| Exam Board | OCR MEI |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2011 |
| Session | January |
| Marks | 16 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Calculate early and late times |
| Difficulty | Moderate -0.5 This is a standard Critical Path Analysis question covering routine D1 techniques (precedence tables, network diagrams, forward/backward passes, float calculations, and cascade charts). While multi-part with several marks, each component follows textbook procedures with no novel problem-solving required. The context is straightforward and the calculations are mechanical, making it slightly easier than an average A-level question. |
| 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 interpretation7.05d Latest start and earliest finish: independent and interfering float7.05e Cascade charts: scheduling and effect of delays |
| Task | Description | Duration (mins) |
| A | Fill kettle and switch on | 0.5 |
| B | Boil kettle | 1.5 |
| C | Cut bread and put in toaster | 0.5 |
| D | Toast bread | 2 |
| E | Put eggs in pan of water and light gas | 1 |
| F | Boil eggs | 5 |
| G | Put tablecloth, cutlery and crockery on table | 2.5 |
| H | Make tea and put on table | 0.5 |
| I | Collect toast and put on table | 0.5 |
| J | Put eggs in cups and put on table | 1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Immediate predecessors: A, C, E and G correct | B1 | |
| Immediate predecessors: B, D and F correct | B1 | |
| Immediate predecessors: H, I and J correct | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Activity-on-arc network | M1 | no follow through; no multiple starts |
| Activities A, G, C, E correctly placed | A1 | |
| Activities B, D, F correctly placed | A1 | no multiple ends |
| Activities H, I, J correctly placed | A1 | \(\sqrt{}\) but no follow through of activity-on-node; \(\sqrt{}\) ditto |
| Forward pass correct | M1 A1 | |
| Backward pass correct | M1 A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Critical activities: E; F; J | B1 | cao |
| Duration: 7 minutes | B1 | cao |
| Floats: A=4.5, B=4.5, C=4, D=4, E=0, F=0, G=3.5, H=4, I=4, J=0 | B1 | cao, blank\(=0\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Cascade/condensed cascade diagram with 9 or 10 activities | M1 | need to have 9 or 10 activities |
| Activities other than B, D and F non-overlapping | A1 | E C A G H I J |
| Correctly finishes in 7 | A1 | cao |
# Question 4:
## Part (i)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Immediate predecessors: A, C, E and G correct | B1 | |
| Immediate predecessors: B, D and F correct | B1 | |
| Immediate predecessors: H, I and J correct | B1 | |
## Parts (ii) & (iii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Activity-on-arc network | M1 | no follow through; no multiple starts |
| Activities A, G, C, E correctly placed | A1 | |
| Activities B, D, F correctly placed | A1 | no multiple ends |
| Activities H, I, J correctly placed | A1 | $\sqrt{}$ but no follow through of activity-on-node; $\sqrt{}$ ditto |
| Forward pass correct | M1 A1 | |
| Backward pass correct | M1 A1 | |
## Part (iv)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Critical activities: E; F; J | B1 | cao |
| Duration: 7 minutes | B1 | cao |
| Floats: A=4.5, B=4.5, C=4, D=4, E=0, F=0, G=3.5, H=4, I=4, J=0 | B1 | cao, blank$=0$ |
## Part (v)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Cascade/condensed cascade diagram with 9 or 10 activities | M1 | need to have 9 or 10 activities |
| Activities other than B, D and F non-overlapping | A1 | E C A G H I J |
| Correctly finishes in 7 | A1 | cao |
---4 The table shows the tasks involved in preparing breakfast, and their durations.
\begin{center}
\begin{tabular}{|l|l|l|}
\hline
Task & Description & Duration (mins) \\
\hline
A & Fill kettle and switch on & 0.5 \\
\hline
B & Boil kettle & 1.5 \\
\hline
C & Cut bread and put in toaster & 0.5 \\
\hline
D & Toast bread & 2 \\
\hline
E & Put eggs in pan of water and light gas & 1 \\
\hline
F & Boil eggs & 5 \\
\hline
G & Put tablecloth, cutlery and crockery on table & 2.5 \\
\hline
H & Make tea and put on table & 0.5 \\
\hline
I & Collect toast and put on table & 0.5 \\
\hline
J & Put eggs in cups and put on table & 1 \\
\hline
\end{tabular}
\end{center}
(i) Show the immediate predecessors for each of these tasks.\\
(ii) Draw an activity on arc network modelling your precedences.\\
(iii) Perform a forward pass and a backward pass to find the early time and the late time for each event.\\
(iv) Give the critical activities, the project duration, and the total float for each activity.\\
(v) Given that only one person is available to do these tasks, and noting that tasks B, D and F do not require that person's attention, produce a cascade chart showing how breakfast can be prepared in the least possible time.
\hfill \mbox{\textit{OCR MEI D1 2011 Q4 [16]}}