| Exam Board | AQA |
|---|---|
| Module | Further AS Paper 2 Discrete (Further AS Paper 2 Discrete) |
| Year | 2024 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Minimum Spanning Trees |
| Type | Draw minimum spanning tree |
| Difficulty | Moderate -0.3 This is a straightforward application of Kruskal's or Prim's algorithm to find a minimum spanning tree, followed by simple addition. While it requires knowledge of a standard algorithm, the execution is mechanical with no problem-solving insight needed. The 4 total marks and routine nature place it slightly below average difficulty. |
| Spec | 7.04b Minimum spanning tree: Prim's and Kruskal's algorithms |
| Answer | Marks |
|---|---|
| 5(a) | Draws a tree with all vertices |
| Answer | Marks | Guidance |
|---|---|---|
| correct | 3.4 | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| edges | 1.1a | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| all vertices labelled | 1.1b | A1 |
| Subtotal | 3 | |
| Q | Marking instructions | AO |
| Answer | Marks |
|---|---|
| 5(b) | Obtains the correct total length for |
| Answer | Marks | Guidance |
|---|---|---|
| Condone missing units | 1.1b | B1F |
| Subtotal | 1 | |
| Question total | 4 | |
| Q | Marking instructions | AO |
Question 5:
--- 5(a) ---
5(a) | Draws a tree with all vertices
labelled and at least four edges
correct | 3.4 | M1
Draws a spanning tree with all
vertices labelled and exactly 6
edges | 1.1a | M1
Draws the fully correct spanning
tree of minimum total length with
all vertices labelled | 1.1b | A1
Subtotal | 3
Q | Marking instructions | AO | Marks | Typical solution
--- 5(b) ---
5(b) | Obtains the correct total length for
their spanning tree from part (a)
Condone missing units | 1.1b | B1F | 84 miles
Subtotal | 1
Question total | 4
Q | Marking instructions | AO | Marks | Typical solutionA network of roads connects the villages $A$, $B$, $C$, $D$, $E$, $F$ and $G$
The weight on each arc in the network represents the distance, in miles, between adjacent villages.
The network is shown in the diagram below.
\includegraphics{figure_5}
\begin{enumerate}[label=5 (\alph*)]
\item Draw, in the space below, the spanning tree of minimum total length for this road network.
[3 marks]
\item Find the total length of the spanning tree drawn in part (a).
[1 mark]
\end{enumerate}
\hfill \mbox{\textit{AQA Further AS Paper 2 Discrete 2024 Q5 [4]}}