| Exam Board | Edexcel |
|---|---|
| Module | P2 (Pure Mathematics 2) |
| Year | 2024 |
| Session | January |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Geometric Sequences and Series |
| Type | Compare two growth models |
| Difficulty | Moderate -0.3 This is a straightforward application of arithmetic and geometric sequences with clear setup. Part (a) requires finding the common difference and applying it; part (b) requires finding the common ratio and applying it once; part (c) requires using standard sum formulas. All steps are routine with no conceptual challenges beyond recognizing which model is which, making it slightly easier than average. |
| Spec | 1.02z Models in context: use functions in modelling1.04h Arithmetic sequences: nth term and sum formulae1.04i Geometric sequences: nth term and finite series sum |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Attempts \(4000 = 300 + 11d\) to find \(d\) | M1 | Accept attempt at \(\frac{4000-300}{11}\) proceeding to a value |
| Uses \(300 + 3"d"\) | M1 | Attempts to find the fourth term using \(300 + 3 \times "336"\) |
| Wheat production in year 4 is awrt 1310 (to nearest 10) (tonnes) | A1 | isw once correct answer seen |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Attempts \(4000 = 300r^{11}\) to find \(r\) | M1 | Implied by \(r =\) awrt 1.3 |
| Finds \(r = (1.266...)\) and multiplies this by 300 | M1 | Dependent on attempt to find \(r\) from \(4000=300r^{11}\) or \(4000=300r^{12}\) |
| Wheat production in year 2 is awrt 380 (to nearest 10) (tonnes) | A1 | isw once correct answer seen |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Attempts \(\frac{12}{2}\{300+4000\}\) or \(\frac{300("1.266..."^{12}-1)}{" 1.266..."-1}\) | M1 | Correct method for sum of either AP or GP |
| Finds \(\frac{12}{2}\{300+4000\} - \frac{300("1.266..."^{12}-1)}{" 1.266..."-1} = (25800 - 17935)\) | dM1 | Both formulae attempted correctly and difference taken; condone use of their \(d\) and \(r\) |
| Difference \(= 7860\) but allow \(7870\) (tonnes) | A1 | Not AWRT; note \(r=1.266\) leads to 7810 which scores M1dM1A0 |
# Question 7:
## Part (a):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Attempts $4000 = 300 + 11d$ to find $d$ | M1 | Accept attempt at $\frac{4000-300}{11}$ proceeding to a value |
| Uses $300 + 3"d"$ | M1 | Attempts to find the fourth term using $300 + 3 \times "336"$ |
| Wheat production in year 4 is awrt 1310 (to nearest 10) (tonnes) | A1 | isw once correct answer seen |
## Part (b):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Attempts $4000 = 300r^{11}$ to find $r$ | M1 | Implied by $r =$ awrt 1.3 |
| Finds $r = (1.266...)$ and multiplies this by 300 | M1 | Dependent on attempt to find $r$ from $4000=300r^{11}$ or $4000=300r^{12}$ |
| Wheat production in year 2 is awrt 380 (to nearest 10) (tonnes) | A1 | isw once correct answer seen |
## Part (c):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Attempts $\frac{12}{2}\{300+4000\}$ or $\frac{300("1.266..."^{12}-1)}{" 1.266..."-1}$ | M1 | Correct method for sum of either AP or GP |
| Finds $\frac{12}{2}\{300+4000\} - \frac{300("1.266..."^{12}-1)}{" 1.266..."-1} = (25800 - 17935)$ | dM1 | Both formulae attempted correctly and difference taken; condone use of their $d$ and $r$ |
| Difference $= 7860$ but allow $7870$ (tonnes) | A1 | **Not AWRT**; note $r=1.266$ leads to 7810 which scores M1dM1A0 |\begin{enumerate}
\item Wheat is grown on a farm.
\end{enumerate}
\begin{itemize}
\item In year 1 , the farm produced 300 tonnes of wheat.
\item In year 12 , the farm is predicted to produce 4000 tonnes of wheat.
\end{itemize}
Model $A$ assumes that the amount of wheat produced on the farm will increase by the same amount each year.\\
(a) Using model $A$, find the amount of wheat produced on the farm in year 4.
Give your answer to the nearest 10 tonnes.
Model $B$ assumes that the amount of wheat produced on the farm will increase by the same percentage each year.\\
(b) Using model $B$, find the amount of wheat produced on the farm in year 2. Give your answer to the nearest 10 tonnes.\\
(c) Calculate, according to the two models, the difference between the total amounts of wheat predicted to be produced on the farm from year 1 to year 12 inclusive. Give your answer to the nearest 10 tonnes.
\hfill \mbox{\textit{Edexcel P2 2024 Q7 [9]}}