| Exam Board | Edexcel |
|---|---|
| Module | P2 (Pure Mathematics 2) |
| Year | 2024 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Find n given sum condition |
| Difficulty | Standard +0.3 This is a straightforward arithmetic series problem requiring standard formulas (nth term and sum). Part (a) involves solving two simultaneous equations, and part (b) requires solving a quadratic inequality. While it has multiple steps, all techniques are routine and commonly practiced in P2, making it slightly easier than average. |
| Spec | 1.04h Arithmetic sequences: nth term and sum formulae1.04k Modelling with sequences: compound interest, growth/decay |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(a+5d=2\) | B1 | One of the two equations correct |
| \(\frac{10}{2}\{2a+9d\}=-80\) | B1 | Both equations correct. May be unsimplified |
| Solves simultaneously \(\Rightarrow d=20,\ a=-98\) | M1 | Solves their two equations in \(a\) and \(d\); one must be correct, finds at least \(a\) or \(d\) |
| \(d=20,\ a=-98\) | A1 | Both correct |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Attempts \(\frac{n}{2}\{2\times-98+(n-1)\times20\}...8000\) | M1 | Attempts sum formula with their \(a\) and \(d\). Accept if set equal to 8001; allow M if 800 or 80000 used (misread) |
| \(5n^2-54n-4000...0 \Rightarrow n=(34.2)\) | dM1 | Sets up and solves 3-term quadratic in \(n\); accept if just positive root given |
| \(n=35\) | A1 | \((n=)35\) stated following correct equation; allow for incorrect inequality |
# Question 2:
## Part (a)
| Answer/Working | Marks | Guidance |
|---|---|---|
| $a+5d=2$ | B1 | One of the two equations correct |
| $\frac{10}{2}\{2a+9d\}=-80$ | B1 | Both equations correct. May be unsimplified |
| Solves simultaneously $\Rightarrow d=20,\ a=-98$ | M1 | Solves their two equations in $a$ and $d$; one must be correct, finds at least $a$ or $d$ |
| $d=20,\ a=-98$ | A1 | Both correct |
## Part (b)
| Answer/Working | Marks | Guidance |
|---|---|---|
| Attempts $\frac{n}{2}\{2\times-98+(n-1)\times20\}...8000$ | M1 | Attempts sum formula with their $a$ and $d$. Accept if set equal to 8001; allow M if 800 or 80000 used (misread) |
| $5n^2-54n-4000...0 \Rightarrow n=(34.2)$ | dM1 | Sets up and solves 3-term quadratic in $n$; accept if just positive root given |
| $n=35$ | A1 | $(n=)35$ stated following correct equation; allow for incorrect inequality |
---\begin{enumerate}
\item In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
\end{enumerate}
In an arithmetic series,
\begin{itemize}
\item the sixth term is 2
\item the sum of the first ten terms is - 80
\end{itemize}
For this series,\\
(a) find the value of the first term and the value of the common difference.\\
(b) Hence find the smallest value of $n$ for which
$$S _ { n } > 8000$$
\hfill \mbox{\textit{Edexcel P2 2024 Q2 [7]}}