Back to Mathematical Modelling

Higher Applications of Mathematics

Using technology for modelling

Using digital tools to fit, compare and check models.

Modelling referenceModelling mixed quiz

Modelling reference

Check variables, formulae, model types, units, errors and assumptions.

Mixed revision quiz

Review Mathematical Modelling with adaptive feedback.

Before you start

  • Be confident substituting numbers into simple formulae.
  • Check the units in the question before calculating.
  • Be ready to explain what an answer means in the real situation.

Method helper

Which model or method do I use?

Does the output change by a fixed amount each step?

Use a linear model.

Is there a starting fee plus a rate per unit?

Use y = mx + c and interpret the intercept.

Does the situation involve area, a turning point or a squared variable?

Use a quadratic model.

Is the amount increasing or decreasing by a percentage repeatedly?

Use an exponential model.

Have you been given a formula and values?

Substitute into the formula carefully.

Do you need to make one variable the subject?

Rearrange the formula one step at a time.

Are measurements rounded or allowed within a range?

Calculate tolerance or error.

Do the units look inconsistent?

Convert units and check dimensional sense.

Are you testing several assumptions or scenarios?

Use technology to compare model outputs.

Does the prediction seem unrealistic?

Comment on model limitations.

Modelling lesson

Key idea

  • This topic focuses on using spreadsheets, graphs and technology outputs to test assumptions and compare scenarios. Mathematical modelling is about using maths to represent a real situation well enough to support a decision.
  • A good model identifies the variables, uses a sensible formula or graph, and states the assumptions being made.
  • For Higher Applications, the interpretation matters. You should explain whether the output is realistic, what it means in context, and what might make the model less reliable.

Key formulae, definitions and methods

  • Keep inputs, calculations and outputs separate.
  • Use a table or graph to test how outputs change when assumptions change.
  • Interpret technology output in context before making a decision.

Worked examples

Modelling walkthrough 1

Build the model

A community group compares energy-cost scenarios for a village hall.

  1. Set up input cells for rate, usage and standing charge.
  2. Use formula cells for monthly and annual cost.
  3. Label outputs clearly with units.

Technology makes it easier to test several scenarios consistently.

Modelling walkthrough 2

Use the model

A community group compares energy-cost scenarios for a village hall.

  1. Change one assumption at a time.
  2. Record how the output changes.
  3. Use a graph or table to compare scenarios.

Changing one input at a time helps identify which assumption matters most.

Modelling walkthrough 3

Evaluate the model

A community group compares energy-cost scenarios for a village hall.

  1. Check formulae and units before trusting the result.
  2. Write a decision sentence based on the output.
  3. Mention limitations such as seasonal use or future tariff changes.

The final decision should refer to outputs, assumptions and limitations.

Watch out

  • Using a model without defining the variables and units.
  • Choosing a linear model when the rate of change is not constant.
  • Treating a model prediction as an exact fact rather than an estimate.
  • Forgetting to convert units before substituting values.
  • Giving a calculation without commenting on assumptions or limitations.

Technology and data connection

Related Higher Applications topics

Spreadsheet: Using spreadsheets for modellingRStudio: Linear regression in RStudioSpreadsheet: Interpreting spreadsheet outputs

Next step

Move into practice

Use the learning notes to identify variables, assumptions and units, then try varied formulas, model types and reasonableness checks.

Modelling mixed quiz