POST UTME CHRISTOPHER UNIVERSITY 2020 Mathematics | Objective

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Question 1 View Details
Find the derivative of the function ( f(x) = \(\frac{1}{x^2 + 1}\)\)\) ) using the chain rule.
A. 2x
B. -2x
Correct C. \(\frac{-2x}{x^2 + 1\) ^2}\)\)
D. \(\frac{2x}{x^2 + 1\) ^2}\)\)

Correct Answer: C

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Question 2 View Details
A circle with center \(C -2, 3 \\) ) and radius 4 passes through the point ( P(1, 2) ). Find the equation of the circle.
Correct 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 + \(y + 3\)^\(2 = 25\)

Correct Answer: A

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Question 3 View Details
Find the sum of the first 10 terms of the geometric series \(2 + 6 + 18 + ldots\).
Correct A. 59049
B. 5904
C. 5904.5
D. 59049.5

Correct Answer: A

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Question 4 View Details
Solve the system of linear equations \(egin{cases} x + 2y - 3z = 7 \ 2x - 3y + z = -3 \ 3x + y - 2z = 2 \end{cases}\).
Correct A. \(x = 1\), \(y = 2\), \(z = 3\)
B. \(x = 2\), \(y = 1\), \(z = 3\)
C. \(x = 1\), \(y = 3\), \(z = 2\)
D. \(x = 3\), \(y = 2\), \(z = 1\)

Correct Answer: A

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Question 5 View Details
Find the area of the triangle with vertices ( A(0, 0), B(3, 0), C(0, 4) ).
Correct A. 6
B. 12
C. 18
D. 24

Correct Answer: A

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Question 6 View Details
Find the equation of the circle with center (2, 3) and radius 4.
Correct 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 + \(y - 3\)^\(2 = 8\)

Correct Answer: A

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Question 7 View Details
Solve the differential equation \(\frac{dy}{dx}\)\) = \(\frac{x^2 + 1}{y^2 + 1}\)\)\).
Correct 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\)

Correct Answer: A

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Question 8 View Details
Find the value of \sum_{\(n = 1\)}^{\infty} \(\frac{1}{n^2}\)\)\) using the formula for the sum of an infinite geometric series.
Correct A. \boxed{\(\frac{\pi^2}{6}\)\)\)}
B. \(\frac{\pi^2}{12}\)\)\)
C. \(\frac{\pi^2}{24}\)\)\)
D. \(\frac{\pi^2}{48}\)\)\)

Correct Answer: A

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Question 9 View Details
Solve the matrix equation \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 5 \ 6 \end{bmatrix}.
Correct 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}

Correct Answer: A

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Question 10 View Details
Find the equation of the line passing through the points (2, 3) and (4, 5).
Correct A. \boxed{\(y = x + 1\)}
B. \(y = x - 1\)
C. \(y = x + 2\)
D. \(y = x - 2\)

Correct Answer: A

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Question 11 View Details
Find the derivative of the function ( f(x) = \(\frac{1}\){\sqrt{1 + \(x^2}}\)\) ) using the chain rule.
A. f'\((x) =\)\(\frac{-x}\){ 1 + \(x^2\) \)^{\(3/2\)}}\)
Correct 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 + \(x^2\) \)^{\(3/2\)}}\)

Correct Answer: B

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Question 12 View Details
Solve for x in the equation \(2x^2 + 5x - 3 = 0\) using the quadratic formula.
Correct 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)}\)

Correct Answer: A

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Question 13 View Details
Find the equation of the circle with center \(-2, 3\) and radius 4.
Correct 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 + \(y - 3\)^\(2 = 16\)

Correct Answer: A

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Question 14 View Details
Find the determinant of the matrix \(\begin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix}\).
Correct 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\(4*8 - 5*7\)

Correct Answer: A

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Question 15 View Details
Find the area under the curve \(y = x^2\) from \(x = 0\) to \(x = 4\).
Correct A. \(\frac{64}{3}\)\)
B. \(\frac{32}{3}\)\)
C. \(\frac{16}{3}\)\)
D. \(\frac{8}{3}\)\)

Correct Answer: A

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