| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2023 |
| Session | September |
| Marks | 8 |
| Topic | Geometric Sequences and Series |
| Type | Total over time period |
| Difficulty | Moderate -0.8 This is a straightforward geometric sequence/series question with clear scaffolding. Part (a) is trivial verification (multiply 250 by 0.9 twice), part (b) applies the GP formula directly (250 × 0.9^12), and part (c) requires summing a GP with first term 250×0.9, common ratio 0.9, and 12 terms. While part (c) involves more algebraic manipulation, the setup is explicit and the techniques are standard A-level content with no novel insight required. Easier than average due to heavy scaffolding and routine application of formulas. |
| Spec | 1.04i Geometric sequences: nth term and finite series sum1.04k Modelling with sequences: compound interest, growth/decay |
Liquid is kept in containers, which due to evaporation and ongoing chemical reactions, at the end of each month the volume of the liquid in these containers reduces by 10% compared with the volume at the start of the same month.
One such container is filled up with 250 litres of liquid.
\begin{enumerate}[label=(\alph*)]
\item Show that the volume of the liquid in the container at the end of the second month is 202.5 litres. [1]
\item Find the volume of the liquid in the container at the end of the twelfth month. [2]
\end{enumerate}
At the start of each month a new container is filled up with 250 litres of liquid, so that at the end of twelve months there are 12 containers with liquid.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Use an algebraic method to calculate the total amount of liquid in the 12 containers at the end of 12 months. [5]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Pure 2023 Q6 [8]}}