Moderate -0.8 This is a straightforward application of the binomial theorem requiring only the first three terms of (2-3x)^5. Students need to recall the binomial expansion formula and perform basic arithmetic with small powers—no problem-solving or insight required, just mechanical calculation. It's easier than average but not trivial since it involves negative coefficients and requires careful arithmetic.
Expressions left in \(^nC_r\) form or with factorials not sufficient
B2 for 2 terms correct numerically, ignoring any sign error, or for 32, \(-240\) and 720 found
B2
or B2 for all correct including signs, but unsimplified
B2
B1 for binomial coefficients 1, 5, 10 used or 1 5 10 10 5 1 seen
B1
SC3 for \(-240x + 720x^2 - 1080x^3\) isw or for \(-243x^5 + 810x^4 - 1080x^3\)
SC3
or SC2 for these terms with sign error(s)
SC2
## Question 7:
| Answer | Marks | Guidance |
|--------|-------|----------|
| $32 - 240x + 720x^2$ isw | 4 marks total | Accept terms listed separately; condone $-240x^1$ |
| B3 for all correct except for sign error(s) | B3 | Expressions left in $^nC_r$ form or with factorials not sufficient |
| B2 for 2 terms correct numerically, ignoring any sign error, or for 32, $-240$ and 720 found | B2 | |
| or B2 for all correct including signs, but unsimplified | B2 | |
| B1 for binomial coefficients 1, 5, 10 used or 1 5 10 10 5 1 seen | B1 | |
| SC3 for $-240x + 720x^2 - 1080x^3$ isw or for $-243x^5 + 810x^4 - 1080x^3$ | SC3 | |
| or SC2 for these terms with sign error(s) | SC2 | |
7 Find the first 3 terms, in ascending powers of $x$, of the binomial expansion of $( 2 - 3 x ) ^ { 5 }$, simplifying each term.
\hfill \mbox{\textit{OCR MEI C1 Q7 [4]}}