OCR FP2 2008 June — Question 1 5 marks

Exam BoardOCR
ModuleFP2 (Further Pure Mathematics 2)
Year2008
SessionJune
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicPartial Fractions
TypePartial fractions with quadratic in denominator
DifficultyStandard +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.
Spec1.02y Partial fractions: decompose rational functions

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.

AnswerMarks
(a) \(2x^2 - 7x - 4 = (2x + 1)(x - 4)\) or \(3x^2 + x - 2 = (3x - 2)(x + 1)\)B1
\(\frac{2x + 1}{3x - 2}\) as final answer; this answer onlyB1
(b) For correct leading term \(x\) in quotientB1
For evidence of correct division processM1
Quotient = \(x - 2\)A1
Remainder = \(x - 3\)A1
| | |
|---|---|
| (a) $2x^2 - 7x - 4 = (2x + 1)(x - 4)$ or $3x^2 + x - 2 = (3x - 2)(x + 1)$ | B1 |
| $\frac{2x + 1}{3x - 2}$ as final answer; this answer only | B1 |
| (b) For correct leading term $x$ in quotient | B1 |
| For evidence of correct division process | M1 |
| Quotient = $x - 2$ | A1 |
| Remainder = $x - 3$ | A1 |
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]}}