| Exam Board | OCR |
|---|---|
| Module | Further Discrete AS (Further Discrete AS) |
| Year | 2022 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Find range for variable duration |
| Difficulty | Standard +0.3 This is a standard critical path analysis question requiring routine forward/backward pass calculations and float determination. Part (c) adds a slight twist by asking for a maximum value of t, but this is a straightforward application of understanding float and critical path concepts—students just need to recognize that B can be delayed by its float amount without affecting project completion time. The question is slightly above average difficulty due to the multi-part nature and the variable constraint in part (c), but remains a textbook-style exercise with no novel problem-solving required. |
| Spec | 7.05a Critical path analysis: activity on arc networks7.05b Forward and backward pass: earliest/latest times, critical activities7.05c Total float: calculation and interpretation |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Forward pass: A(5), C(6), D(4), F(3), giving values \(\ | 4\ | 14\ |
| Backward pass: B(3), E(2), giving \(\ | 3\ | 7\ |
| Final diagram correct | A1 | cao |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(A=0, C=0, F=0\) | B1 | A, C and \(F=0\) |
| \(B=4, D=2, E=5, G=5\) correct or ft from (a) | B1 FT | B, D, E and G correct or ft their values from (a) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Longest route is now \(BDF = t+7\) | M1 | Consider any route starting with B, or (their)\(7+(16-\text{their } 14)\) or \(16-(3+4)\), or implied from answer \(t=9\) |
| Maximum value of \(t=9\) | A1 | 9 as answer |
# Question 2:
## Part (a)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Forward pass: A(5), C(6), D(4), F(3), giving values $\|4\|14\|$; nodes $\|0\|0\|$, $\|5\|7\|$ shown | B1 | Forward pass all correct |
| Backward pass: B(3), E(2), giving $\|3\|7\|$, $\|5\|10\|$ with values not increasing working from end to start | M1 | Backward pass with values not increasing working from end to start |
| Final diagram correct | A1 | cao |
## Part (b)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $A=0, C=0, F=0$ | B1 | A, C and $F=0$ |
| $B=4, D=2, E=5, G=5$ correct or ft from (a) | B1 FT | B, D, E and G correct or ft their values from (a) |
## Part (c)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Longest route is now $BDF = t+7$ | M1 | Consider any route starting with B, or (their)$7+(16-\text{their } 14)$ or $16-(3+4)$, or implied from answer $t=9$ |
| Maximum value of $t=9$ | A1 | 9 as answer |
---2 The activities involved in a project and their durations, in hours, are represented in the activity network below.\\
\includegraphics[max width=\textwidth, alt={}, center]{74b6f747-7045-4902-8b21-0b59c007f7f6-3_446_1139_338_230}
\begin{enumerate}[label=(\alph*)]
\item Carry out a forward pass and a backward pass through the network.
\item Calculate the float for each activity.
A delay means that activity B cannot finish until $t$ hours have elapsed from the start of the project.
\item Determine the maximum value of $t$ for which the project can be completed in 16 hours.
\end{enumerate}
\hfill \mbox{\textit{OCR Further Discrete AS 2022 Q2 [7]}}