Modelling througout the Applied Maths Course
Mathematical Modelling is not an isolated skill — it is the foundation of the entire Leaving Certificate Applied Mathematics specification.
The Modelling Project simply gives you a formal opportunity to apply skills you have been developing all year across all four strands of the course:
- Strand 1 – Mathematical Modelling
Understanding the modelling cycle, formulating problems, making and testing assumptions, refining models, and interpreting results. - Strand 2 – Modelling with Networks and Graphs
Representing real‑world systems as networks, identifying constraints, optimising routes, and understanding trade‑offs. - Strand 3 – Modelling the Physical World
Applying mechanics to real‑world motion, forces, and energy situations, making simplifying assumptions to allow analysis. - Strand 4 – Modelling a Changing World
Using difference and differential equations to describe and predict how systems evolve over time, refining models for improved accuracy.
The core skill running through all these strands is the ability to translate a real‑world scenario into a mathematical form and then refine it through analysis, testing, and iteration.
Understanding Assumptions
Every formula and model you meet in Applied Maths carries built‑in assumptions.
Recognising these assumptions is vital – in the exam, in your project, and in real‑life problem solving.
Some examples:
- UVAST equations assume constant acceleration, motion in a straight line, and no air resistance.
- Newton’s Laws assume an inertial frame of reference and often neglect small forces such as air resistance or rolling resistance unless explicitly included.
- Projectile motion models typically assume a flat launch and landing height, uniform gravitational field, and no aerodynamic effects.
- Circular motion models assume a constant radius, a perfectly rigid connection, and no energy loss through friction.
- Statistical regression models assume a particular relationship (often linear) between variables and that the data is representative of the population.
Why These Assumptions Matter
- If you apply a formula without checking its assumptions, your model may be invalid for the real situation.
- Understanding assumptions lets you adapt or refine the model when conditions change.
- In the Modelling Project, clearly stating and justifying your assumptions is worth marks in the Structure & Communication and Mathematical Modelling criteria.
Linking Topics Through Modelling
One of the most valuable habits you can build is to link topics together rather than treating them as separate chapters.
Real‑world problems rarely fit neatly into one topic – they usually require a combination of approaches.
Example 1 – Mechanics & Differential Equations
A bungee jump can start as a constant acceleration model, but once the cord stretches, you need Hooke’s Law and possibly a differential equation to model the motion.
Example 2 – Projectiles & Air Resistance
Begin with a standard parabolic model, then refine it using resistive forces proportional to v or v2 to see how the range changes compared to the simplified model.
Example 3 – Mechanics
Gather experimental motion data, fit a regression model, then compare it to the theoretical prediction to see how close your assumptions are to reality.
Practical Steps to Build Modelling Skills
To make modelling second nature:
- Identify assumptions in every question you answer.
- Challenge the model – ask when it would fail or need refinement.
- Link topics – think about which other parts of the course could be applied to make the solution more realistic.
- Test sensitivity – try adjusting one variable or assumption to see how it changes the results.
Why This Improves Your Project
Students who practise modelling throughout the course are better prepared for the project because they can:
- Quickly spot which mathematical tools suit the problem.
- Justify why they used a particular model and how they refined it.
- Confidently combine multiple strands in one investigation.
- Explain limitations and possible improvements clearly in their report.
Exam Questions for Building Modelling Skills
2025 HL Q2
2023 Deferred HL Q4
2023 Deferred HL Q5
2023 Deferred HL Q10
2023 HL Q6
SEC Sample HL Q7
SEC Sample HL Q8