Back to Planning and Decision Making

Higher Applications of Mathematics

Risk and decision making

Balancing likelihood, impact and practical constraints.

Planning referencePlanning mixed quiz

Planning reference

Check networks, timing, float, PERT, Gantt charts, risk and expected value.

Mixed revision quiz

Review Planning and Decision Making with adaptive feedback.

Before you start

  • Be confident reading information from tables and diagrams.
  • Check time units, costs and probabilities before calculating.
  • Be ready to explain what the result means for the project or decision.

Method helper

Which planning method do I use?

Do tasks depend on other tasks being completed first?

Draw an activity network.

Are task times uncertain?

Use PERT estimates.

Do you need the minimum project duration?

Find the critical path.

Do you need to know which activities can be delayed?

Calculate float.

Do you need to show a project schedule on a timeline?

Create a Gantt chart.

Are you comparing uncertain financial outcomes?

Calculate expected value.

Are you comparing options with risk, cost and benefit?

Use risk and decision making.

Do you need a written recommendation?

Explain the decision in context with limitations.

Planning lesson

Key idea

  • This topic focuses on comparing options using cost, benefit, risk, uncertainty and practical constraints. Planning and decision making uses mathematics to organise real projects and compare choices under constraints.
  • A good planning answer identifies the activities or options, uses the correct method, and explains the result in the context of the project.
  • For Higher Applications, the conclusion matters. You should mention timing, risk, cost, uncertainty or limitations where they affect the decision.

Key definitions, methods and formulae

  • Risk combines likelihood and impact.
  • A decision should compare financial and non-financial factors.
  • A strong recommendation states evidence, context and limitations.

Worked examples

Planning walkthrough 1

Set up the information

A council chooses between two flood-prevention plans for a riverside community.

  1. List the options being compared.
  2. Identify costs, benefits, risks and who is affected.
  3. Separate known facts from assumptions.

Good decisions combine mathematical evidence with practical judgement.

Planning walkthrough 2

Carry out the method

A council chooses between two flood-prevention plans for a riverside community.

  1. Use calculations such as expected value where useful.
  2. Compare worst-case and likely outcomes.
  3. Consider practical constraints such as time, budget and public impact.

Risk is not only about probability; impact matters too.

Planning walkthrough 3

Interpret the decision

A council chooses between two flood-prevention plans for a riverside community.

  1. Make a recommendation.
  2. Justify it with numbers and context.
  3. Mention one limitation or piece of missing information.

A balanced conclusion explains why one option is preferred.

Watch out

  • Ignoring dependencies and allowing activities to start too early.
  • Mixing time units, such as hours and days, without converting.
  • Choosing the cheapest option without considering risk or impact.
  • Treating expected value as a guaranteed outcome.
  • Giving a schedule or calculation without explaining what it means for the project.

Connected topics

Related Higher Applications topics

Finance: InsuranceFinance: Tax, inflation and financial planningModelling: Using technology for modelling

Next step

Move into practice

Use the learning notes to read dependencies and constraints, then try varied schedules, precedence tables and decision contexts.

Planning mixed quiz