| Exam Board | OCR MEI |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2015 |
| Session | June |
| Marks | 16 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Calculate early and late times |
| Difficulty | Moderate -0.3 This is a standard critical path analysis question requiring routine application of well-defined algorithms (drawing network, forward/backward pass, identifying critical path, and resource scheduling). While multi-part with several marks, it involves no novel problem-solving—just methodical execution of textbook procedures that D1 students practice extensively. |
| 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 | Duration (mins) | Immediate predecessor(s) | |
| A | select mounting | 5 | - |
| B | glue picture to mounting | 5 | A |
| C | allow mounting glue to dry | 20 | B |
| D | measure for frame | 5 | A |
| E | select type of frame | 10 | A |
| F | cut four frame pieces | 5 | D, E |
| G | pin and glue frame pieces together | 5 | F |
| H | allow frame glue to dry | 20 | G |
| I | cut and bevel glass | 30 | D |
| J | fit glass to frame | 5 | H, I |
| K | fit mounted picture to frame | 5 | C, J |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Activity on arc diagram with correct structure | M1 | activity on arc |
| F & I correctly placed | A1 | F & I |
| J correctly placed | A1 | J |
| K correctly placed | A1 | K |
| Rest of activities correct | A1 | rest |
| [5] | ||
| Forward pass correct | M1A1\(\checkmark\) | forward pass |
| Backward pass correct | M1A1\(\checkmark\) | backward pass |
| Minimum completion time \(= 55\) minutes | B1cao | time |
| Critical activities \(= \) A, E, F, G, H, J, K | B1cao | critical activities |
| [6] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| e.g. (each cell represents 5 minutes): \(1^{st}\) person: A, E, E, F, G, \(\ldots\), J, K | M1 | A, E, F, G allocated OK |
| \(2^{nd}\) person: B, D, I, I, I, I, I, I | A1 | B, D, I, J, K OK |
| Other activities: C, C, C, C and H, H, H, H correctly timed | B1 | C and H correctly timed |
| [3] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| e.g. \(1^{st}\) person: A, D, I, I, I, I, I, I, J, K; \(2^{nd}\) person: B, E, E, F, G | B1 | a correct schedule for two people |
| 50 minutes | B1 | 50 minutes seen |
| [2] |
# Question 5:
## Part (i) & (ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Activity on arc diagram with correct structure | M1 | activity on arc |
| F & I correctly placed | A1 | F & I |
| J correctly placed | A1 | J |
| K correctly placed | A1 | K |
| Rest of activities correct | A1 | rest |
| | **[5]** | |
| Forward pass correct | M1A1$\checkmark$ | forward pass |
| Backward pass correct | M1A1$\checkmark$ | backward pass |
| Minimum completion time $= 55$ minutes | B1cao | time |
| Critical activities $= $ A, E, F, G, H, J, K | B1cao | critical activities |
| | **[6]** | |
## Part (iii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| e.g. (each cell represents 5 minutes): $1^{st}$ person: A, E, E, F, G, $\ldots$, J, K | M1 | A, E, F, G allocated OK |
| $2^{nd}$ person: B, D, I, I, I, I, I, I | A1 | B, D, I, J, K OK |
| Other activities: C, C, C, C and H, H, H, H correctly timed | B1 | C and H correctly timed |
| | **[3]** | |
## Part (iv):
| Answer | Marks | Guidance |
|--------|-------|----------|
| e.g. $1^{st}$ person: A, D, I, I, I, I, I, I, J, K; $2^{nd}$ person: B, E, E, F, G | B1 | a correct schedule for two people |
| 50 minutes | B1 | 50 minutes seen |
| | **[2]** | |
---5 The table lists activities which are involved in framing a picture. The table also lists their durations and their immediate predecessors. Except for activities C and H, each activity is undertaken by one person. Activities C and H require no people.
\begin{center}
\begin{tabular}{|l|l|l|l|}
\hline
\multicolumn{2}{|c|}{Activity} & Duration (mins) & Immediate predecessor(s) \\
\hline
A & select mounting & 5 & - \\
\hline
B & glue picture to mounting & 5 & A \\
\hline
C & allow mounting glue to dry & 20 & B \\
\hline
D & measure for frame & 5 & A \\
\hline
E & select type of frame & 10 & A \\
\hline
F & cut four frame pieces & 5 & D, E \\
\hline
G & pin and glue frame pieces together & 5 & F \\
\hline
H & allow frame glue to dry & 20 & G \\
\hline
I & cut and bevel glass & 30 & D \\
\hline
J & fit glass to frame & 5 & H, I \\
\hline
K & fit mounted picture to frame & 5 & C, J \\
\hline
\end{tabular}
\end{center}
(i) Draw an activity on arc network for these activities.\\
(ii) Mark on your diagram the early time and the late time for each event. Give the minimum completion time and the critical activities.
A picture is to be framed as quickly as possible. Two people are available to do the job.\\
(iii) Produce a schedule to show how two people can complete the picture framing in the minimum time.
To reduce the completion time an instant glue is to be used. This will reduce the time for activities C and H to 0 minutes.\\
(iv) Produce a schedule for two people to complete the framing in the new minimum completion time, and give that time.
\hfill \mbox{\textit{OCR MEI D1 2015 Q5 [16]}}