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ScotlandApplications of MathematicsSyllabus dot point

How do you represent a project schedule over time and use it to plan resources and deadlines?

Representing project activities over time with Gantt charts and PERT, scheduling activities and resources, and using the schedule to track progress and manage deadlines.

A focused answer to the SQA Higher Applications of Mathematics planning content, covering Gantt charts, PERT, representing activities over time, scheduling parallel tasks and resources, and tracking progress against a plan.

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  1. What this dot point is asking
  2. The Gantt chart
  3. PERT and activity timing
  4. Scheduling parallel tasks and resources
  5. Tracking progress and deadlines
  6. Try this

What this dot point is asking

The SQA wants you to represent a project schedule over time using a Gantt chart (and to know what PERT contributes), schedule activities including parallel tasks and limited resources, and use the schedule to track progress and meet deadlines. This complements critical-path analysis by showing the plan against a calendar.

The Gantt chart

A Gantt chart is a bar chart of a schedule. Time runs along the horizontal axis (days or weeks), and each activity is a horizontal bar whose left edge is its start, whose length is its duration, and whose right edge is its finish.

The chart's strength is that it makes the schedule visual: you can see immediately which activities overlap, where there is spare time, and whether a deadline is met.

PERT and activity timing

PERT (programme evaluation and review technique) is a project-planning method built around the network of activities and their timing. It is closely related to critical-path analysis and often uses three time estimates for each activity, an optimistic, a most likely and a pessimistic duration, to allow for uncertainty in how long work will take.

Scheduling parallel tasks and resources

Activities that do not depend on each other can run in parallel, which shortens the schedule. But running in parallel needs enough resources: people, machines or rooms. If a resource is limited, parallel activities may have to run one after another instead.

Tracking progress and deadlines

A Gantt chart is also a tracking tool. As work proceeds you mark how much of each bar is complete, compare it with where the plan says it should be, and see whether the project is on schedule. If a critical activity falls behind, the chart shows the knock-on effect on later activities and the finish date, so the manager can act early.

Try this

Q1. Activity A (44 days) is followed by B (33 days). On a Gantt chart, on which day does B start at the earliest? [1 mark]

  • Cue. A occupies days 11 to 44, so B starts on day 55.

Q2. Two independent activities of 33 and 55 days share one worker. How long do they take together? [2 marks]

  • Cue. In sequence they take 3+5=83 + 5 = 8 days, because one worker cannot do both at once.

Q3. Give one advantage of a Gantt chart over a plain list of activities. [1 mark]

  • Cue. It shows the schedule visually, so overlaps, spare time and deadlines are clear at a glance.

Exam-style practice questions

Practice questions written in the style of SQA exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

SQA Higher Apps style5 marksA project has activities A (22 days), B (44 days, after A), C (33 days, after A) and D (22 days, after B and C). Describe how the activities would appear on a Gantt chart and state on which day D can begin at the earliest.
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A runs on days 11 to 22. B and C both depend only on A, so they run in parallel starting on day 33: B on days 33 to 66 and C on days 33 to 55 (2 marks).

On a Gantt chart each activity is a horizontal bar against a time axis; bars for B and C overlap because they run at the same time, and D's bar starts only after both finish (1 mark).

D needs both B (finishing day 66) and C (finishing day 55), so the later finish is day 66, and D can begin at the earliest on day 77 (2 marks). Markers reward placing parallel activities as overlapping bars and identifying the later predecessor finish.

SQA Higher Apps style4 marksA team can only carry out one activity at a time. Explain how this resource constraint changes the schedule of two parallel activities, and give one benefit of using a Gantt chart to manage it.
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If two activities could run in parallel but only one team is available, they must instead run one after the other, so the schedule lengthens by the duration of the second activity (2 marks).

A Gantt chart shows the resource clash visually, because the two bars would overlap in time; the manager can then shift one bar to a later slot (1 mark).

A benefit is that the chart makes overlaps, spare time and deadlines easy to see at a glance, helping plan staff and track progress (1 mark). Markers reward recognising that limited resources serialise parallel tasks and a clear benefit of the visual schedule.

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