| Date | November 2010 | Marks available | 4 | Reference code | 10N.1.hl.TZ0.3 |
| Level | HL only | Paper | 1 | Time zone | TZ0 |
| Command term | Expand and Simplify | Question number | 3 | Adapted from | N/A |
Question
Expand and simplify \({\left( {{x^2} - \frac{2}{x}} \right)^4}\).
Markscheme
\({\left( {{x^2} - \frac{2}{x}} \right)^4} = {({x^2})^4} + 4{({x^2})^3}\left( { - \frac{2}{x}} \right) + 6{({x^2})^2}{\left( { - \frac{2}{x}} \right)^2} + 4({x^2}){\left( { - \frac{2}{x}} \right)^3} + {\left( { - \frac{2}{x}} \right)^4}\) (M1)
\( = {x^8} - 8{x^5} + 24{x^2} - \frac{{32}}{x} + \frac{{16}}{{{x^4}}}\) A3
Note: Deduct one A mark for each incorrect or omitted term.
[4 marks]
Examiners report
Most candidates solved this question correctly with most candidates who explained how they obtained their coefficients using Pascal’s triangle rather than the combination formula.
Syllabus sections
Topic 1 - Core: Algebra » 1.3 » The binomial theorem: expansion of \({\left( {a + b} \right)^n}\), \(n \in N\) .
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