OCR MEI C4 — Question 5 5 marks

Exam BoardOCR MEI
ModuleC4 (Core Mathematics 4)
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicPartial Fractions
TypeSolve rational equation
DifficultyModerate -0.3 This is a straightforward rational equation requiring finding a common denominator, clearing fractions, and solving the resulting quadratic. While it involves multiple algebraic steps, it's a standard textbook exercise with no conceptual difficulty beyond routine manipulation—slightly easier than average for A-level.
Spec1.02c Simultaneous equations: two variables by elimination and substitution1.02k Simplify rational expressions: factorising, cancelling, algebraic division
5 Solve the equation \(\frac { 2 x } { x - 2 } - \frac { 4 x } { x + 1 } = 3\).
Question 5:
AnswerMarks Guidance
\(\frac{2x}{x-2} - \frac{4x}{x+1} = 3\)
\(\Rightarrow 2x(x+1)-4x(x-2)=3(x-2)(x+1)\)M1 Clearing fractions
\(\Rightarrow 2x^2+2x-4x^2+8x = 3x^2-3x-6\)M1 expanding brackets
\(\Rightarrow 0=5x^2-13x-6 = (5x+2)(x-3)\)A1 oe
\(\Rightarrow x=-\frac{2}{5}\) or \(3\)M1 A1 cao factorising or formula [5] 
## Question 5:

$\frac{2x}{x-2} - \frac{4x}{x+1} = 3$ | |

$\Rightarrow 2x(x+1)-4x(x-2)=3(x-2)(x+1)$ | M1 | Clearing fractions

$\Rightarrow 2x^2+2x-4x^2+8x = 3x^2-3x-6$ | M1 | expanding brackets

$\Rightarrow 0=5x^2-13x-6 = (5x+2)(x-3)$ | A1 | oe

$\Rightarrow x=-\frac{2}{5}$ or $3$ | M1 A1 cao | factorising or formula [5] |

---
5 Solve the equation $\frac { 2 x } { x - 2 } - \frac { 4 x } { x + 1 } = 3$.

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