POST UTME COVENANT UNIVERSITY 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A right circular cone has a height of 20 cm and a base radius of 10 cm. Find the volume of the cone.
A. 2000\pi cm^3
B. 1000\pi cm^3
C. 500\pi cm^3
D. 2500\pi cm^3
Question 2
Find the value of [ \log_{10} left\( \frac{1}{\sqrt{2}} \right \) ].
A. \( -\frac{1}{2} \)
B. \( -\frac{3}{2} \)
C. \( -\frac{1}{4} \)
D. \( -\frac{3}{4} \)
Question 3
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \) u\sing the quadratic formula.
A. \( x = -2 \)
B. \( x = -1 \)
C. \( x = 0 \)
D. \( x = 1 \)
Question 4
A line passes through the points (2, 3) and (4, 5). What is the equation of the line in slope-intercept form?
A. y = x + 1
B. y = x - 1
C. y = -x + 1
D. y = x + 2
Question 5
A circle has a diameter of 10 cm. What is the area of the circle?
A. 50\pi
B. 75\pi
C. 100\pi
D. 125\pi
Question 6
A cylindrical \tank has a height of 10m and a radius of 4m. If the \tank is filled with water to a height of 6m, find the volume of water in the \tank.
A. ( 120pi ) m³
B. ( 240pi ) m³
C. ( 480pi ) m³
D. ( 960pi ) m³
Question 7
Find the equation of the line pas\sing through the points ( (1, 2) ) and ( (3, 4) ).
A. \( y = 2x - 1 \)
B. \( y = 2x + 1 \)
C. \( y = 3x - 2 \)
D. \( y = 3x + 2 \)
Question 8
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. x < -1 or x > \frac{3}{2}
B. x < -1 or x < \frac{3}{2}
C. x > -1 or x > \frac{3}{2}
D. x > -1 or x < \frac{3}{2}
Question 9
Find the derivative of the function ( f(x) = \frac{1}{2x^2 + 3x - 1} ) u\sing the quotient rule.
A. \( \frac{-2x + 3}{\( 2x^2 + 3x - 1 \ \)^2} )
B. \( \frac{2x + 3}{\( 2x^2 + 3x - 1 \ \)^2} )
C. \( \frac{2x^2 + 3x - 1}{\( 2x^2 + 3x - 1 \ \)^2} )
D. \( \frac{2x^2 + 3x - 1}{\( 2x^2 + 3x - 1 \ \)^3} )
Question 10
A fair six-sided die is rolled 5 times. What is the probability that the sum of the numbers obtained is greater than 20?
A. \( \frac{1}{6} \)
B. \( \frac{1}{3} \)
C. \( \frac{1}{2} \)
D. \( \frac{2}{3} \)
Question 11
Solve the system of linear equations u\sing matrices:\n\n\( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 7 \ 11 \end{bmatrix} \)
A. \( x = 3, y = 2 \)
B. \( x = 2, y = 3 \)
C. \( x = 1, y = 4 \)
D. \( x = 4, y = 1 \)
Question 12
Simplify the expression \( 2x^2 + 3x - 1 \ \) \times \( x^2 - 2x + 1 \) ).
A. \( 2x^4 - 7x^3 + 8x^2 + x - 1 \)
B. \( 2x^4 - 7x^3 + 8x^2 - x - 1 \)
C. \( 2x^4 - 7x^3 + 8x^2 + 2x - 1 \)
D. \( 2x^4 - 7x^3 + 8x^2 - 2x - 1 \)
Question 13
In a circle with center $O$ and radius $5$, a chord $AB$ is drawn such that $OA = 3$. Find the length of the chord $AB$.
A. \sqrt{91}
B. \sqrt{121}
C. \sqrt{169}
D. \sqrt{289}
Question 14
A rec\tangular prism has a length of 6 cm, a width of 4 cm, and a height of 3 cm. Find the volume of the prism.
A. 72 cm^3
B. 96 cm^3
C. 108 cm^3
D. 120 cm^3
Question 15
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
A. ( f'(x) = \frac{-2x}{\( x^2 + 1 \)^2} )
B. ( f'(x) = \frac{2x}{\( x^2 + 1 \)^2} )
C. ( f'(x) = \frac{2}{\( x^2 + 1 \)^2} )
D. ( f'(x) = \frac{-2}{\( x^2 + 1 \)^2} )

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