Easy -1.2 This is a straightforward application of the binomial theorem with a small positive integer power (n=5). Students need only substitute into the standard formula and simplify three terms—pure recall and routine calculation with no problem-solving required. Easier than average for A-level.
First term must be 243; writing just \(3^5\) is B0
\(+5\times(3)^4(-2x) = -810x\)
B1
Term must be simplified to \(-810x\); the \(x\) is required
\(+\frac{5\times4}{2}(3)^3(-2x)^2 = +1080x^2\)
M1
Attempt at Binomial for third term; must have \(x^2\) (or no \(x\)), attempt at Binomial Coefficient and powers of 3 and 2
\(+1080x^2\)
A1
c.a.o; if \(1080x^2\) written with no working, awarded both M1 A1
Total: [4]
## Question 1:
| Working/Answer | Marks | Guidance |
|---|---|---|
| $(3-2x)^5 = 243$ | B1 | First term must be 243; writing just $3^5$ is B0 |
| $+5\times(3)^4(-2x) = -810x$ | B1 | Term must be simplified to $-810x$; the $x$ is required |
| $+\frac{5\times4}{2}(3)^3(-2x)^2 = +1080x^2$ | M1 | Attempt at Binomial for third term; must have $x^2$ (or no $x$), attempt at Binomial Coefficient and powers of 3 and 2 |
| $+1080x^2$ | A1 | c.a.o; if $1080x^2$ written with no working, awarded both M1 A1 |
| **Total: [4]** | | |
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Find the first 3 terms, in ascending powers of $x$, of the binomial expansion of $( 3 - 2 x ) ^ { 5 }$, giving each term in its simplest form.\\
(4)\\
\hfill \mbox{\textit{Edexcel C2 2009 Q1 [4]}}