Question 2 - A-Level Maths

Edexcel FD1 2020 June — Question 2 15 marks

Exam Board	Edexcel
Module	FD1 (Further Decision 1)
Year	2020
Session	June
Marks	15
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Critical Path Analysis
Type	Explain dummy activities
Difficulty	Moderate -0.3 This is a standard Further Maths Decision 1 question covering routine critical path analysis techniques. Part (a) requires explaining dummy activities (textbook knowledge), parts (b)-(c) involve mechanical application of forward/backward pass algorithms, and parts (d)-(e) are standard resource histogram construction and analysis. While multi-part with several marks, all components are direct applications of taught methods with no novel problem-solving required.
Spec	7.05a Critical path analysis: activity on arc networks 7.05b Forward and backward pass: earliest/latest times, critical activities

2. \begin{figure}[h]

\includegraphics[alt={},max width=\textwidth]{bd357978-6464-43fd-854f-4188b5408e91-03_688_1102_267_482} \captionsetup{labelformat=empty} \caption{Figure 1}

\end{figure} The network in Figure 1 shows the activities that need to be undertaken to complete a project. Each activity is represented by an arc and the duration, in hours, of the corresponding activity is shown in brackets.

Explain why each of the dummy activities is required.
Complete the table in the answer book to show the immediately preceding activities for each activity.
1. Complete Diagram 1 in the answer book to show the early event times and the late event times.
2. State the minimum completion time for the project.
3. State the critical activities. Each activity requires one worker. Each worker is able to do any of the activities. Once an activity is started it must be completed without interruption.
On Grid 1 in the answer book, draw a resource histogram to show the number of workers required at each time when each activity begins at its earliest possible start time.
Determine whether or not the project can be completed in the minimum possible time using fewer workers than the number indicated by the resource histogram in (d). You must justify your answer with reference to the resource histogram and the completed Diagram 1.

Show mark scheme Show mark scheme source

Question 2:

Part (a)

Answer	Marks	Guidance
Answer	Marks	Guidance
Dummy at end of activity B required as F (and G) are dependent on B only, but H is dependent on both B and C	B1	AO 2.4
Dummy at end of K required as two activities cannot start at the same event and finish at the same event	B1	AO 2.4

Part (b)

Answer	Marks	Guidance
Answer	Marks	Guidance
IPA table correct for: I = E,F; J = G,H; K = D,I; L = D,I	B1	AO 1.1b
IPA table correct for: E = A; F = B; G = B; H = B,C	B1	AO 1.1b

Part (c)(i)

Answer	Marks	Guidance
Answer	Marks	Guidance
Forward pass correct (early event times)	M1	AO 1.1b
Forward pass fully correct	A1	AO 1.1b
Backward pass correct (late event times)	M1	AO 1.1b
Backward pass fully correct; all values: 0,6,7,8,7,12,11,15,11,15,20,21	A1	AO 1.1b

Part (c)(ii)

Answer	Marks	Guidance
Answer	Marks	Guidance
Minimum completion time: 21 hours	A1ft	AO 1.1b

Part (c)(iii)

Answer	Marks	Guidance
Answer	Marks	Guidance
Critical activities: A, E, I, L	A1	AO 1.1b

Part (d)

Answer	Marks	Guidance
Answer	Marks	Guidance
Cascade (Gantt) chart started correctly	M1	AO 1.1b
Chart substantially correct	A1	AO 1.1b
Fully correct chart with all activities placed correctly on timeline 0–23	A1	AO 1.1b

Question 2:

Part (e)

Answer	Marks	Guidance
Answer	Mark	Guidance
Currently five workers are required between time 7 and 10, so one of the non-critical activities D, F, G or H would have to be delayed and start after time 10	M1	Explanation involving need to delay just one non-critical activity (must mention one of D, F, G or H) to start after time 10
e.g. Activity H could be delayed and start at time 10 (as it has sufficient total float and can finish as late as time 15) so the project can be completed with fewer workers; J could be delayed too and start at time 15	A1	Dependent on correct histogram and correct answer to (c)(i). Correct deduction possible to complete with fewer workers. A0 if mention of delaying activity F

# Question 2:

## Part (a)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Dummy at end of activity B required as F (and G) are dependent on B only, but H is dependent on both B and C | B1 | AO 2.4 |
| Dummy at end of K required as two activities cannot start at the same event and finish at the same event | B1 | AO 2.4 |

## Part (b)
| Answer | Marks | Guidance |
|--------|-------|----------|
| IPA table correct for: I = E,F; J = G,H; K = D,I; L = D,I | B1 | AO 1.1b |
| IPA table correct for: E = A; F = B; G = B; H = B,C | B1 | AO 1.1b |

## Part (c)(i)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Forward pass correct (early event times) | M1 | AO 1.1b |
| Forward pass fully correct | A1 | AO 1.1b |
| Backward pass correct (late event times) | M1 | AO 1.1b |
| Backward pass fully correct; all values: 0,6,7,8,7,12,11,15,11,15,20,21 | A1 | AO 1.1b |

## Part (c)(ii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Minimum completion time: 21 hours | A1ft | AO 1.1b |

## Part (c)(iii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Critical activities: A, E, I, L | A1 | AO 1.1b |

## Part (d)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Cascade (Gantt) chart started correctly | M1 | AO 1.1b |
| Chart substantially correct | A1 | AO 1.1b |
| Fully correct chart with all activities placed correctly on timeline 0–23 | A1 | AO 1.1b |

# Question 2:

## Part (e)
| Answer | Mark | Guidance |
|--------|------|----------|
| Currently five workers are required between time 7 and 10, so one of the non-critical activities D, F, G or H would have to be delayed and start after time 10 | M1 | Explanation involving need to delay just one non-critical activity (must mention one of D, F, G or H) to start after time 10 |
| e.g. Activity H could be delayed and start at time 10 (as it has sufficient total float and can finish as late as time 15) so the project can be completed with fewer workers; J could be delayed too and start at time 15 | A1 | Dependent on correct histogram and correct answer to (c)(i). Correct deduction possible to complete with fewer workers. A0 if mention of delaying activity F |

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Show LaTeX source

2.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{bd357978-6464-43fd-854f-4188b5408e91-03_688_1102_267_482}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}

The network in Figure 1 shows the activities that need to be undertaken to complete a project. Each activity is represented by an arc and the duration, in hours, of the corresponding activity is shown in brackets.
\begin{enumerate}[label=(\alph*)]
\item Explain why each of the dummy activities is required.
\item Complete the table in the answer book to show the immediately preceding activities for each activity.
\item \begin{enumerate}[label=(\roman*)]
\item Complete Diagram 1 in the answer book to show the early event times and the late event times.
\item State the minimum completion time for the project.
\item State the critical activities.

Each activity requires one worker. Each worker is able to do any of the activities. Once an activity is started it must be completed without interruption.
\end{enumerate}\item On Grid 1 in the answer book, draw a resource histogram to show the number of workers required at each time when each activity begins at its earliest possible start time.
\item Determine whether or not the project can be completed in the minimum possible time using fewer workers than the number indicated by the resource histogram in (d). You must justify your answer with reference to the resource histogram and the completed Diagram 1.
\end{enumerate}

\hfill \mbox{\textit{Edexcel FD1 2020 Q2 [15]}}

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