Gce Model Questions Vol1 2024 Further Mathematics Question 38

Practice objective / multiple choice question 38 from the 2024 Gce Model Questions Vol1 Further Mathematics examination.

Gce Model Questions Vol1 2024 Further Mathematics Objective / Multiple Choice Medium Difficulty
Question 38 GCE_MODEL_QUESTIONS_VOL1 • 2024 • FURTHER_MATHEMATICS • objective

Find the value of the parameter \(a\) for which the rational function \(\dfrac{x^{2}+ax+1}{(x+1)(x^{2}+2x+5)}\) can be written as \(\dfrac{A}{x+1}+\dfrac{Bx+C}{x^{2}+2x+5}\) where \(B\) is an integer and the numerator of the quadratic part is a constant multiple of the derivative of its denominator. Then evaluate \(\displaystyle\int \frac{x^{2}+ax+1}{(x+1)(x^{2}+2x+5)}\,dx\).

Answer Options

Correct Answer A. a = 2; \(\displaystyle\int = \frac12\ln\big((x+1)^{2}+4\big)+C\)
B. a = 2; \(\displaystyle\int = \frac12\ln\big((x+2)^{2}+4\big)+C\)
C. a = 2; \(\displaystyle\int = \frac13\ln\big((x+1)^{2}+4\big)+C\)
D. a = 1; \(\displaystyle\int = \frac12\ln\big((x+1)^{2}+4\big)+C\)
Correct Answer
A
Correct Option:
a = 2; \(\displaystyle\int = \frac12\ln\big((x+1)^{2}+4\big)+C\)

About This Question

This is Gce Model Questions Vol1 2024 Further Mathematics Question 38. It is one of the objective questions from the 2024 Gce Model Questions Vol1 Further Mathematics examination.

Difficulty level: Medium .

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