| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2023 |
| Session | September |
| Marks | 5 |
| Topic | Binomial Theorem (positive integer n) |
| Type | Numerical approximation using expansion |
| Difficulty | Moderate -0.8 This is a straightforward binomial expansion question requiring routine application of the formula for the first three terms, followed by a standard substitution to approximate a numerical value. The manipulation to recognize 2.995^8 = (3 - 0.005)^8 × 2^8 is mechanical, and all steps follow textbook procedures with no problem-solving insight required. |
| Spec | 1.04a Binomial expansion: (a+b)^n for positive integer n |
3.
\begin{enumerate}[label=(\alph*)]
\item Find the first three terms, in ascending powers of $x$, of the expansion of
$$\left( 3 - \frac { x } { 2 } \right) ^ { 8 }$$
[3 marks]
\item Use your expansion to estimate the value of $2.995 ^ { 8 }$.\\[0pt]
[2 marks]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Pure 2023 Q3 [5]}}