| Exam Board | OCR MEI |
|---|---|
| Module | Paper 2 (Paper 2) |
| Year | 2019 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Geometric Sequences and Series |
| Type | Compound growth applications |
| Difficulty | Standard +0.3 This is a straightforward application of geometric sequences with clear scaffolding through parts (a)-(e). Part (a) requires simple division to find r=3, parts (b)-(c) use standard GP formulas, part (d) involves solving an inequality with the sum formula, and part (e) asks for interpretation. While multi-part, each step is routine and the context guides students through the problem without requiring novel insight or complex reasoning. |
| Spec | 1.04i Geometric sequences: nth term and finite series sum1.04j Sum to infinity: convergent geometric series |r|<1 |
| Day | 1 | 2 | 3 |
| Number of new cases | 8 | 24 | 72 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(3\) | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \([8 \times 3^4 =]\ 648\) | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(\dfrac{8(3^n - 1)}{3-1} = 4(3^n - 1)\) or \(-4(1-3^n)\) | B1 | use of formula for sum of gp; mark the final answer; or \(4\times3^n - 4\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| their \(4(3^n - 1) = 185\,207\) or \(3^n = 46303(.75)\) | M1 | M0 for eg \(8\times3^{n-1}\); allow use of \(<\) or \(\leq\) for up to 3 marks; allow M1 only for use of \(>\) or \(\geq\); or \(3^9 = 19683\) and \(3^{10} = 59049\) seen for M1 |
| awrt 9.8 cao | A1 | no FT available here; then A1 (comparison with 46 303) |
| \([=]\ 9\) | A1 | not from wrong working |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Unlikely because eg some of the population will be immune to the virus / some of the population will not be exposed to the virus / medical intervention / extrapolation / movement of people in and out of town | B1 | any sensible reason; it's unlikely that everyone will be affected oe is insufficient |
## Question 13(a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $3$ | B1 | |
---
## Question 13(b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $[8 \times 3^4 =]\ 648$ | B1 | |
---
## Question 13(c):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\dfrac{8(3^n - 1)}{3-1} = 4(3^n - 1)$ or $-4(1-3^n)$ | B1 | use of formula for sum of gp; mark the final answer; or $4\times3^n - 4$ |
---
## Question 13(d):
| Answer | Marks | Guidance |
|--------|-------|----------|
| their $4(3^n - 1) = 185\,207$ or $3^n = 46303(.75)$ | M1 | **M0** for eg $8\times3^{n-1}$; allow use of $<$ or $\leq$ for up to 3 marks; allow **M1** only for use of $>$ or $\geq$; or $3^9 = 19683$ **and** $3^{10} = 59049$ seen for **M1** |
| awrt 9.8 cao | A1 | no FT available here; then **A1** (comparison with 46 303) |
| $[=]\ 9$ | A1 | not from wrong working |
---
## Question 13(e):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Unlikely because eg some of the population will be immune to the virus / some of the population will not be exposed to the virus / medical intervention / extrapolation / movement of people in and out of town | B1 | any sensible reason; it's unlikely that everyone will be affected oe is insufficient |
---13 The population of Melchester is 185207. During a nationwide flu epidemic the number of new cases in Melchester are recorded each day. The results from the first three days are shown in Fig. 13.
\begin{table}[h]
\begin{center}
\begin{tabular}{ | l | c | c | c | }
\hline
Day & 1 & 2 & 3 \\
\hline
Number of new cases & 8 & 24 & 72 \\
\hline
\end{tabular}
\captionsetup{labelformat=empty}
\caption{Fig. 13}
\end{center}
\end{table}
A doctor notices that the numbers of new cases on successive days are in geometric progression.
\begin{enumerate}[label=(\alph*)]
\item Find the common ratio for this geometric progression.
The doctor uses this geometric progression to model the number of new cases of flu in Melchester.
\item According to the model, how many new cases will there be on day 5?
\item Find a formula for the total number of cases from day 1 to day $n$ inclusive according to this model, simplifying your answer.
\item Determine the maximum number of days for which the model could be viable in Melchester.
\item State, with a reason, whether it is likely that the model will be viable for the number of days found in part (d).
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Paper 2 2019 Q13 [7]}}