Question 6 - A-Level Maths

Edexcel FD1 2024 June — Question 6 11 marks

Exam Board	Edexcel
Module	FD1 (Further Decision 1)
Year	2024
Session	June
Marks	11
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Critical Path Analysis
Type	Schedule with limited workers - create schedule/chart
Difficulty	Standard +0.8 This is a multi-part critical path analysis question requiring network drawing with dummies, identification of critical path, float calculations, and resource-constrained rescheduling when activity duration changes. While the techniques are standard for FD1, the combination of network construction, multiple float calculations, and particularly part (c) requiring re-analysis of a 3-worker schedule after a duration change demands careful systematic work across multiple concepts, placing it moderately above average difficulty.
Spec	7.05a Critical path analysis: activity on arc networks 7.05b Forward and backward pass: earliest/latest times, critical activities 7.05c Total float: calculation and interpretation

6. The precedence table below shows the 12 activities required to complete a project.

Activity	Immediately preceding activities
A	-
B	-
C	-
D	A
E	A, B, C
F	A, B, C
G	C
H	D, E
I	D, E
J	D, E
K	F, G, J
L	F, G

Draw the activity network described in the precedence table, using activity on arc. Your activity network must contain the minimum number of dummies only.
(5) Each of the activities shown in the precedence table requires one worker. The project is to be completed in the minimum possible time. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{7f7546eb-0c1a-40da-bdf0-31e0574a9867-11_303_1547_296_260} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} Figure 3 shows a schedule for the project using three workers.
1. State the critical path for the network.
2. State the minimum completion time for the project.
3. Calculate the total float on activity B.
4. Calculate the total float on activity G. Immediately after the start of the project, it is found that the duration of activity I, as shown in Figure 3, is incorrect. In fact, activity I will take 8 hours.
  The durations of all the other activities remain as shown in Figure 3.
Determine whether the project can still be completed in the minimum completion time using only three workers when the duration of activity I is 8 hours. Your answer must make specific reference to workers, times and activities.

Show mark scheme Show mark scheme source

Question 6:

Part (a)

Answer	Marks	Guidance
Answer	Mark	Guidance
Network diagram with at least nine labelled activities, one start, at least two dummies	M1	AO2.1
Activities A, B, C, D and G dealt with correctly	A1	AO1.1b
Activities E, F, H, I, J and first two dummies (with arrows) at ends of A and C dealt with correctly (H and I interchangeable)	A1	AO1.1b
Activities K, L and dummy at end of F/G (with arrow) dealt with correctly	A1	AO1.1b
Final dummy (with arrow) for uniqueness of H/I; all arrows present for every activity; one finish; no additional dummies	A1	AO1.1b

Part (b)(i)

Answer	Marks	Guidance
Answer	Mark	Guidance
Critical path: \(C - E - J - K\)	B1	AO1.1b; CAO, must be in this order

Part (b)(ii)

Answer	Marks	Guidance
Answer	Mark	Guidance
Minimum completion time: \(20\)	B1	AO1.1b; CAO

Part (b)(iii)

Answer	Marks	Guidance
Answer	Mark	Guidance
Total float on activity B is \(2\)	B1	AO1.1b; CAO

Part (b)(iv)

Answer	Marks	Guidance
Answer	Mark	Guidance
Total float on activity G is \(4\)	B1	AO3.1b; CAO

Part (c)

Answer	Marks	Guidance
Answer	Mark	Guidance
Indication that activities I and L have swapped workers, OR activity H has swapped worker and I now starts at 12	B1	AO2.4
Completely correct reasoning: H and L (in either order) in interval \(12\)–\(20\); I done in interval \(12\)–\(20\) (starts at 12, not just ends at 20); concludes yes, project can be completed by 3 workers. Must not include incorrect statement	B1	AO2.4

# Question 6:

## Part (a)
| Answer | Mark | Guidance |
|--------|------|----------|
| Network diagram with at least nine labelled activities, one start, at least two dummies | M1 | AO2.1 |
| Activities A, B, C, D and G dealt with correctly | A1 | AO1.1b |
| Activities E, F, H, I, J and first two dummies (with arrows) at ends of A and C dealt with correctly (H and I interchangeable) | A1 | AO1.1b |
| Activities K, L and dummy at end of F/G (with arrow) dealt with correctly | A1 | AO1.1b |
| Final dummy (with arrow) for uniqueness of H/I; all arrows present for every activity; one finish; no additional dummies | A1 | AO1.1b |

## Part (b)(i)
| Answer | Mark | Guidance |
|--------|------|----------|
| Critical path: $C - E - J - K$ | B1 | AO1.1b; CAO, must be in this order |

## Part (b)(ii)
| Answer | Mark | Guidance |
|--------|------|----------|
| Minimum completion time: $20$ | B1 | AO1.1b; CAO |

## Part (b)(iii)
| Answer | Mark | Guidance |
|--------|------|----------|
| Total float on activity B is $2$ | B1 | AO1.1b; CAO |

## Part (b)(iv)
| Answer | Mark | Guidance |
|--------|------|----------|
| Total float on activity G is $4$ | B1 | AO3.1b; CAO |

## Part (c)
| Answer | Mark | Guidance |
|--------|------|----------|
| Indication that activities I and L have swapped workers, OR activity H has swapped worker and I now starts at 12 | B1 | AO2.4 |
| Completely correct reasoning: H and L (in either order) in interval $12$–$20$; I done in interval $12$–$20$ (starts at 12, not just ends at 20); concludes yes, project can be completed by 3 workers. Must not include incorrect statement | B1 | AO2.4 |

---

Show LaTeX source

6. The precedence table below shows the 12 activities required to complete a project.

\begin{center}
\begin{tabular}{|l|l|}
\hline
Activity & Immediately preceding activities \\
\hline
A & - \\
\hline
B & - \\
\hline
C & - \\
\hline
D & A \\
\hline
E & A, B, C \\
\hline
F & A, B, C \\
\hline
G & C \\
\hline
H & D, E \\
\hline
I & D, E \\
\hline
J & D, E \\
\hline
K & F, G, J \\
\hline
L & F, G \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Draw the activity network described in the precedence table, using activity on arc.

Your activity network must contain the minimum number of dummies only.\\
(5)

Each of the activities shown in the precedence table requires one worker. The project is to be completed in the minimum possible time.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{7f7546eb-0c1a-40da-bdf0-31e0574a9867-11_303_1547_296_260}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{center}
\end{figure}

Figure 3 shows a schedule for the project using three workers.
\item \begin{enumerate}[label=(\roman*)]
\item State the critical path for the network.
\item State the minimum completion time for the project.
\item Calculate the total float on activity B.
\item Calculate the total float on activity G.

Immediately after the start of the project, it is found that the duration of activity I, as shown in Figure 3, is incorrect. In fact, activity I will take 8 hours.\\
The durations of all the other activities remain as shown in Figure 3.
\end{enumerate}\item Determine whether the project can still be completed in the minimum completion time using only three workers when the duration of activity I is 8 hours. Your answer must make specific reference to workers, times and activities.
\end{enumerate}

\hfill \mbox{\textit{Edexcel FD1 2024 Q6 [11]}}

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