| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2022 |
| Session | June |
| Marks | 9 |
| Topic | Geometric Sequences and Series |
| Type | Compare two growth models |
| Difficulty | Easy -1.2 This is a straightforward application of arithmetic and geometric sequences with clear context. Part (a) requires finding the common difference of an AP and calculating the second term. Part (b) requires finding the common ratio of a GP and calculating the second term. Part (c) requires summing both sequences using standard formulas. All techniques are routine A-level content with no problem-solving insight needed—students simply identify the model type and apply memorized formulas. |
| Spec | 1.04h Arithmetic sequences: nth term and sum formulae1.04i Geometric sequences: nth term and finite series sum1.04j Sum to infinity: convergent geometric series |r|<1 |
A small company which makes batteries for electric cars has a 10 year plan for growth.
In year 1 the company will make 2600 batteries.
In year 10 the company aims to make 12000 batteries.
In order to calculate the number of batteries it will need to make each year from year 2 to year 9, the company considers two models.
Model A assumes that the number of batteries it will make each year will increase by the same number each year.
\begin{enumerate}[label=(\alph*)]
\item According to model A, determine the number of batteries the company will make in year 2. Give your answer to the nearest whole number of batteries. [3]
\end{enumerate}
Model B assumes that the numbers of batteries it will make each year will increase by the same percentage each year.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item According to model B, determine the number of batteries the company will make in year 2. Give your answer to the nearest 10 batteries. [3]
\end{enumerate}
Sam calculates the total number of batteries made from year 1 to year 10 inclusive, using each of the two models.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Calculate the difference between the two totals, giving your answer to the nearest 100 batteries. [3]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Pure 2022 Q6 [9]}}