \( x^2 - 4 \ \) > 2 ).
A. \( x > 2 \)
B. \( x < 2 \)
C. \( x > 4 \)
D. \( x < 4 \)
Question 10
Solve the system of equations u\sing matrices: \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix} \).
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. \( egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 4 \ 3 \end{bmatrix} \)

Master the Exam!

You've seen a preview, but there are thousands more questions plus AI tutor to break down complex solutions.

Unlock Full Access Available for Android & Windows
Help others prepare! Share this practice hub: