| Exam Board | Edexcel |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2014 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Partial Fractions |
| Type | Simplify algebraic fractions by addition or subtraction |
| Difficulty | Moderate -0.8 This is a reverse partial fractions question requiring algebraic manipulation to combine three fractions over a common denominator. Students must recognize that 4x²-9 = (2x+3)(2x-3), find the LCD, and simplify. While it involves multiple steps, it's a straightforward procedural task with no conceptual difficulty or problem-solving insight required, making it easier than average. |
| Spec | 1.02k Simplify rational expressions: factorising, cancelling, algebraic division |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Factorise \(4x^2 - 9 = (2x-3)(2x+3)\) | B1 | For factorising \(4x^2-9\) to \((2x-3)(2x+3)\) at any point. Not scored for combining terms and writing product as \(4x^2-9\) |
| \(\frac{3}{2x+3} - \frac{1}{2x-3} + \frac{6}{4x^2-9} = \frac{3(2x-3)-1(2x+3)+6}{(2x+3)(2x-3)}\) | M1 | Use of common denominator – combines three fractions to form one. Denominator must be correct, at least one numerator adapted. Condone missing brackets |
| \(= \frac{4x-6}{(2x+3)(2x-3)}\) | A1 | Correct simplified intermediate answer. Must be correct \(\frac{\text{Linear}}{\text{Quadratic}}\). Accept \(\frac{4x-6}{(2x+3)(2x-3)}\) or \(\frac{8x^2-18}{(2x+3)(4x^2-9)}\) |
| \(= \frac{2(2x-3)}{(2x+3)(2x-3)} = \frac{2}{2x+3}\) | A1 | cao \(= \frac{2}{2x+3}\). Allow recovery from invisible brackets for all 4 marks |
## Question 1:
| Answer/Working | Mark | Guidance |
|---|---|---|
| Factorise $4x^2 - 9 = (2x-3)(2x+3)$ | B1 | For factorising $4x^2-9$ to $(2x-3)(2x+3)$ at any point. Not scored for combining terms and writing product as $4x^2-9$ |
| $\frac{3}{2x+3} - \frac{1}{2x-3} + \frac{6}{4x^2-9} = \frac{3(2x-3)-1(2x+3)+6}{(2x+3)(2x-3)}$ | M1 | Use of common denominator – combines three fractions to form one. Denominator must be correct, at least one numerator adapted. Condone missing brackets |
| $= \frac{4x-6}{(2x+3)(2x-3)}$ | A1 | Correct simplified intermediate answer. Must be correct $\frac{\text{Linear}}{\text{Quadratic}}$. Accept $\frac{4x-6}{(2x+3)(2x-3)}$ or $\frac{8x^2-18}{(2x+3)(4x^2-9)}$ |
| $= \frac{2(2x-3)}{(2x+3)(2x-3)} = \frac{2}{2x+3}$ | A1 | cao $= \frac{2}{2x+3}$. Allow recovery from invisible brackets for all 4 marks |
---\begin{enumerate}
\item Express
\end{enumerate}
$$\frac { 3 } { 2 x + 3 } - \frac { 1 } { 2 x - 3 } + \frac { 6 } { 4 x ^ { 2 } - 9 }$$
as a single fraction in its simplest form.\\
\hfill \mbox{\textit{Edexcel C3 2014 Q1 [4]}}