IE · Subject guide
Applied Mathematics
Leaving Certificate Applied Mathematics (NCCA specification), Higher and Ordinary Level, with the SEC examination.
01 · Overview
Applied Mathematics
Leaving Certificate Applied Mathematics (NCCA specification), Higher and Ordinary Level, with the SEC examination.
- Subject guide
- Leaving Certificate
- Topics mapped
- 16
02 · Complete topic map
Complete topic map
Every topic recorded for this subject in the curriculum is reproduced below in its full hierarchy. The descriptions reflect the mapped scope without implying additional exam rules.
- 01
Mathematical Modelling (the problem-solving cycle)
The unifying strand in which learners use a systematic, iterative cycle to formulate real-world problems, translate them into mathematics, compute solutions and evaluate and refine them.
- 02
Formulating and Translating Problems
Researching a problem's background, identifying relevant variables, decomposing it into manageable parts, making simplifying assumptions and abstracting the knowledge needed to build a model.
- 03
Networks and Graphs
Representing real situations as networks, using terminology such as vertex, edge, weight, path and cycle, and distinguishing connected/disconnected and directed/undirected graphs.
- 04
Matrices and Adjacency
Representing graphs with adjacency matrices, reconstructing graphs from them, performing square-matrix multiplication and interpreting matrix products.
- 05
Minimum Spanning Trees and Optimisation Algorithms
Understanding trees and spanning trees and applying Kruskal's and Prim's algorithms to optimise networks, including reasoning about greedy versus dynamic-programming approaches.
- 06
Dynamic Programming and Shortest Paths
Applying Bellman's Principle of Optimality and Dijkstra's algorithm to find shortest paths in weighted networks for multi-stage problems such as routing, stock control and resource allocation.
- 07
Project Scheduling Networks
Applying network analysis to project scheduling using critical path, early and late times and floats to plan and optimise activities.
- 08
Kinematics: Motion in One Dimension
Describing particle motion using displacement, velocity, acceleration and time, with displacement-time and velocity-time graphs and the constant-acceleration equations of motion.
- 09
Calculus Applied to Motion
Interpreting velocity and acceleration as derivatives, using differentiation, the chain rule and integration to relate the motion quantities, and deriving the kinematic formulae via calculus.
- 10
Vectors and Projectile Motion
Using elementary vector algebra and calculus to represent motion in two dimensions and to solve projectile problems involving time of flight, maximum height and range.
- 11
Forces and Newton's Laws
Drawing free-body diagrams and applying Newton's laws in vector form to find resultant forces and solve dynamics problems on smooth and rough horizontal and inclined planes, including friction and resistive (drag) forces.
- 12
Momentum, Impulse and Collisions
Applying conservation of momentum, impulse and Newton's experimental law to elastic and inelastic collisions in one and two dimensions, including connected masses and the coefficient of restitution.
- 13
Work, Energy and Circular Motion
Using work, kinetic and gravitational potential energy and conservation of energy (including elastic springs and strings) to analyse motion, plus the dynamics of a particle in horizontal or vertical circular motion.
- 14
Difference Equations (incremental change)
Using recurrence relations and first- and second-order difference equations to model discretely changing phenomena such as Malthusian and restricted growth, loan repayment, supply and demand and the spread of disease.
- 15
Differential Equations (continuous change)
Deriving and solving differential equations (separable first-order, and second-order reducible to first-order) using analytic, numerical and graphical methods to model continuously changing phenomena and interpreting the solutions in context.
- 16
The Modelling Project
A coursework component based on an annual SEC brief in which students complete the full modelling cycle for an authentic real-world problem and submit a written report worth 20% of the grade.
03 · Where this subject applies
Where this subject applies
These pathways and regions are explicitly connected to the subject in the curriculum.
Levels and pathways
Higher Level
Higher Level — the more demanding level, with broader and deeper content and the H1–H8 grade scale.
Ordinary Level
Ordinary Level — the foundational level covering the core of the syllabus, graded O1–O8.
Regions
All registered regions
04 · Official sources
Official sources
The public sources below are referenced directly by this subject or by one of its topics.
This editorial selection points to the relevant official bodies. Always confirm current requirements, dates and exceptional arrangements with your school and the responsible authority.
2
Public references
IE · EuraStudy Guides
Place this subject inside the complete curriculum.
Open the curriculum guide to see every subject and topic, or continue to EuraStudy Summa to begin working with the material.