POST UTME CHRISTOPHER UNIVERSITY 2021 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 parabola \( y = x^2 \) and the line \( y = 2x \) about the x-axis.
A. \frac{4}{5}
B. \frac{4}{3}
C. \frac{4}{15}
D. \frac{4}{9}
Question 2
Solve the system of equations \( x + y = 2 \) and \( x - y = 1 \) u\sing substitution.
A. x = \frac{3}{2}, y = \frac{1}{2}
B. x = \frac{1}{2}, y = \frac{3}{2}
C. x = 2, y = 1
D. x = 1, y = 2
Question 3
Find the equation of the line pas\sing through the points ( (2,3) ) and ( (4,5) ).
A. \( y = \frac{1}{2}x + \frac{1}{2} \)
B. \( y = 2x - 1 \)
C. \( y = \frac{1}{2}x - 2 \)
D. \( y = 2x + 1 \)
Question 4
Find the equation of the circle with center ( (2,3) ) and radius \( r = 4 \).
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 )
Question 5
Find the equation of the line pas\sing through the points \( (2, 3) \) and \( (4, 5) \) u\sing the slope-intercept form.
A. y = \frac{2}{2}x + 1
B. y = \frac{2}{4}x + 1
C. y = \frac{4}{2}x + 1
D. y = \frac{4}{4}x + 1
Question 6
Find the derivative of the function \( f(x) = \frac{1}{x^2 + 1} \) u\sing the chain rule.
A. \frac{-2x}{\( x^2 + 1 \)^2}
B. \frac{2x}{\( x^2 + 1 \)^2}
C. \frac{-2}{x^2 + 1}
D. \frac{2}{x^2 + 1}
Question 7
Solve the equation \( x^3 + 2x^2 - 7x + 12 = 0 \) u\sing the rational root theorem.
A. x = 1
B. x = -1
C. x = 3
D. x = -3
Question 8
Solve the equation [ \sin^2 x + \cos^2 x = 1 \] for [ x \in \left[ 0, \frac{\pi}{2} \right] \].
A. 0
B. \frac{\pi}{4}
C. \frac{\pi}{2}
D. \frac{3\pi}{4}
Question 9
Find the volume of the frustum of a cone with height \( h = 10 \) cm, and radii of the bases \( r_1 = 4 \) cm and \( r_2 = 6 \) cm.
A. \( \frac{1}{3} pi \( 4^2 + 6^2 + 4 cdot 6 \ \) cdot 10 )
B. \( \frac{1}{3} pi \( 4^2 + 6^2 - 4 cdot 6 \ \) cdot 10 )
C. \( \frac{1}{3} pi \( 4^2 + 6^2 + 4 cdot 6 \ \) cdot 5 )
D. \( \frac{1}{3} pi \( 4^2 + 6^2 - 4 cdot 6 \ \) cdot 5 )
Question 10
Find the determinant of the matrix [ egin{pmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{pmatrix} ].
A. 0
B. 1
C. 2
D. 3
Question 11
Find the surface area of the solid formed by revolving the region bounded by the parabola \( y = x^2 \) and the line \( y = 2x \) about the x-axis.
A. \frac{8}{3}
B. \frac{4}{3}
C. \frac{8}{5}
D. \frac{4}{5}
Question 12
Find the sum of the first 5 terms of the geometric series [ 2 + 6 + 18 + \cdots \].
A. 62
B. 64
C. 66
D. 68
Question 13
Solve the system of equations \( x + y = 4 \) and \( x^2 + y^2 = 16 \).
A. \( x = 2, y = 2 \)
B. \( x = 2, y = 2 \) or \( x = -2, y = -2 \)
C. \( x = 2, y = 2 \) or \( x = -2, y = -2 \) or \( x = 0, y = 4 \)
D. \( x = 2, y = 2 \) or \( x = -2, y = -2 \) or \( x = 4, y = 0 \)
Question 14
In a geometric sequence, the first term is 2 and the common ratio is 3. Find the sum of the first 5 terms.
A. -1102
B. -1020
C. -1000
D. -980
Question 15
Find the determinant of the matrix [ egin{array}{ccc} 2 & 3 & 4 \ 5 & 1 & 2 \ 3 & 2 & 1 \end{array} ].
A. -1
B. 1
C. 2
D. 3

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