Standard +0.3 This is a standard FP2 partial fractions question with a linear and irreducible quadratic factor. While it requires handling the parameter 'a' and setting up the form A/(x-2a) + (Bx+C)/(x²+a²), the method is routine for Further Maths students. The algebraic manipulation is straightforward once the correct form is identified, making it slightly above average difficulty due to the parameter but still a textbook exercise.
1 It is given that \(\mathrm { f } ( x ) = \frac { 2 a x } { ( x - 2 a ) \left( x ^ { 2 } + a ^ { 2 } \right) }\), where \(a\) is a non-zero constant. Express \(\mathrm { f } ( x )\) in partial fractions.
1 It is given that $\mathrm { f } ( x ) = \frac { 2 a x } { ( x - 2 a ) \left( x ^ { 2 } + a ^ { 2 } \right) }$, where $a$ is a non-zero constant. Express $\mathrm { f } ( x )$ in partial fractions.
\hfill \mbox{\textit{OCR FP2 2008 Q1 [5]}}