| Exam Board | AQA |
|---|---|
| Module | Further Paper 3 Discrete (Further Paper 3 Discrete) |
| Year | 2024 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Schedule with limited workers - determine minimum time |
| Difficulty | Standard +0.3 This is a standard critical path analysis question with resource scheduling. Part (a) requires reading the critical path from a completed network (trivial). Part (b) is a routine resource histogram construction. Part (c) involves resource leveling with a constraint, which requires some scheduling logic but follows standard algorithms taught in Further Maths Discrete. The question is methodical rather than conceptually challenging, making it slightly easier than average for Further Maths content. |
| Spec | 7.05b Forward and backward pass: earliest/latest times, critical activities7.05c Total float: calculation and interpretation7.05d Latest start and earliest finish: independent and interfering float |
| Answer | Marks | Guidance |
|---|---|---|
| 10(a) | States BDGJK and no others | 1.1b |
| Subtotal | 1 | |
| Q | Marking instructions | AO |
| Answer | Marks | Guidance |
|---|---|---|
| 10(b) | Draws a resource histogram with at | |
| least 10 labelled activities | 3.1b | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| correctly | 1.1b | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| histogram | 1.1b | A1 |
| Subtotal | 3 | |
| Q | Marking instructions | AO |
| Answer | Marks |
|---|---|
| 10(c) | Shows that activities A, B and C |
| Answer | Marks | Guidance |
|---|---|---|
| on histogram | 3.1b | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| levelled resource histogram | 1.1b | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Condone missing units | 3.2a | A1 |
| Subtotal | 3 | |
| Question total | 7 | |
| Question Paper total | 50 |
Question 10:
--- 10(a) ---
10(a) | States BDGJK and no others | 1.1b | B1 | BDGJK
Subtotal | 1
Q | Marking instructions | AO | Marks | Typical solution
--- 10(b) ---
10(b) | Draws a resource histogram with at
least 10 labelled activities | 3.1b | M1 | See next page
Draws a resource histogram with
activities A, B, C, D & E drawn
correctly | 1.1b | A1
Draws a fully correct resource
histogram | 1.1b | A1
Subtotal | 3
Q | Marking instructions | AO | Marks | Typical solution
--- 10(c) ---
10(c) | Shows that activities A, B and C
cannot be carried out simultaneously
on histogram | 3.1b | M1 | See next page
96 days
Draws a fully correct, labelled and
levelled resource histogram | 1.1b | A1
Obtains 96 days
Condone missing units | 3.2a | A1
Subtotal | 3
Question total | 7
Question Paper total | 50
PMT
MARK SCHEME – A-LEVEL FURTHER MATHEMATICS – 7367/3D – JUNE 2024
10(b)
10(c)
17A project is undertaken by Higton Engineering Ltd.
The project is broken down into 11 separate activities $A$, $B$, $\ldots$, $K$
Figure 3 below shows a completed activity network for the project, along with the earliest start time, duration, latest finish time and the number of workers required for each activity. All times and durations are given in days.
\includegraphics{figure_3}
\begin{enumerate}[label=(\alph*)]
\item Write down the critical path.
[1 mark]
\item Using Figure 4 below, draw a resource histogram for the project to show how the project can be completed in the minimum possible time.
Assume that each activity is to start as early as possible.
[3 marks]
\includegraphics{figure_4}
\item Higton Engineering Ltd only has four workers available to work on the project.
Find the minimum completion time for the project.
Use Figure 5 below in your answer.
[3 marks]
\includegraphics{figure_5}
Minimum completion time _____________________________________
\end{enumerate}
\hfill \mbox{\textit{AQA Further Paper 3 Discrete 2024 Q10 [7]}}