Critical path analysis questions

Practice questions covering critical path analysis from this specification. Attempt the questions below; real-paper references for this topic are being imported.

Questions to attempt

6 questions on Critical path analysis, each with its mark scheme and worked method. Reveal the answer when you have had a go.

D1-4.1 · Modelling of a project by an activity network, from a precedence table.
Q1
ORIGINAL
Year 1
Year 1: this is the AS subject content the exam board publishes, which is what most schools teach in Year 12.
1.
A project has the precedence table: $A$ and $B$ have no predecessors; $C$ has immediate predecessor $A$ ; $D$ has immediate predecessors $A$ and $B$ ; $E$ has immediate predecessor $C$ ; $F$ has immediate predecessor $C$ ; $G$ has immediate predecessors $D$ and $E$ ; $H$ has immediate predecessors $F$ and $G$ . Describe an activity network for this project, giving the event numbers of every arc.
(7)
(Total for Question 1 is 7 marks)
D1-4.2 · Completion of the precedence table for a given activity network.
Q2
ORIGINAL
Year 1
Year 1: this is the AS subject content the exam board publishes, which is what most schools teach in Year 12.
2.
An activity network on events $1$ to $6$ has: $A$ from $1$ to $2$ ; $B$ from $1$ to $3$ ; a dummy from $2$ to $3$ ; $C$ from $2$ to $4$ ; $D$ from $3$ to $4$ ; $E$ from $3$ to $5$ ; $F$ from $4$ to $5$ ; $G$ from $5$ to $6$ . Write down the complete precedence table.
(7)
(Total for Question 2 is 7 marks)
D1-4.3 · Algorithm for finding the critical path. Earliest and latest event times. Earliest and latest start and finish times for activities. Identification of critical activities and critical path(s).
Q3
ORIGINAL
Year 1
Year 1: this is the AS subject content the exam board publishes, which is what most schools teach in Year 12.
3.
A project has activities with durations $A=5$ , $B=4$ , $C=6$ , $D=3$ , $E=7$ , $F=2$ , $G=4$ , $H=5$ and precedence $A$ : none; $B$ : none; $C$ : $A$ ; $D$ : $A$ and $B$ ; $E$ : $C$ ; $F$ : $C$ ; $G$ : $D$ and $E$ ; $H$ : $F$ and $G$ . Find the project duration and the critical path.
(7)
(Total for Question 3 is 7 marks)
D1-4.4 · Calculation of the total float of an activity. Construction of Gantt (cascade) charts.
Q4
ORIGINAL
Year 1
Year 1: this is the AS subject content the exam board publishes, which is what most schools teach in Year 12.
4.
For a project of duration $24$ with activities $A=5$ , $B=7$ , $C=4$ , $D=6$ , $E=3$ , $F=8$ , $G=2$ , $H=5$ and precedence $A$ : none; $B$ : none; $C$ : $A$ ; $D$ : $A$ ; $E$ : $B$ ; $F$ : $C$ and $D$ ; $G$ : $D$ and $E$ ; $H$ : $F$ and $G$ , calculate the total float of every activity.
(7)
(Total for Question 4 is 7 marks)
D1-4.5 · Construct resource histograms (including resource levelling) based on the number of workers required to complete each activity.
Q5
ORIGINAL
Year 2
Year 2: this is content the exam board adds beyond the AS subject content, for the full A-level.
5.
A project has activities $A$ of duration $3$ needing $2$ workers, $B$ of duration $4$ needing $1$ worker, $C$ of duration $2$ needing $3$ workers, $D$ of duration $5$ needing $2$ workers and $E$ of duration $3$ needing $1$ worker, with precedence $A$ : none; $B$ : none; $C$ : $A$ ; $D$ : $B$ ; $E$ : $C$ and $D$ . Find the project duration and the critical activities.
(5)
(Total for Question 5 is 5 marks)
D1-4.6 · Scheduling the activities using the least number of workers required to complete the project.
Q6
ORIGINAL
Year 2
Year 2: this is content the exam board adds beyond the AS subject content, for the full A-level.
6.
A project has durations $A=5$ , $B=4$ , $C=6$ , $D=3$ , $E=7$ , $F=2$ , $G=4$ , $H=5$ with precedence $A$ : none; $B$ : none; $C$ : $A$ ; $D$ : $A$ and $B$ ; $E$ : $C$ ; $F$ : $C$ ; $G$ : $D$ and $E$ ; $H$ : $F$ and $G$ . The critical time is $27$ and the critical path is $A$ , $C$ , $E$ , $G$ , $H$ . Find a lower bound for the number of workers and construct a schedule attaining it.
(8)
(Total for Question 6 is 8 marks)

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Printable question pack — D1-4 Critical path analysisAll 60 questions across 6 specification points — 54 more than the 6 above — with the full mark scheme. Guest accessible · browser print.

D1-4 Critical path analysis revision notes

Real-paper references

Real-paper references for this module are being imported — the questions above are the site's own, exam-faithful, marked.

Reference rows contain series, paper, question number, marks and classification metadata only. Pearson's question papers open on Pearson's own website.

Questions to attempt

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