| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Geometric Sequences and Series |
| Type | Find year when threshold exceeded |
| Difficulty | Moderate -0.3 This is a straightforward geometric progression question requiring standard formulas (nth term and sum). Part (i) is direct substitution, part (ii) requires solving an inequality with logarithms (standard C2 content), and part (iii) applies the GP sum formula. While multi-step, it involves routine application of well-practiced techniques with no novel insight required, making it slightly easier than average. |
| Spec | 1.04i Geometric sequences: nth term and finite series sum1.04k Modelling with sequences: compound interest, growth/decay |
The amounts of oil pumped from an oil well in each of the years 2001 to 2004 formed a geometric progression with common ratio 0.9. The amount pumped in 2001 was 100 000 barrels.
\begin{enumerate}[label=(\roman*)]
\item Calculate the amount pumped in 2004. [2]
\end{enumerate}
It is assumed that the amounts of oil pumped in future years will continue to follow the same geometric progression. Production from the well will stop at the end of the first year in which the amount pumped is less than 5000 barrels.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{1}
\item Calculate in which year the amount pumped will fall below 5000 barrels. [4]
\item Calculate the total amount of oil pumped from the well from the year 2001 up to and including the final year of production. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR C2 Q8 [9]}}