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Subjects · Leaving Cert Applied Maths

Leaving Cert Applied Maths: Project scheduling & critical path

How often Project scheduling & critical path comes up on the Applied Maths papers, every year it was asked, and questions to try.

HL Asked on 2 of the last 3 Higher Level papers, most recently in 2024. most years

OL Asked on 2 of the last 3 Ordinary Level papers, most recently in 2024. most years

Project scheduling & critical path, Higher Level(6 marks)

Quick ones on Project scheduling & critical path.

(a)Forward pass: the early time of an event with several incoming activities is…?
  1. The smallest of the incoming totals
  2. The largest of the incoming totals
  3. The sum of all incoming durations
(b)What is a dummy activity in an activity network?
  1. An activity that can be left out of the plan
  2. The activity with the most float
  3. A zero-time activity that only shows dependency
(c)Backward pass: the late time of an event with several outgoing activities is…?
  1. The smallest of the outgoing values
  2. Its early time plus the float
  3. The largest of the outgoing values
Show the answers

(a) The largest of the incoming totals

(b) A zero-time activity that only shows dependency

(c) The smallest of the outgoing values

Your turn: Higher Level questions on Project scheduling & critical path.

Higher Level

Asked on 2 of the last 3 Higher Level papers, most recently in 2024. most years

Every paper, year by year

YearWhere it came up
2025Not asked
2024Q10
2023Q9

Links open the State Examinations Commission’s paper for that year.

More Project scheduling & critical path questions

Project scheduling & critical path, 2 marks

In the backward pass, the late time of the final event is set equal to…?

  1. Zero
  2. The sum of all activity durations
  3. Its early time
Show the answer

Its early time

The project should finish as soon as possible, so the finish event's latest allowed time is its earliest time. The backward pass then subtracts durations from there.

Project scheduling & critical path, 2 marks

An activity on the critical path is delayed by 3 days. Effect on the project?

  1. It finishes 6 days late
  2. It finishes 3 days late
  3. It is not delayed
Show the answer

It finishes 3 days late

Critical activities have zero float, so any delay passes straight through to the end of the project, day for day.

Project scheduling & critical path, 2 marks

An event has early time 10 and late time 13. Is it on the critical path?

  1. No, its early and late times differ
  2. Yes, every event is on it
  3. Only if an activity of 3 days leaves it
Show the answer

No, its early and late times differ

Critical events have equal early and late times: there is no slack. Here the event could happen up to 3 time units late without delaying the project.

Ordinary Level

Asked on 2 of the last 3 Ordinary Level papers, most recently in 2024. most years

Every paper, year by year

YearWhere it came up
2025Not asked
2024Q9
2023Q10

Links open the State Examinations Commission’s paper for that year.

More Project scheduling & critical path questions

Project scheduling & critical path, 3 marks

Activity: start event ET = 5, end event LT = 14, duration 6 hours. Its float?

  1. 9 hours
  2. 8 hours
  3. 3 hours
Show the answer

3 hours

Float = LT(end) − ET(start) − duration = 14 − 5 − 6 = 3 hours. The activity can be delayed up to 3 hours without delaying the project.

Project scheduling & critical path, 2 marks

What is the critical path of a project?

  1. The path with the most activities
  2. The longest path through the activity network
  3. The shortest path through the network
Show the answer

The longest path through the activity network

The project cannot finish until the longest chain of dependent activities is done, so that chain sets the minimum project time. Delaying any of it delays the project.

Project scheduling & critical path, 3 marks

Activity X has a float of 4 days and is delayed by 3 days. Effect on the project?

  1. No delay to the project
  2. A 3-day delay to the finish
  3. A 1-day delay to the finish
Show the answer

No delay to the project

A delay no bigger than the float is absorbed. 3 is less than 4, so the finish date is unchanged, though X now has only 1 day of float left.

Other Applied Maths topics

All of Leaving Cert Applied Maths