| Exam Board | AQA |
|---|---|
| Module | Further AS Paper 2 Discrete (Further AS Paper 2 Discrete) |
| Year | 2021 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Network Flows |
| Type | Add supersource and/or supersink |
| Difficulty | Moderate -0.5 This is a straightforward application of basic max-flow min-cut concepts in network theory. Parts (a) and (b) require simply summing capacities across given cuts (1 mark each suggests direct calculation), while part (c) is a standard construction technique. No complex algorithm application or proof required, just routine procedural work on a familiar Further Maths topic. |
| Spec | 7.02p Networks: weighted graphs, modelling connections |
| Answer | Marks | Guidance |
|---|---|---|
| 3(a) | Finds the correct value of Cut X | |
| Condone missing/incorrect units | 1.1b | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Total | 1 | |
| Q | Marking instructions | AO |
| Answer | Marks | Guidance |
|---|---|---|
| 3(b) | Finds the correct value of Cut Y | |
| Condone missing/incorrect units | 1.1b | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Total | 1 | |
| Q | Marking instructions | AO |
| Answer | Marks |
|---|---|
| 3(c) | Identifies at least one sink of the |
| Answer | Marks | Guidance |
|---|---|---|
| PI | 1.1a | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| and appropriate weights | 1.1b | A1 |
| Total | 2 | |
| Question total | 4 | |
| Q | Marking instructions | AO |
Question 3:
--- 3(a) ---
3(a) | Finds the correct value of Cut X
Condone missing/incorrect units | 1.1b | B1 | 25 + 30 + 40
= 95 m3 s–1
Total | 1
Q | Marking instructions | AO | Marks | Typical solution
--- 3(b) ---
3(b) | Finds the correct value of Cut Y
Condone missing/incorrect units | 1.1b | B1 | 25 + 30 + 40
= 95 m3 s–1
Total | 1
Q | Marking instructions | AO | Marks | Typical solution
--- 3(c) ---
3(c) | Identifies at least one sink of the
network
PI | 1.1a | M1 | Nodes F and D are sinks
Draws correct arcs with arrows
and appropriate weights | 1.1b | A1
Total | 2
Question total | 4
Q | Marking instructions | AO | Marks | Typical solutionThe diagram shows a network of pipes.
Each pipe is labelled with its upper capacity in $\mathrm{m}^3 \mathrm{s}^{-1}$
\includegraphics{figure_3}
\begin{enumerate}[label=(\alph*)]
\item Find the value of Cut $X$
[1 mark]
\item Find the value of Cut $Y$
[1 mark]
\item Add a supersink $T$ to the network.
[2 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA Further AS Paper 2 Discrete 2021 Q3 [4]}}