Moderate -0.8 This is a straightforward binomial expansion question requiring students to identify two terms from (1+3x)^10 that contribute to x^2 when multiplied by the linear factor. It involves routine application of the binomial theorem formula and simple arithmetic, making it easier than average but not trivial since it requires careful term selection and coefficient calculation.
Correct second term \(30x\) in expansion of \((1+3x)^{10}\)
B1
WWW, may be implied later.
Correct third term \(+405x^2\)
B1
Ignore subsequent terms, may be implied later.
Multiply \((2-5x)\) by *their* \(30x+405x^2\) to obtain two \(x^2\) terms only
M1
Expect \(-150x^2, 810x^2\)
Coefficient is \(660\)
A1
Must be clearly identified. Allow final answer \(660x^2\)
Total: 4
## Question 1:
| Answer | Mark | Guidance |
|--------|------|----------|
| Correct second term $30x$ in expansion of $(1+3x)^{10}$ | B1 | WWW, may be implied later. |
| Correct third term $+405x^2$ | B1 | Ignore subsequent terms, may be implied later. |
| Multiply $(2-5x)$ by *their* $30x+405x^2$ to obtain two $x^2$ terms only | M1 | Expect $-150x^2, 810x^2$ |
| Coefficient is $660$ | A1 | Must be clearly identified. Allow final answer $660x^2$ |
| **Total: 4** | | |
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