Critical path analysis practice

New project networks every time: fill in the earliest start and latest finish times, find the critical path and float, and see what a delay does. Check each answer or print a key.

Question types
Question types
Conventions

Set

    Your answers save on this device as you type.

    What you practice

    Each set makes new projects and draws the network the way your course does. Complete the forward and backward pass, read the order back from a drawing with dummies, find total and free float, work out what a delay does, or draw the network yourself and compare with the key. Common slips get a note: the smallest EST instead of the largest, a forgotten dummy, the duration left out of the float.

    Pick your course first. Boards draw networks differently and some ask for free float, so each sheet prints its course’s conventions.

    Example: total float

    In set FTEXCM (AQA, Edexcel, WJEC) a gym fit-out has seven activities. A (3 days) and B (2) start the project; C (3) and D (11) follow A; E (8) follows B; F (3) follows C; G (5) needs both D and E. Node 5, where G starts, takes the larger of 3 + 11 = 14 and 2 + 8 = 10, so its EST is 14 and the project takes 14 + 5 = 19 days along the critical path A, D, G. C runs from node 2 (EST 3) to node 4 (LFT 16), so its total float is 16 − 3 − 3 = 10 days. Open set FTEXCM

    Questions

    How do you find the critical path?

    Do a forward pass for the earliest start times and a backward pass for the latest finish times. Critical activities have no total float: on an activity-on-arrow network, both their nodes have EST equal to LFT and the duration fills the gap exactly. They make the longest path, and its length is the minimum project duration.

    How do you calculate total float?

    Total float = LFT at the end of the activity − duration − EST at its start. On an activity-on-node box it is LS − ES. It is how long the activity can be delayed without making the whole project late.

    What is the difference between total float and free float?

    Total float is how long an activity can slip without delaying the project. Free float is how long it can slip without delaying the next activity: EST at the end − duration − EST at the start. Free float is never more than total float. OCR and Cambridge 9609 ask for both; AQA and Edexcel Business ask only for total float.

    What is a dummy activity?

    A dashed arrow that takes no time. It shows that an activity must wait for another one when the two cannot share a node without giving the wrong order. Cambridge 9609 and Further Maths Decision 1 networks use dummies. The other A-level Business specifications do not mention dummies, so their networks here are drawn without them.

    What goes in the nodes of a network diagram?

    In A-level Business networks each circle has the node number on the left, the earliest start time top right and the latest finish time bottom right. Decision 1 uses two boxes, the early event time above the late event time. Activity-on-node boxes show ES, duration and EF on top and LS, float and LF below.

    What happens if an activity is delayed?

    If it is critical, the whole project finishes late by the same amount. If it has float, the project is only late by the part of the delay beyond its total float. Cutting a critical activity shortens the project, but only until another path becomes the longest.

    Do you start counting at day 0 or day 1?

    A-level Business and Decision 1 networks start at 0, so a 4-day activity starting at 0 finishes at 4. Some PMP prep courses start at day 1, so it runs from day 1 to day 4 and EF = ES + duration − 1. The floats and the project length come out the same. Pick the course that matches yours.

    Sources, read October 27, 2026: AQA A-level Business 3.10.3; Edexcel A level Business 3.3.4 (PDF); OCR H431 (PDF); Eduqas A level Business (PDF); WJEC CPA activity (PDF); Cambridge 9609 syllabus 2026 to 2028 (PDF), 9.3.5, and its mark schemes; Edexcel Further Maths, Decision 1 topic 4 (PDF).