June 2025 Paper 1 Q4
4 The first three terms, in ascending powers of \(x\), of the binomial expansion of \((1-8x)^{\frac{1}{2}}\) are
\[1 + nx - 8x^2\]where \(n\) is a constant.
(a) State the range of values of \(x\) for which the expansion is valid.
Circle your answer. [1 mark]
- \(|x| \gt -8\)
- \(|x| \gt -\dfrac{1}{8}\)
- \(|x| \lt \dfrac{1}{8}\)
- \(|x| \lt 8\)
(b) State the value of the constant \(n\)
Circle your answer. [1 mark]
- \(-16\)
- \(-4\)
- \(\dfrac{1}{2}\)
- \(4\)
| Scheme | Marks | AO |
|---|---|---|
| Circles third option | B1 | 1.1b |
| (1) |
Typical solution
\(|x| \lt \dfrac{1}{8}\)
| Scheme | Marks | AO |
|---|---|---|
| Circles second option | B1 | 1.1b |
| (1) | ||
| (2 marks) |
Typical solution
\(-4\)