Moderate -0.8 This is a straightforward application of the binomial theorem requiring students to identify the correct term (r=3) and calculate using the formula. It's simpler than average as it involves direct substitution into a well-practiced formula with small numbers, though it requires careful handling of the negative sign and coefficient.
M3 for \(10 \times 5^2 \times (-2[x])^3\); or M2 for two of these elements or M1 for 10 or \((5\times4\times3)/(3\times2\times1)\); condone \(x^3\) in ans; equivs: M3 for e.g. \(5^5 \times 10 \times \left(-\frac{2}{5}[x]\right)^3\); o.e. [\(5^5\) may be outside a bracket for whole expansion of all terms], M2 for two of these elements etc; similarly for factor of 2 taken out at start
# Question 8:
| $-2000$ | 4 | M3 for $10 \times 5^2 \times (-2[x])^3$; or M2 for two of these elements or M1 for 10 or $(5\times4\times3)/(3\times2\times1)$; condone $x^3$ in ans; equivs: M3 for e.g. $5^5 \times 10 \times \left(-\frac{2}{5}[x]\right)^3$; o.e. [$5^5$ may be outside a bracket for whole expansion of all terms], M2 for two of these elements etc; similarly for factor of 2 taken out at start |
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