POST UTME CHRISTOPHER UNIVERSITY 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{1 + x^2}} ) u\sing the chain rule.
A. f'(x) = \frac{-x}{\( 1 + x^2 \)^{3/2}}
B. f'(x) = \frac{x}{\( 1 + x^2 \)^{3/2}}
C. f'(x) = \frac{1}{\( 1 + x^2 \)^{3/2}}
D. f'(x) = \frac{-1}{\( 1 + x^2 \)^{3/2}}
Question 2
Solve the matrix equation \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 5 \ 6 \end{bmatrix}.
A. \boxed{\begin{bmatrix} 1 \ 2 \end{bmatrix}}
B. \begin{bmatrix} 2 \ 3 \end{bmatrix}
C. \begin{bmatrix} 3 \ 4 \end{bmatrix}
D. \begin{bmatrix} 4 \ 5 \end{bmatrix}
Question 3
Find the area of the triangle with vertices ( A(0, 0), B(3, 0), C(0, 4) ).
A. 6
B. 12
C. 18
D. 24
Question 4
A circle with center \( C\( -2, 3 \ \) ) and radius 4 passes through the point ( P(1, 2) ). Find the equation of the circle.
A. \( x + 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x + 2 \)^2 + \( y - 3 \)^2 = 25
C. \( x - 2 \)^2 + \( y + 3 \)^2 = 16
D. \( x - 2 \)^2 + \( y + 3 \)^2 = 25
Question 5
Solve the system of linear equations \( egin{cases} x + 2y - 3z = 7 \ 2x - 3y + z = -3 \ 3x + y - 2z = 2 \end{cases} \).
A. x = 1, y = 2, z = 3
B. x = 2, y = 1, z = 3
C. x = 1, y = 3, z = 2
D. x = 3, y = 2, z = 1
Question 6
Find the equation of the circle with center \( -2, 3 \) and radius 4.
A. \( x + 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 2 \)^2 + \( y + 3 \)^2 = 16
C. \( x + 2 \)^2 + \( y + 3 \)^2 = 16
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
Question 7
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \).
A. \frac{64}{3}
B. \frac{32}{3}
C. \frac{16}{3}
D. \frac{8}{3}
Question 8
Find the value of \sum_{n=1}^{\infty} \frac{1}{n^2} u\sing the formula for the sum of an infinite geometric series.
A. \boxed{\frac{\pi^2}{6}}
B. \frac{\pi^2}{12}
C. \frac{\pi^2}{24}
D. \frac{\pi^2}{48}
Question 9
Find the sum of the first 10 terms of the geometric series \( 2 + 6 + 18 + ldots \).
A. 59049
B. 5904
C. 5904.5
D. 59049.5
Question 10
Solve the differential equation \frac{dy}{dx} = \frac{x^2 + 1}{y^2 + 1}.
A. \boxed{y = \tan^{-1}x + C}
B. y = \tan^{-1}x - C
C. y = \tan^{-1}x + C^2
D. y = \tan^{-1}x - C^2
Question 11
Solve for x in the equation \( 2x^2 + 5x - 3 = 0 \) u\sing the quadratic formula.
A. x = \frac{-5 \pm \sqrt{5^2 - 4\( 2)\( -3 \ \)}}{2(2)}
B. x = \frac{-5 \pm \sqrt{5^2 - 4(2)(3)}}{2(2)}
C. x = \frac{-5 \pm \sqrt{5^2 - 4\( 2)\( -1 \ \)}}{2(2)}
D. x = \frac{-5 \pm \sqrt{5^2 - 4(2)(1)}}{2(2)}
Question 12
Find the equation of the line pas\sing through the points (2, 3) and (4, 5).
A. \boxed{y = x + 1}
B. y = x - 1
C. y = x + 2
D. y = x - 2
Question 13
Find the determinant of the matrix \( \begin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \).
A. 1\( 5*9 - 6*8 \) - 2\( 4*9 - 6*7 \) + 3\( 4*8 - 5*7 \)
B. 1\( 5*9 - 6*8 \) - 2\( 4*9 - 6*7 \) - 3\( 4*8 - 5*7 \)
C. 1\( 5*9 - 6*8 \) + 2\( 4*9 - 6*7 \) + 3\( 4*8 - 5*7 \)
D. 1\( 5*9 - 6*8 \) + 2\( 4*9 - 6*7 \) - 3\( 4*8 - 5*7 \)
Question 14
Find the equation of the circle with center (2, 3) and radius 4.
A. \boxed{\( x - 2 \)^2 + \( y - 3 \)^2 = 16}
B. \( x - 2 \)^2 + \( y - 3 \)^2 = 20
C. \( x - 2 \)^2 + \( y - 3 \)^2 = 12
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 8
Question 15
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
A. 2x
B. -2x
C. \frac{-2x}{\( x^2 + 1 \)^2}
D. \frac{2x}{\( x^2 + 1 \)^2}

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