OCR MEI C4 — Question 4 6 marks

Exam BoardOCR MEI
ModuleC4 (Core Mathematics 4)
Marks6
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicPartial Fractions
TypePartial fractions with quadratic in denominator
DifficultyModerate -0.5 This is a straightforward partial fractions question with a standard form (linear factor times irreducible quadratic). It requires setting up A/x + (Bx+C)/(x²+4), equating coefficients, and solving a simple system. The technique is routine for C4 level with no conceptual challenges, making it slightly easier than average.
Spec1.02y Partial fractions: decompose rational functions
4 Express \(\frac { 4 } { x \left( x ^ { 2 } + 4 \right) }\) in partial fractions.
Question 4:
AnswerMarks Guidance
\(\frac{4}{x(x^2+4)} = \frac{A}{x} + \frac{Bx+C}{x^2+4} = \frac{A(x^2+4)+(Bx+C)x}{x(x^2+4)}\)M1 correct partial fractions
\(\Rightarrow 4 = A(x^2+4)+(Bx+C)x\)M1
\(x=0 \Rightarrow 4=4A \Rightarrow A=1\)B1 \(A=1\)
coefft of \(x^2\): \(0=A+B \Rightarrow B=-1\)DM1 Substitution or equating coefficients
coeffts of \(x\): \(0=C\)A1 \(B=-1\)
\(\Rightarrow \frac{4}{x(x^2+4)} = \frac{1}{x} - \frac{x}{x^2+4}\)A1 \(C=0\) [6] 
## Question 4:

$\frac{4}{x(x^2+4)} = \frac{A}{x} + \frac{Bx+C}{x^2+4} = \frac{A(x^2+4)+(Bx+C)x}{x(x^2+4)}$ | M1 | correct partial fractions

$\Rightarrow 4 = A(x^2+4)+(Bx+C)x$ | M1 |

$x=0 \Rightarrow 4=4A \Rightarrow A=1$ | B1 | $A=1$

coefft of $x^2$: $0=A+B \Rightarrow B=-1$ | DM1 | Substitution or equating coefficients

coeffts of $x$: $0=C$ | A1 | $B=-1$

$\Rightarrow \frac{4}{x(x^2+4)} = \frac{1}{x} - \frac{x}{x^2+4}$ | A1 | $C=0$ [6] |

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4 Express $\frac { 4 } { x \left( x ^ { 2 } + 4 \right) }$ in partial fractions.

\hfill \mbox{\textit{OCR MEI C4  Q4 [6]}}
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