OCR FP2 2011 June — Question 1 5 marks

Exam BoardOCR
ModuleFP2 (Further Pure Mathematics 2)
Year2011
SessionJune
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicPartial Fractions
TypePartial fractions with quadratic in denominator
DifficultyModerate -0.3 This is a standard partial fractions question with an irreducible quadratic factor. While it's Further Maths content (FP2), the technique is routine: set up A/(x+3) + (Bx+C)/(x²+9), equate coefficients or substitute values, and solve. The algebra is straightforward with no complications, making it slightly easier than average despite being Further Maths.
Spec4.05c Partial fractions: extended to quadratic denominators
1 Express \(\frac { 2 x + 3 } { ( x + 3 ) \left( x ^ { 2 } + 9 \right) }\) in partial fractions.
Question 1:
AnswerMarks Guidance
Answer/WorkingMark Guidance
\(\frac{2x+3}{(x+3)(x^2+9)} \equiv \frac{A}{x+3} + \frac{Bx+C}{x^2+9}\)B1 For correct form seen anywhere with letters or values
\(A = -\frac{1}{6}\)B1 For correct \(A\) (cover up or otherwise)
\(2x+3 \equiv A(x^2+9) + (Bx+C)(x+3)\)M1 For equating coefficients at least once (or substituting values) into correct identity
\(B = \frac{1}{6}\), \(C = \frac{3}{2}\)A1 For correct \(B\) and \(C\)
\(\Rightarrow \frac{-1}{6(x+3)} + \frac{x+9}{6(x^2+9)}\)A1 For correct final statement cao, oe
Total: 5 
# Question 1:

| Answer/Working | Mark | Guidance |
|---|---|---|
| $\frac{2x+3}{(x+3)(x^2+9)} \equiv \frac{A}{x+3} + \frac{Bx+C}{x^2+9}$ | B1 | For correct form seen anywhere with letters or values |
| $A = -\frac{1}{6}$ | B1 | For correct $A$ (cover up or otherwise) |
| $2x+3 \equiv A(x^2+9) + (Bx+C)(x+3)$ | M1 | For equating coefficients at least once (or substituting values) into correct identity |
| $B = \frac{1}{6}$, $C = \frac{3}{2}$ | A1 | For correct $B$ and $C$ |
| $\Rightarrow \frac{-1}{6(x+3)} + \frac{x+9}{6(x^2+9)}$ | A1 | For correct final statement cao, oe |
| **Total: 5** | | |

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1 Express $\frac { 2 x + 3 } { ( x + 3 ) \left( x ^ { 2 } + 9 \right) }$ in partial fractions.

\hfill \mbox{\textit{OCR FP2 2011 Q1 [5]}}
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Q1 5 Q2 7 Q3 8 Q4 9 Q5 12 Q6 10 Q7 10 Q8 11