| Exam Board | AQA |
|---|---|
| Module | Further Paper 3 Discrete (Further Paper 3 Discrete) |
| Year | 2024 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Minimum Spanning Trees |
| Type | Apply Prim's algorithm from vertex |
| Difficulty | Moderate -0.8 This is a standard minimum spanning tree problem requiring direct application of Kruskal's or Prim's algorithm with no complications. The question is routine for Further Maths students: identify it's an MST problem, apply the algorithm to find edges, sum weights, and state one practical limitation. The 4-mark allocation and straightforward structure confirm this is below average difficulty even for Further Maths. |
| Spec | 7.04b Minimum spanning tree: Prim's and Kruskal's algorithms |
| Answer | Marks |
|---|---|
| 5(a)(i) | Sets up a model of finding a |
| Answer | Marks | Guidance |
|---|---|---|
| arcs and at least 5 arcs correct | 3.3 | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| spanning tree | 3.4 | A1 |
| Subtotal | 2 | |
| Q | Marking instructions | AO |
| Answer | Marks | Guidance |
|---|---|---|
| 5(a)(ii) | Obtains 775 hours | |
| FT their minimum spanning tree | 3.2a | B1F |
| Answer | Marks | Guidance |
|---|---|---|
| Subtotal | 1 | |
| Q | Marking instructions | AO |
| Answer | Marks |
|---|---|
| 5(b) | Recognises a valid limitation of |
| Answer | Marks | Guidance |
|---|---|---|
| connectedness of the network | 3.5b | E1 |
| Answer | Marks | Guidance |
|---|---|---|
| Subtotal | 1 | |
| Question total | 4 | |
| Q | Marking instructions | AO |
Question 5:
--- 5(a)(i) ---
5(a)(i) | Sets up a model of finding a
minimum spanning tree with 9
arcs and at least 5 arcs correct | 3.3 | M1 | X–A: 100
A–D: 75
D–G: 95
G–H: 75
D–E: 100
B–E: 65
E–I: 95
F–I: 45
C–E: 125
Finds the correct minimum
spanning tree | 3.4 | A1
Subtotal | 2
Q | Marking instructions | AO | Marks | Typical solution
--- 5(a)(ii) ---
5(a)(ii) | Obtains 775 hours
FT their minimum spanning tree | 3.2a | B1F | 100 + 75 + 95 + 75 + 100 + 65
+ 95 + 45 + 125
= 775 hours
Subtotal | 1
Q | Marking instructions | AO | Marks | Typical solution
--- 5(b) ---
5(b) | Recognises a valid limitation of
the model in the context of the
question related to the
connectedness of the network | 3.5b | E1 | If an electrical connection fails, it
may result in more than one car
park being unable to charge
electric cars.
Subtotal | 1
Question total | 4
Q | Marking instructions | AO | Marks | Typical solutionThe owners of a sports stadium want to install electric car charging points in each of the stadium's nine car parks.
An engineer creates a plan which requires installing electrical connections so that each car park is connected, directly or indirectly, to the stadium's main electricity power supply.
The engineer produces the network shown below, where the nodes represent the stadium's main electricity power supply $X$ and the nine car parks $A$, $B$, $\ldots$, $I$
\includegraphics{figure_5}
Each arc represents a possible electrical connection which could be installed.
The weight on each arc represents the time, in hours, it would take to install the electrical connection. The electrical connections can only be installed one at a time.
To reduce disruption, the owners of the sports stadium want the required electrical connections to be installed in the minimum possible total time.
\begin{enumerate}[label=(\alph*)]
\item \begin{enumerate}[label=(\roman*)]
\item Determine the electrical connections that should be installed.
[2 marks]
\item Find the minimum possible total time needed to install the required electrical connections.
[1 mark]
\end{enumerate}
\item Following the installation of the electrical connections, some of the car parks have an indirect connection to the stadium's main electricity power supply.
Give one limitation of this installation.
[1 mark]
\end{enumerate}
\hfill \mbox{\textit{AQA Further Paper 3 Discrete 2024 Q5 [4]}}