OCR Pure 1 2018 March — Question 9

Exam BoardOCR
ModulePure 1 (Pure Mathematics 1)
Year2018
SessionMarch
TopicPartial Fractions
TypeRepeated linear factor with series expansion

9
  1. Express \(\frac { 5 + 4 x - 3 x ^ { 2 } } { ( 1 - 2 x ) ( 2 + x ) ^ { 2 } }\) in three partial fractions.
  2. Hence find the first three terms in the expansion of \(\frac { 5 + 4 x - 3 x ^ { 2 } } { ( 1 - 2 x ) ( 2 + x ) ^ { 2 } }\) in ascending powers of \(x\).
  3. State the set of values for which the expansion in part (ii) is valid.