Higher Applications of Mathematics
Quick reference cards for activity networks, critical path, PERT estimates, Gantt charts, expected value, risk and decisions.
A task that must be completed as part of a project.
Use when breaking a project into smaller steps.
Name each activity clearly, often with a letter such as A or B.
Book transport is one activity in a school trip plan.
The time an activity is expected to take.
Use when scheduling or finding project length.
Record durations in consistent units such as hours or days.
Printing posters may take 2 days.
A rule showing that one activity must happen before another.
Use when activities cannot all start at the same time.
List immediate predecessors before drawing a network.
Tickets must be designed before they can be printed.
A network diagram where each node is an activity.
Use to show project order, dependencies and timing.
Draw arrows from prerequisite activities to later activities.
A -> C means A must finish before C starts.
The earliest time an activity can begin.
Use during the forward pass of critical path analysis.
Earliest start is the largest earliest finish of its predecessors.
If predecessors finish at 4 and 7, earliest start is 7.
The earliest time an activity can be completed.
Use to find the minimum project duration.
Earliest finish = earliest start + duration.
Start 7, duration 3 gives finish 10.
The latest time an activity can start without delaying the project.
Use during the backward pass.
Latest start = latest finish - duration.
Latest finish 12, duration 5 gives latest start 7.
The latest time an activity can finish without delaying the project.
Use to calculate float and identify critical activities.
Work backwards from the final project time.
If the next activity must start by 9, the latest finish is 9.
How long an activity can be delayed without delaying the project.
Use to decide which tasks have spare time.
Float = latest start - earliest start.
Latest start 8 and earliest start 5 gives float 3.
An activity with zero float.
Use when identifying tasks that control the project duration.
Critical activities have earliest start equal to latest start.
A delay to a critical activity delays the project.
The chain of critical activities from start to finish.
Use to find the minimum project time.
Follow activities with zero float through the network.
A-C-F may be the critical path for a community event.
A weighted estimate using optimistic, likely and pessimistic times.
Use when task duration is uncertain.
Expected time = (optimistic + 4 x likely + pessimistic) / 6.
(2 + 4 x 3 + 8) / 6 = 3.67 days.
A timeline chart showing when activities happen.
Use to communicate schedules clearly.
Draw bars against a time scale for each activity.
A bar from day 3 to day 6 shows a 3-day activity.
A long-run average value using probabilities and outcomes.
Use to compare uncertain options.
Expected value = sum of probability x value.
0.2 x 100 + 0.8 x 10 = 28.
The chance and impact of an uncertain event.
Use when a decision could have different outcomes.
Consider likelihood, impact and possible control measures.
Bad weather is a risk for an outdoor school event.
A comparison of costs, benefits, risks and practical constraints.
Use when choosing between realistic options.
Compare values, explain assumptions and justify the decision.
A cheaper option may not be best if delay risk is high.