OCR MEI C4 — Question 5 3 marks

Exam BoardOCR MEI
ModuleC4 (Core Mathematics 4)
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicPartial Fractions
TypeSimplify algebraic fractions by addition or subtraction
DifficultyEasy -1.2 This is a straightforward algebraic manipulation requiring factorisation of x²-1 and finding a common denominator. It's simpler than typical partial fractions work (which involves decomposing rather than combining) and requires only basic fraction addition skills with no problem-solving insight needed.
Spec1.02k Simplify rational expressions: factorising, cancelling, algebraic division
5 Express \(\frac { x } { x ^ { 2 } - 1 } + \frac { 2 } { x + 1 }\) as a single fraction, simplifying your answer.
Question 5:
AnswerMarks Guidance
AnswerMarks Guidance
\(\frac{x}{x^2-1} + \frac{2}{x+1} = \frac{x}{(x-1)(x+1)} + \frac{2}{x+1}\)B1 \(x^2 - 1 = (x+1)(x-1)\)
\(= \frac{x + 2(x-1)}{(x-1)(x+1)}\)M1 Correct method for addition of fractions
\(= \frac{3x-2}{(x+1)(x-1)}\)A1 or \(\frac{3x-2}{x^2-1}\). Do not isw for incorrect subsequent cancelling 
## Question 5:

| Answer | Marks | Guidance |
|--------|-------|----------|
| $\frac{x}{x^2-1} + \frac{2}{x+1} = \frac{x}{(x-1)(x+1)} + \frac{2}{x+1}$ | B1 | $x^2 - 1 = (x+1)(x-1)$ |
| $= \frac{x + 2(x-1)}{(x-1)(x+1)}$ | M1 | Correct method for addition of fractions |
| $= \frac{3x-2}{(x+1)(x-1)}$ | A1 | or $\frac{3x-2}{x^2-1}$. Do not isw for incorrect subsequent cancelling |

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5 Express $\frac { x } { x ^ { 2 } - 1 } + \frac { 2 } { x + 1 }$ as a single fraction, simplifying your answer.

\hfill \mbox{\textit{OCR MEI C4  Q5 [3]}}
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Q1 5 Q2 5 Q3 5 Q4 5 Q5 3 Q6 5 Q7 8 Q8 3 Q9 8 Q10 8