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OCR A Level Further Maths

Topic questions Decision mathematics Critical path analysis

Critical path analysis

5 questions · 59 marks · about 1 hour

Critical path analysis questions

TopicCritical path analysis

OCR H245 Critical path analysis 5 questions

Discrete Mathematics June 2025, Question 4 14 marks

The table shows the activities involved in a project, together with the immediate predecessors and the duration of each activity in hours.

ActivityImmediate PredecessorsDuration (hours)
A–5
B–4
CA3
DB3
ED2
FB5
GC, E2
HD5
IG3
JC, E, H1
KD, F2
(a)(i)

By constructing an activity network for the project, determine the minimum time in

which the project can be completed.

[5]
Reveal mark scheme Mark scheme for question 4(a)(i)
(a)(ii)

State the critical activities.

[1]
Reveal mark scheme Mark scheme for question 4(a)(ii)
(b)

Calculate the interfering float for each non-critical activity.

[3]
Reveal mark scheme Mark scheme for question 4(b)
(c)

Each activity requires one worker. When an activity is started it must be completed without interruption.

Use the diagram in the Printed Answer Booklet to determine the minimum number of workers needed to complete the project in the minimum completion time.

Each column in the diagram represents 1 hour. For each worker, write the letter of the activity they are doing in each box, or leave the box blank if the worker is resting for that hour. You

may not need to use all the rows or columns in the table.

[3]
Reveal mark scheme Mark scheme for question 4(c)
(d)

Activity C takes an additional t hours, but all other timings are unchanged.

Determine the range of values of t that result in an increase in the minimum project

completion time.

[2]
Reveal mark scheme Mark scheme for question 4(d)

Discrete Mathematics June 2024, Question 4 16 marks

Figure for question 4
(a)

By carrying out a forward pass, determine the minimum project completion time.

[2]
Reveal mark scheme Mark scheme for question 4(a)
(b)

By carrying out a backward pass, determine the (total) float for each activity.

[4]
Reveal mark scheme Mark scheme for question 4(b)
(c)

For each non‑critical activity, determine the independent float and the interfering float.

[3]
Reveal mark scheme Mark scheme for question 4(c)
(d)

Construct a cascade chart showing all the critical activities on one row and each non‑critical activity on a separate row, starting at its earliest start time, and using dashed lines to indicate

(total) float. You may not need to use all the grid.

[3]
Reveal mark scheme Mark scheme for question 4(d)
(e)

Each activity requires exactly one worker.

Construct a schedule to show how exactly two workers can complete the project as quickly as

possible. You may not need to use all the grid.

[2]
Reveal mark scheme Mark scheme for question 4(e)
(f)

Issues with deliveries delay the earliest possible start of activity D by 3 hours.

Construct a schedule to show how exactly two workers can complete the project with this

delay as quickly as possible. You may not need to use all the grid.

[2]
Reveal mark scheme Mark scheme for question 4(f)

Discrete Mathematics June 2023, Question 1 7 marks

The table below shows the activities involved in a project together with the immediate predecessors and the duration of each activity.

ActivityImmediate predecessorsDuration (hours)
A–2
BA3
C–4
DC2
EB, C2
FD, E3
GE2
HF, G1
(a)

Model the project using an activity network.

[3]
Reveal mark scheme Mark scheme for question 1(a)
(b)

Determine the minimum project completion time.

[2]
Reveal mark scheme Mark scheme for question 1(b)
(c)

The start of activity C is delayed by 2 hours.

Determine the minimum project completion time with this delay.

[2]
Reveal mark scheme Mark scheme for question 1(c)

Discrete Mathematics June 2022, Question 2 9 marks

The table below shows the activities involved in a project together with the immediate predecessors and the duration of each activity.

ActivityImmediate predecessorsDuration (minutes)
A‑4
B‑1
CA2
DA, B5
ED1
FB, C2
GD, F5
HE, F4
(a)

Model the project using an activity network.

[3]
Reveal mark scheme Mark scheme for question 2(a)
(b)

Determine the minimum project completion time.

[3]
Reveal mark scheme Mark scheme for question 2(b)
(c)

Calculate the total float for each non‑critical activity.

[3]
Reveal mark scheme Mark scheme for question 2(c)

Discrete Mathematics November 2020, Question 6 13 marks

Figure for question 6
Reveal mark scheme Mark scheme for question 6
(a)

Suppose that the minimum completion time for the project is 15 minutes.

(a)(i)

By calculating the early event times, determine the range of values for x.

[3]
Reveal mark scheme Mark scheme for question 6(a)(i)
(a)(ii)

By calculating the late event times, determine which activities must be critical.

[3]
Reveal mark scheme Mark scheme for question 6(a)(ii)
(b)

The table shows the number of workers needed for each activity.

ActivityABCDEFGHIJK
Workers2112n121114

Determine the maximum possible value for n if 5 workers can complete the project in

15 minutes. Explain your reasoning.

[4]
Reveal mark scheme Mark scheme for question 6(b)
(c)

The duration of activity F is reduced to 1.5 minutes, but only 4 workers are available. The minimum completion time is no longer 15 minutes.

Determine the minimum project completion time in this situation.

[1]
Reveal mark scheme Mark scheme for question 6(c)
(d)

Find the maximum possible value for x for this minimum project completion time.

[1]
Reveal mark scheme Mark scheme for question 6(d)
(e)

Find the maximum possible value for n for this minimum project completion time.

[1]
Reveal mark scheme Mark scheme for question 6(e)

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