| Exam Board | AQA |
|---|---|
| Module | Further AS Paper 2 Discrete (Further AS Paper 2 Discrete) |
| Year | 2022 |
| Session | June |
| Marks | 2 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Graph Theory Fundamentals |
| Type | Subgraph identification |
| Difficulty | Easy -1.2 This question tests basic definitions from graph theory: a tree with n vertices has n-1 edges (pure recall), and a simple connected graph on n vertices has at most n(n-1)/2 edges (standard formula). Both parts require only direct application of memorized formulas with no problem-solving or insight needed, making this significantly easier than average A-level questions. |
| Spec | 7.02b Graph terminology: tree, simple, connected, simply connected7.02d Complete graphs: K_n and number of arcs |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(3\) | B1 | Circles correct answer; AO1.2 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(5\) | B1 | Circles correct answer; AO1.1b |
## Question 1:
### Part (a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $3$ | B1 | Circles correct answer; AO1.2 |
### Part (b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $5$ | B1 | Circles correct answer; AO1.1b |
---1 The connected graph $G$ is shown below.\\
\includegraphics[max width=\textwidth, alt={}, center]{ecbeedf5-148e-40ad-b8a2-a7aa3db4a115-02_542_834_630_603}
The graphs $A$ and $B$ are subgraphs of $G$\\
Both $A$ and $B$ have four vertices.
1
\begin{enumerate}[label=(\alph*)]
\item The graph $A$ is a tree with $x$ edges.\\
State the value of $x$
Circle your answer.
3459
1
\item The graph $B$ is simple-connected with $y$ edges.\\
Find the maximum possible value of $y$\\
Circle your answer.
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\end{enumerate}
\hfill \mbox{\textit{AQA Further AS Paper 2 Discrete 2022 Q1 [2]}}