| Exam Board | AQA |
|---|---|
| Module | Further AS Paper 2 Discrete (Further AS Paper 2 Discrete) |
| Year | 2021 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Dynamic Programming |
| Type | Zero-sum game stable solution |
| Difficulty | Standard +0.3 This is a standard game theory question on zero-sum games requiring identification of play-safe strategies (finding row minima and column maxima) and analyzing outcomes. While it requires understanding of game theory concepts from Further Maths, the procedures are algorithmic and well-practiced. The 6 total marks and straightforward structure place it slightly above average difficulty for A-level, but below typical Further Maths proof or multi-step optimization problems. |
| Spec | 7.08c Pure strategies: play-safe strategies and stable solutions |
| Answer | Marks | Guidance |
|---|---|---|
| 6(a) | Finds row minima | 1.1a |
| Answer | Marks | Guidance |
|---|---|---|
| strategy for Vaya | 1.1b | A1 |
| Finds column maxima | 1.1a | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| strategies for Wynne | 1.1b | A1 |
| Total | 4 | |
| Q | Marking instructions | AO |
| Answer | Marks |
|---|---|
| 6(b) | Translates the problem to a |
| Answer | Marks | Guidance |
|---|---|---|
| part (a) | 3.1b | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| for Wynne | 2.2a | A1F |
| Total | 2 | |
| Question total | 6 | |
| Q | Marking instructions | AO |
Question 6:
--- 6(a) ---
6(a) | Finds row minima | 1.1a | M1 | Row minima = (–250, –100, –200)
max(row minima) = –100
Play-safe strategy for Vaya is V
2
Column maxima = (75, 300, 75)
min(column maxima) = 75
Play-safe strategies for Wynne are
W and W
1 3
Correctly finds play-safe
strategy for Vaya | 1.1b | A1
Finds column maxima | 1.1a | M1
Correctly finds both play-safe
strategies for Wynne | 1.1b | A1
Total | 4
Q | Marking instructions | AO | Marks | Typical solution
--- 6(b) ---
6(b) | Translates the problem to a
mathematical process by
identifying possible outcomes or
strategies
FT the play-safe strategies from
part (a) | 3.1b | M1 | Wynne always plays W
2
Vaya either plays V or V
1 3
Best outcome for Wynne is to gain
200 each time the game is played.
Deduces correct best outcome
for Wynne | 2.2a | A1F
Total | 2
Question total | 6
Q | Marking instructions | AO | Marks | Typical solutionVaya and Wynne are playing a zero-sum game.
The game is represented by the pay-off matrix for Vaya.
\includegraphics{figure_6}
\begin{enumerate}[label=(\alph*)]
\item Find the play-safe strategies for Vaya and Wynne.
Fully justify your answer.
[4 marks]
\item Vaya and Wynne decide not to play their play-safe strategies.
Deduce the best possible outcome for Wynne.
[2 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA Further AS Paper 2 Discrete 2021 Q6 [6]}}