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Date November 2008 Marks available 3 Reference code 08N.2.sl.TZ0.2
Level SL only Paper 2 Time zone TZ0
Command term Find Question number 2 Adapted from N/A

Question

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

[3]
a.

Find the term in \({x^3}\) in \((3x + 4){(x - 2)^4}\) .

[3]
b.

Markscheme

evidence of expanding     M1

e.g. \({(x - 2)^4} = {x^4} + 4{x^3}( - 2) + 6{x^2}{( - 2)^2} + 4x{( - 2)^3} + {( - 2)^4}\)     A2     N2

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

[3 marks]

a.

finding coefficients, \(3 \times 24( = 72)\) , \(4 \times( - 8)( = - 32)\)     (A1)(A1)

term is \(40{x^3}\)     A1     N3

[3 marks]

b.

Examiners report

Where candidates recognized the binomial nature of the expression, many completed the expansion successfully, although some omitted the negative signs.

a.

Where candidates recognized the binomial nature of the expression, many completed the expansion successfully, although some omitted the negative signs. Few recognized that only the multiplications that achieve an index of 3 are required in part (b) and distributed over the entire expression. Others did not recognize that two terms in the expansion must be combined.

b.

Syllabus sections

Topic 1 - Algebra » 1.2 » Laws of exponents; laws of logarithms.
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