OCR MEI C4 — Question 3 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 standard partial fractions question with an irreducible quadratic factor. It requires setting up the form A/x + (Bx+C)/(x²+1), equating coefficients or substituting values, and solving a simple system of equations. While it involves more algebra than a purely linear denominator case, it's a routine textbook exercise that follows a well-defined procedure with no conceptual surprises, making it slightly easier than average.
Spec1.02y Partial fractions: decompose rational functions
3 Express \(\frac { 3 x + 2 } { x \left( x ^ { 2 } + 1 \right) }\) in partial fractions.
Question 3:
AnswerMarks Guidance
\(\frac{3x+2}{x(x^2+1)} = \frac{A}{x} + \frac{Bx+C}{x^2+1}\)M1 correct partial fractions
\(\Rightarrow 3x+2 = A(x^2+1)+(Bx+C)x\)M1
\(x=0 \Rightarrow 2=A\)B1
coefft of \(x^2\): \(0=A+B \Rightarrow B=-2\)M1 equating coefficients
coefft of \(x\): \(3=C\)A1 at least one of \(B,C\) correct
\(\Rightarrow \frac{3x+2}{x(x^2+1)} = \frac{2}{x} + \frac{3-2x}{x^2+1}\)A1 [6] 
## Question 3:

$\frac{3x+2}{x(x^2+1)} = \frac{A}{x} + \frac{Bx+C}{x^2+1}$ | M1 | correct partial fractions

$\Rightarrow 3x+2 = A(x^2+1)+(Bx+C)x$ | M1 |

$x=0 \Rightarrow 2=A$ | B1 |

coefft of $x^2$: $0=A+B \Rightarrow B=-2$ | M1 | equating coefficients

coefft of $x$: $3=C$ | A1 | at least one of $B,C$ correct

$\Rightarrow \frac{3x+2}{x(x^2+1)} = \frac{2}{x} + \frac{3-2x}{x^2+1}$ | A1 | [6] |

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

\hfill \mbox{\textit{OCR MEI C4  Q3 [6]}}
This paper (7 questions)
View full paper
Q1 4 Q2 5 Q3 6 Q4 6 Q5 5 Q6 8 Q7 18