Question 1 - A-Level Maths

OCR MEI C4 — Question 1 3 marks

Exam Board	OCR MEI
Module	C4 (Core Mathematics 4)
Marks	3
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Partial Fractions
Type	Solve rational equation
Difficulty	Moderate -0.8 This is a straightforward rational equation requiring only algebraic manipulation: multiply through by x(x+1) to clear denominators, expand to get a quadratic, then solve. It's simpler than average A-level questions as it involves routine techniques with no conceptual depth or multi-step problem-solving.
Spec	1.02k Simplify rational expressions: factorising, cancelling, algebraic division

1 Solve the equation. $$\frac { 8 } { x } - \frac { 9 } { x + 1 } = 1$$

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Question 1:

Answer	Marks	Guidance
Answer/Working	Marks	Guidance
$\frac{8}{x} - \frac{9}{x+1} = 1$	M1
$\Rightarrow 8(x+1) - 9x = x(x+1)$	A1
$\Rightarrow 0 = x^2 + 2x - 8$
$\Rightarrow 0 = (x+4)(x-2)$
$\Rightarrow x = -4$ or $2$	A1
Total: 3 marks

## Question 1:

| Answer/Working | Marks | Guidance |
|---|---|---|
| $\frac{8}{x} - \frac{9}{x+1} = 1$ | M1 | |
| $\Rightarrow 8(x+1) - 9x = x(x+1)$ | A1 | |
| $\Rightarrow 0 = x^2 + 2x - 8$ | | |
| $\Rightarrow 0 = (x+4)(x-2)$ | | |
| $\Rightarrow x = -4$ or $2$ | A1 | |
| **Total: 3 marks** | | |

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1 Solve the equation.

$$\frac { 8 } { x } - \frac { 9 } { x + 1 } = 1$$

\hfill \mbox{\textit{OCR MEI C4  Q1 [3]}}

This paper (9 questions)

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Q1 3 Q2 4 Q3 4 Q4 5 Q5 8 Q6 6 Q7 6 Q8 19 Q9 17

Answer	Marks	Guidance
Answer/Working	Marks	Guidance
\(\frac{8}{x} - \frac{9}{x+1} = 1\)	M1
\(\Rightarrow 8(x+1) - 9x = x(x+1)\)	A1
\(\Rightarrow 0 = x^2 + 2x - 8\)
\(\Rightarrow 0 = (x+4)(x-2)\)
\(\Rightarrow x = -4\) or \(2\)	A1
Total: 3 marks