OCR MEI C4 2010 June — Question 1 3 marks

Exam BoardOCR MEI
ModuleC4 (Core Mathematics 4)
Year2010
SessionJune
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, finding a common denominator, and simplifying. It's simpler than a typical partial fractions question (which involves decomposing rather than combining) and requires only routine algebraic skills with no problem-solving insight.
Spec1.02k Simplify rational expressions: factorising, cancelling, algebraic division
1 Express \(\frac { x } { x ^ { 2 } - 1 } + \frac { 2 } { x + 1 }\) as a single fraction, simplifying your answer.
Question 1:
AnswerMarks Guidance
Answer/WorkingMarks Guidance
\(x^2 - 1 = (x+1)(x-1)\)B1
\(\frac{x}{(x-1)(x+1)} + \frac{2}{x+1} = \frac{x + 2(x-1)}{(x-1)(x+1)}\)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
*Or:* \(\frac{x(x+1)+2(x^2-1)}{(x^2-1)(x+1)} = \frac{3x^2+x-2}{(x^2-1)(x+1)}\)M1 correct method for addition of fractions
\(= \frac{(3x-2)(x+1)}{(x^2-1)(x+1)}\)B1 \((3x-2)(x+1)\); accept denominator as \(x^2-1\) or \((x-1)(x+1)\)
\(= \frac{3x-2}{x^2-1}\)A1 [3] do not isw for incorrect subsequent cancelling 
# Question 1:

| Answer/Working | Marks | Guidance |
|---|---|---|
| $x^2 - 1 = (x+1)(x-1)$ | B1 | |
| $\frac{x}{(x-1)(x+1)} + \frac{2}{x+1} = \frac{x + 2(x-1)}{(x-1)(x+1)}$ | 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 |
| *Or:* $\frac{x(x+1)+2(x^2-1)}{(x^2-1)(x+1)} = \frac{3x^2+x-2}{(x^2-1)(x+1)}$ | M1 | correct method for addition of fractions |
| $= \frac{(3x-2)(x+1)}{(x^2-1)(x+1)}$ | B1 | $(3x-2)(x+1)$; accept denominator as $x^2-1$ or $(x-1)(x+1)$ |
| $= \frac{3x-2}{x^2-1}$ | A1 [3] | do not isw for incorrect subsequent cancelling |

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

\hfill \mbox{\textit{OCR MEI C4 2010 Q1 [3]}}
This paper (8 questions)
View full paper
Q1 3 Q2 8 Q3 5 Q4 5 Q5 8 Q6 7 Q7 18 Q8 18