| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2020 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Identify guaranteed critical activities |
| Difficulty | Moderate -0.8 Part (a) is a standard network drawing exercise requiring careful dummy placement (5 marks). Parts (b) and (c) are straightforward logical deductions: if K is critical, trace back its predecessors (D, then A and B); if all durations equal, find the longest path by counting activities. This is routine D1 material 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 |
| Activity | Immediately preceding activities |
| A | - |
| B | - |
| C | A |
| D | A, B |
| E | C, D |
| F | D |
| G | C |
| H | G |
| I | G |
| J | E, F, I |
| K | F |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| (a) [Network diagram with 8 activities (labelled on arc), one start and at least two dummies placed] | A1 A1 A1 A1 A1 (5) | In (a) condone lack of, or incorrect, numbered events throughout – also 'dealt with correctly' means that the activity starts from the correct event but may not finish at the correct event (use the table below to check this). Activity on node is M0. If an arc is not labelled, for example, if the arc for activity D is not labelled (but the arc is present) then this will lose the first A mark and the final (CSO) A mark – they can still earn the second A mark on the bod. If two or more arcs are not labelled then mark according to the scheme. Assume that a solid line is an activity which has not been labelled rather than a dummy (even if in the incorrect place for where a dummy should be). Ignore incorrect or lack of arrows on the activities for the first four marks only. a1M1: Eight activities (labelled on arc), one start and at least two dummies placed. a1A1: Activities A, B, C, 1st dummy (+ correct arrow on this dummy – this is the dummy at the end of A) and D dealt with correctly. a2A1: 2nd and 3rd dummies (+ correct arrows on these dummies – these dummies are the ones at the end of C and D) and E, F and G dealt with correctly. a3A1: 4th dummy (+ correct arrow on this dummy – this is the dummy at the end of F) and activities H, I, J and K dealt with correctly. a4A1: CSO – all arrows present and correctly placed with one finish. Please check all arcs carefully for arrows – if there are no arrows on any dummies then M1 only. Note that additional (but unnecessary) 'correct' dummies that still maintain precedence for the network should only be penalised with the final A mark if earned. |
| (b) D and F are guaranteed to be critical | B1 (1) | b1B1: CAO (D and F) and no other activities stated as critical (however, ignore K if stated too). |
| (c) Critical path: \(A – C – G – I – J\) | B1 (1) 7 marks | c1B1: CAO (\(A – C – G – I – J\)). |
| Answer | Marks | Guidance |
|--------|-------|----------|
| (a) [Network diagram with 8 activities (labelled on arc), one start and at least two dummies placed] | A1 A1 A1 A1 A1 (5) | In (a) condone lack of, or incorrect, numbered events throughout – also 'dealt with correctly' means that the activity starts from the correct event but may not finish at the correct event (use the table below to check this). Activity on node is M0. If an arc is not labelled, for example, if the arc for activity D is not labelled (but the arc is present) then this will lose the first A mark and the final (CSO) A mark – they can still earn the second A mark on the bod. If two or more arcs are not labelled then mark according to the scheme. Assume that a solid line is an activity which has not been labelled rather than a dummy (even if in the incorrect place for where a dummy should be). Ignore incorrect or lack of arrows on the activities for the first four marks only. a1M1: Eight activities (labelled on arc), one start and at least two dummies placed. a1A1: Activities A, B, C, 1st dummy (+ correct arrow on this dummy – this is the dummy at the end of A) and D dealt with correctly. a2A1: 2nd and 3rd dummies (+ correct arrows on these dummies – these dummies are the ones at the end of C and D) and E, F and G dealt with correctly. a3A1: 4th dummy (+ correct arrow on this dummy – this is the dummy at the end of F) and activities H, I, J and K dealt with correctly. a4A1: CSO – all arrows present and correctly placed with one finish. **Please check all arcs carefully for arrows – if there are no arrows on any dummies then M1 only.** Note that additional (but unnecessary) 'correct' dummies that still maintain precedence for the network should only be penalised with the final A mark if earned. |
| (b) D and F are guaranteed to be critical | B1 (1) | b1B1: CAO (D and F) and no other activities stated as critical (however, ignore K if stated too). |
| (c) Critical path: $A – C – G – I – J$ | B1 (1) 7 marks | c1B1: CAO ($A – C – G – I – J$). |
---4. (a) Draw the activity network described by the precedence table below, using activity on arc. Use dummies only where necessary.\\
(5)
\begin{center}
\begin{tabular}{|l|l|}
\hline
Activity & Immediately preceding activities \\
\hline
A & - \\
\hline
B & - \\
\hline
C & A \\
\hline
D & A, B \\
\hline
E & C, D \\
\hline
F & D \\
\hline
G & C \\
\hline
H & G \\
\hline
I & G \\
\hline
J & E, F, I \\
\hline
K & F \\
\hline
\end{tabular}
\end{center}
Given that K is a critical activity,\\
(b) state which other activities must also be critical.\\
(1)
Given instead that all activities shown in the precedence table have the same duration and K is not necessarily critical,\\
(c) state the critical path for the network.\\
(1)\\
\hfill \mbox{\textit{Edexcel D1 2020 Q4 [7]}}