POST UTME COAL CITY UNIVERSITY 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve for x in the equation \( \frac{x}{2} + 5 = 3x - 2 \) u\sing the method of substitution.
A. \( x = 4 \)
B. \( x = -2 \)
C. \( x = 2 \)
D. \( x = -4 \)
Question 2
Find the volume of the frustum of a cone with radii 6 cm and 4 cm and height 10 cm.
A. 1000\pi cm^3
B. 1200\pi cm^3
C. 1500\pi cm^3
D. 1800\pi cm^3
Question 3
Solve the system of linear equations \begin{align*} x + y &= 2 \ x - 2y &= -3 \end{align*}
A. \left\( -1, \frac{5}{2} \right \)
B. \left\( 1, -1 \right \)
C. \left\( -1, -1 \right \)
D. \left\( 1, \frac{5}{2} \right \)
Question 4
A particle moves along the curve y = x^3 - 6x^2 + 9x + 2. Find the equation of the \tangent line at the point where x = 1.
A. y = 3x - 5
B. y = 3x - 7
C. y = 3x - 9
D. y = 3x - 11
Question 5
Find the derivative of the function f(x) = 3x^2 + 2x - 5.
A. 6x + 2
B. 6x - 2
C. 3x + 2
D. 3x - 2
Question 6
Solve the system of linear equations \( egin{cases} 2x + 3y = 7 \ 4x - 2y = -3 \end{cases} \).
A. \( x = 1, y = 2 \)
B. \( x = 2, y = 1 \)
C. \( x = 1, y = 1 \)
D. \( x = 2, y = 2 \)
Question 7
Find the determinant of the matrix \( egin{bmatrix} 2 & 3 & 1 \ 4 & 1 & 2 \ 3 & 2 & 4 \end{bmatrix} \).
A. ( 10 )
B. \( -10 \)
C. ( 20 )
D. \( -20 \)
Question 8
Find the derivative of the function ( f(x) = 3x^2 + 2x - 5 ) u\sing the power rule.
A. 6x + 2
B. 6x - 2
C. 3x^2 + 2
D. 3x^2 - 2
Question 9
A die is rolled 5 times. Find the probability that exactly 3 of the rolls result in an even number.
A. \frac{125}{512}
B. \frac{1}{32}
C. \frac{5}{32}
D. \frac{1}{16}
Question 10
Find the area under the curve y = x^2 + 1 from x = 0 to x = 2.
A. 7
B. 9
C. 11
D. 13
Question 11
A sequence is defined as a_1 = 2, a_2 = 4, a_n = a_{n-1} + 2. Find the 10th term of the sequence.
A. 20
B. 22
C. 24
D. 26
Question 12
Find the value of \( \frac{d}{dx} left\( \frac{1}{x^2 + 1} \right \ \) ) u\sing the chain rule.
A. \( \frac{-2x}{\( x^2 + 1 \ \)^2} )
B. \( \frac{2x}{\( x^2 + 1 \ \)^2} )
C. \( \frac{2}{\( x^2 + 1 \ \)^2} )
D. \( \frac{-2}{\( x^2 + 1 \ \)^2} )
Question 13
Find the derivative of the function f(x) = 3x^2 + 2x - 5.
A. 6x + 2
B. 6x - 2
C. 3x + 2
D. 3x - 2
Question 14
Find the sum of the first 10 terms of the arithmetic progression 2, 5, 8, ...
A. 155
B. 165
C. 175
D. 185
Question 15
Find the equation of the circle with center (2, 3) and radius 4.
A. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 3 \)^2 + \( y - 2 \)^2 = 16
C. \( x + 2 \)^2 + \( y + 3 \)^2 = 16
D. \( x - 3 \)^2 + \( y - 2 \)^2 = 25

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