Moderate -0.8 This is a straightforward application of the binomial theorem requiring only substitution into the formula nCr × a^(n-r) × b^r with given values. It's a single-step calculation with no problem-solving or conceptual challenge, making it easier than average but not trivial since students must identify the correct term and perform the arithmetic accurately.
Throughout, condone \(x\)s included eg \((2x)^4\); allow 4 for \(70\,000x^4\) www; may also include other terms in expansion; allow marks even if wrong term selected; mark the coefficient of \(x^4\)
Or M2 for two of these elements multiplied
Or for all three elements seen together (eg in table) but not multiplied; may be unsimplified, but do not allow 35 in factorial form unless evaluated later
Or M1 for 35 oe or for \(1\ 7\ 21\ 35\ 35\ 21\ 7\ 1\) row of Pascal's triangle seen
[4]
## Question 7:
| Answer | Marks | Guidance |
|--------|-------|----------|
| $70\,000$ www | M3 for $35 \times 5^3 \times 2^4$ oe | Throughout, condone $x$s included eg $(2x)^4$; allow 4 for $70\,000x^4$ www; may also include other terms in expansion; allow marks even if wrong term selected; mark the coefficient of $x^4$ |
| | Or M2 for two of these elements multiplied | Or for all three elements seen together (eg in table) but not multiplied; may be unsimplified, but do not allow 35 in factorial form unless evaluated later |
| | Or M1 for 35 oe or for $1\ 7\ 21\ 35\ 35\ 21\ 7\ 1$ row of Pascal's triangle seen | |
| | **[4]** | |
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