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Date May 2010 Marks available 3 Reference code 10M.1.sl.TZ1.3
Level SL only Paper 1 Time zone TZ1
Command term Expand Question number 3 Adapted from N/A

Question

Expand \({(2 + x)^4}\) and simplify your result.

[3]
a.

Hence, find the term in \({x^2}\) in \({(2 + x)^4}\left( {1 + \frac{1}{{{x^2}}}} \right)\) .

[3]
b.

Markscheme

evidence of expanding     M1

e.g. \({2^4} + 4({2^3})x + 6({2^2}){x^2} + 4(2){x^3} + {x^4}\) , \((4 + 4x + {x^2})(4 + 4x + {x^2})\)

\({(2 + x)^4} = 16 + 32x + 24{x^2} + 8{x^3} + {x^4}\)     A2     N2

[3 marks]

a.

finding coefficients 24 and 1     (A1)(A1)

term is \(25{x^2}\)     A1     N3

[3 marks]

b.

Examiners report

Surprisingly few candidates employed the binomial theorem, choosing instead to expand by repeated use of the distributive property. This earned full marks if done correctly, but often proved prone to error.

a.

Candidates often expanded the entire expression in part (b). Few recognized that only two distributions are required to answer the question. Some gave the coefficient as the final answer.

b.

Syllabus sections

Topic 1 - Algebra » 1.3 » The binomial theorem: expansion of \({\left( {a + b} \right)^n}\), \(n \in \mathbb{N}\) .
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