| Date | May 2013 | Marks available | 4 | Reference code | 13M.1.hl.TZ2.3 |
| Level | HL only | Paper | 1 | Time zone | TZ2 |
| Command term | Expand | Question number | 3 | Adapted from | N/A |
Question
Expand \({(2 - 3x)^5}\) in ascending powers of x, simplifying coefficients.
Markscheme
clear attempt at binomial expansion for exponent 5 M1
\({2^5} + 5 \times {2^4} \times ( - 3x) + \frac{{5 \times 4}}{2} \times {2^3} \times {( - 3x)^2} + \frac{{5 \times 4 \times 3}}{6} \times {2^2} \times {( - 3x)^3}\)
\( + \frac{{5 \times 4 \times 3 \times 2}}{{24}} \times 2 \times {( - 3x)^4} + {( - 3x)^5}\) (A1)
Note: Only award M1 if binomial coefficients are seen.
\( = 32 - 240x + 720{x^2} - 1080{x^3} + 810{x^4} - 243{x^5}\) A2
Note: Award A1 for correct moduli of coefficients and powers. A1 for correct signs.
Total [4 marks]
Examiners report
Generally well done. The majority of candidates obtained a quintic with correct alternating signs. A few candidates made arithmetic errors. A small number of candidates multiplied out the linear expression, often correctly.
