Moderate -0.8 This is a straightforward application of the binomial theorem requiring students to identify the correct term (r=4), apply the formula with n=6, and perform arithmetic with small numbers. It's a standard textbook exercise testing direct recall of the binomial coefficient formula with minimal problem-solving, making it easier than average but not trivial since it requires careful calculation.
M3 for \(15 \times 5^2 \times 2^3\); or M2 for two of these elements correct with multiplication or all three elements correct but without multiplication (e.g. in list or with addition signs); or M1 for 15 soi or for \(1 \; 6 \; 15 ...\) seen in Pascal's triangle; SC2 for \(20000[x^3]\)
$6000$ | 4 | M3 for $15 \times 5^2 \times 2^3$; or M2 for two of these elements correct with multiplication or all three elements correct but without multiplication (e.g. in list or with addition signs); or M1 for 15 soi or for $1 \; 6 \; 15 ...$ seen in Pascal's triangle; SC2 for $20000[x^3]$ | condone inclusion of $x^4$ eg $(2x)^4$; condone omission of brackets in $2x^4$ if 16 used; allow M3 for correct term seen (often all terms written down) but then wrong term evaluated or all evaluated and correct term not identified; $15 \times 5^2 \times (2y)^4$ earns M3 even if followed by $15 \times 25 \times 2$ calculated; no MR for wrong power evaluated but SC for fourth term evaluated