| Exam Board | SPS |
|---|---|
| Module | SPS FM Pure (SPS FM Pure) |
| Year | 2023 |
| Session | November |
| Marks | 6 |
| Topic | Taylor series |
| Type | Use series to find error or validity |
| Difficulty | Moderate -0.3 This is a straightforward application of standard Maclaurin series. Part (a) requires recall of ln(1+x) series and substitution. Part (b) is routine percentage error calculation. Part (c) tests understanding of radius of convergence (x=1 is outside |2x|<1), which is a standard conceptual check. The question is slightly easier than average due to being mostly procedural with minimal problem-solving required. |
| Spec | 4.08a Maclaurin series: find series for function4.08b Standard Maclaurin series: e^x, sin, cos, ln(1+x), (1+x)^n |
(a) Use a Maclaurin series to find a quadratic approximation for $\ln(1 + 2x)$. [1]
(b) Find the percentage error in using the approximation in part (a) to calculate $\ln(1.2)$. [3]
(c) Jane uses the Maclaurin series in part (a) to try to calculate an approximation for $\ln 3$.
Explain whether her method is valid. [2]
\hfill \mbox{\textit{SPS SPS FM Pure 2023 Q5 [6]}}