| Exam Board | OCR |
|---|---|
| Module | Further Discrete AS (Further Discrete AS) |
| Year | 2023 |
| Session | June |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Principle of Inclusion/Exclusion |
| Type | Exactly One Event Occurs |
| Difficulty | Moderate -0.8 This is a straightforward application of the two-set inclusion-exclusion formula |T ∪ B| = |T| + |B| - |T ∩ B|, with all values given directly. Part (a) is trivial recall, and part (b) requires only direct substitution: 7 = 2 + 6 - x, giving x = 1. No problem-solving or conceptual challenge beyond recognizing the standard formula. |
| Spec | 7.01a Types of problem: existence, construction, enumeration, optimisation7.01k Inclusion-exclusion: for two sets |
| Answer | Marks | Guidance |
|---|---|---|
| 1 | (a) | Find a bus or train (or both) that can be used |
| to travel from home to town | B1 | |
| [1] | 1.1 | Any appropriate problem, request or question, in context, that |
| Answer | Marks | Guidance |
|---|---|---|
| 1 | (b) | 7 = 6 + 2 – n(BT) |
| Answer | Marks |
|---|---|
| 1 journey by both bus and train | M1 |
| Answer | Marks |
|---|---|
| [2] | 2.5 |
| 2.2a | Use inclusion-exclusion (soi) |
| Answer | Marks |
|---|---|
| 1 | 0 |
| 1 | 0 |
Question 1:
1 | (a) | Find a bus or train (or both) that can be used
to travel from home to town | B1
[1] | 1.1 | Any appropriate problem, request or question, in context, that
would require a construction for its solution
1 | (b) | 7 = 6 + 2 – n(BT)
8 – 7
1 journey by both bus and train | M1
A1
[2] | 2.5
2.2a | Use inclusion-exclusion (soi)
Maybe shown as a Venn diagram o.e.
5 1 1
Bus Train
1
seen as answer
(not picked out from Venn diagram, unless clearly indicated)
1 | 0
1 | 01 Jane wants to travel from home to the local town.
Jane can do this by train, by bus or by both train and bus.
\begin{enumerate}[label=(\alph*)]
\item Give an example of a problem that Jane could be answering that would give a construction problem.
A website gives Jane all the possible buses and trains that she could use.\\
Jane finds 7 possible ways to make the journey.
\begin{itemize}
\item 2 of the 7 journeys involve travelling by train for at least part of the journey
\item 6 of the 7 journeys involve travelling by bus for at least part of the journey
\item Use the inclusion-exclusion principle to find how many of the 7 journeys involve travelling by both train and bus.
\end{itemize}
\end{enumerate}
\hfill \mbox{\textit{OCR Further Discrete AS 2023 Q1 [3]}}