OCR MEI C4 2006 January — Question 1 5 marks

Exam BoardOCR MEI
ModuleC4 (Core Mathematics 4)
Year2006
SessionJanuary
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicSimultaneous equations
TypeLine intersecting reciprocal curve
DifficultyModerate -0.3 This is a straightforward algebraic manipulation question requiring students to find a common denominator, clear fractions, and solve the resulting quadratic. While it involves rational expressions, it's a standard C4 technique with no conceptual difficulty or problem-solving insight required—slightly easier than average due to its routine nature.
Spec1.02k Simplify rational expressions: factorising, cancelling, algebraic division
1 Solve the equation \(\frac { 2 x } { x - 2 } - \frac { 4 x } { x + 1 } = 3\).
Question 1 (Section A):
AnswerMarks Guidance
\(\frac{2x}{x-2} - \frac{4x}{x+1} = 3\) Solve equation
\(2x(x+1) - 4x(x-2) = 3(x-2)(x+1)\)M1 Multiply through by \((x-2)(x+1)\)
\(2x^2+2x - 4x^2+8x = 3(x^2-x-2)\)M1 Expand both sides
\(-2x^2+10x = 3x^2-3x-6\)A1 Simplify LHS
\(5x^2-13x-6=0\)A1 Collect terms
\((5x+2)(x-3)=0\)M1 Factorise
\(x = -\frac{2}{5}\) or \(x=3\)A1 Both solutions 
## Question 1 (Section A):

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

$2x(x+1) - 4x(x-2) = 3(x-2)(x+1)$ | M1 | Multiply through by $(x-2)(x+1)$

$2x^2+2x - 4x^2+8x = 3(x^2-x-2)$ | M1 | Expand both sides

$-2x^2+10x = 3x^2-3x-6$ | A1 | Simplify LHS

$5x^2-13x-6=0$ | A1 | Collect terms

$(5x+2)(x-3)=0$ | M1 | Factorise

$x = -\frac{2}{5}$ or $x=3$ | A1 | Both solutions

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

\hfill \mbox{\textit{OCR MEI C4 2006 Q1 [5]}}
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Q1 5 Q2 5 Q3 6 Q4 6 Q5 7 Q6 7 Q7 17 Q8 19