Moderate -0.8 This is a straightforward partial fractions decomposition with two distinct linear factors. It requires only the standard cover-up method or equating coefficients—a routine technique with no conceptual difficulty. The arithmetic is simple and it's a single-step process, making it easier than average A-level questions.
5 Express
$$\frac { 5 ( x - 3 ) } { ( 2 x - 11 ) ( 4 - 3 x ) }$$
in the form
$$\frac { A } { ( 2 x - 11 ) } + \frac { B } { ( 4 - 3 x ) }$$
where \(A\) and \(B\) are integers.
\(\frac{5(x-3)}{(2x-11)(4-3x)} \equiv \frac{A}{(2x-11)}+\frac{B}{(4-3x)}\), so \(5(x-3)\equiv A(4-3x)+B(2x-11)\)
M1 (1.1a)
Forms identity/equation; either compares coefficients or substitutes a value for \(x\); PI by correct \(A\) or \(B\)
\(A=-1\)
A1 (1.1b)
\(B=1\)
A1 (1.1b)
## Question 5:
| Answer/Working | Marks | Guidance |
|---|---|---|
| $\frac{5(x-3)}{(2x-11)(4-3x)} \equiv \frac{A}{(2x-11)}+\frac{B}{(4-3x)}$, so $5(x-3)\equiv A(4-3x)+B(2x-11)$ | M1 (1.1a) | Forms identity/equation; either compares coefficients or substitutes a value for $x$; PI by correct $A$ or $B$ |
| $A=-1$ | A1 (1.1b) | |
| $B=1$ | A1 (1.1b) | |
5 Express
$$\frac { 5 ( x - 3 ) } { ( 2 x - 11 ) ( 4 - 3 x ) }$$
in the form
$$\frac { A } { ( 2 x - 11 ) } + \frac { B } { ( 4 - 3 x ) }$$
where $A$ and $B$ are integers.
\hfill \mbox{\textit{AQA Paper 2 2021 Q5 [3]}}