| Exam Board | Edexcel |
|---|---|
| Module | Paper 1 (Paper 1) |
| Session | Specimen |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Geometric Sequences and Series |
| Type | Total over time period |
| Difficulty | Standard +0.8 This is a multi-step geometric series problem requiring (a) sum of GP over 14 terms with r=1.012, then (b) a more complex calculation splitting each year's harvest into two pricing tiers and summing. Part (b) requires careful reasoning about when harvests exceed 2000 tonnes and applying piecewise pricing, making it more challenging than standard GP sum questions but still within typical A-level scope. |
| Spec | 1.04i Geometric sequences: nth term and finite series sum1.04k Modelling with sequences: compound interest, growth/decay |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Total amount \(= \frac{2100(1-(1.012)^{14})}{1-1.012}\) or \(\frac{2100((1.012)^{14}-1)}{1.012-1}\) | M1 | AO 3.1b; \(a=2100\), \(r=1.012\), \(n=13\) or \(14\) |
| \(= 31806.9948... = 31800\) (tonnes) (3 s.f.) | A1 | AO 1.1b |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Total Cost \(= 5.15(2000(14)) + 6.45(31806.9948... - (2000)(14))\) | M1 | AO 3.1b |
| M1 | AO 1.1b | |
| \(= 5.15(28000) + 6.45(3806.9948...)\) | ||
| \(= 144200 + 24555.116...\) | ||
| \(= 168755.116... = £169000\) (nearest £1000) | A1 | AO 3.2a |
## Question 8:
### Part (a):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Total amount $= \frac{2100(1-(1.012)^{14})}{1-1.012}$ or $\frac{2100((1.012)^{14}-1)}{1.012-1}$ | M1 | AO 3.1b; $a=2100$, $r=1.012$, $n=13$ or $14$ |
| $= 31806.9948... = 31800$ (tonnes) (3 s.f.) | A1 | AO 1.1b |
### Part (b):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Total Cost $= 5.15(2000(14)) + 6.45(31806.9948... - (2000)(14))$ | M1 | AO 3.1b |
| | M1 | AO 1.1b |
| $= 5.15(28000) + 6.45(3806.9948...)$ | | |
| $= 144200 + 24555.116...$ | | |
| $= 168755.116... = £169000$ (nearest £1000) | A1 | AO 3.2a |\begin{enumerate}
\item There were 2100 tonnes of wheat harvested on a farm during 2017.
\end{enumerate}
The mass of wheat harvested during each subsequent year is expected to increase by $1.2 \%$ per year.\\
(a) Find the total mass of wheat expected to be harvested from 2017 to 2030 inclusive, giving your answer to 3 significant figures.
Each year it costs
\begin{itemize}
\item £5.15 per tonne to harvest the first 2000 tonnes of wheat
\item £6.45 per tonne to harvest wheat in excess of 2000 tonnes\\
(b) Use this information to find the expected cost of harvesting the wheat from 2017 to 2030 inclusive. Give your answer to the nearest $\pounds 1000$
\end{itemize}
\hfill \mbox{\textit{Edexcel Paper 1 Q8 [5]}}