Ireland · NCCA Curriculum Specifications
6th Year Applied Mathematics.
This curriculum aligns with the Leaving Certificate Applied Mathematics specification for 6th Year students in Ireland. It focuses on developing students' problem-solving and analytical skills through mathematical modelling, kinematics, dynamics, and network analysis.
01Mathematical Modelling and Networks
Students explore the mathematical modelling cycle and apply graph theory to solve real-world network problems. This unit emphasises translating authentic situations into mathematical structures.
An introduction to formulating, solving, interpreting, and evaluating mathematical models. Students learn to make assumptions and define variables for complex problems.
Students investigate the properties of graphs, including vertices, edges, degrees, and paths. This forms the foundation for analysing complex networks.
Application of algorithms such as Dijkstra's and Kruskal's to find shortest paths and minimum spanning trees. Students solve logistical and routing problems.
Using activity networks to schedule and manage projects efficiently. Students calculate early and late start times to identify the critical path.
02Kinematics and Projectiles
This unit covers the geometry of motion, focusing on linear acceleration, relative velocity, and projectile motion in two dimensions. Students model physical movement using vector mathematics.
Review and extension of the equations of linear motion with constant acceleration. Students apply vector notation to displacement, velocity, and acceleration.
Analysing the motion of one object from the perspective of another moving object. Applications include navigating ships and aircraft in crosswinds.
Modelling the parabolic trajectory of objects launched into the air under the influence of gravity. Students calculate maximum height, time of flight, and range.
Extending projectile motion concepts to scenarios where the landing surface is sloped. Students resolve vectors parallel and perpendicular to the incline.
03Dynamics and Connected Systems
Students investigate the causes of motion using Newton's laws. The unit explores friction, connected particles, and the principles of momentum and collisions.
Applying Newton's three laws of motion to solve dynamic problems. Students construct free-body diagrams to resolve forces acting on particles.
Modelling the effects of static and kinetic friction on moving bodies. Students analyse objects sliding up or down inclined planes.
Solving problems involving masses connected by light inextensible strings passing over smooth pulleys. Students determine common acceleration and string tension.
Investigating the conservation of linear momentum and Newton's law of restitution. Students model direct and oblique collisions between elastic spheres.
04Difference Equations and System Dynamics
This unit introduces discrete mathematics through difference equations. Students model dynamic systems such as population growth and financial amortisation over discrete time steps.
Formulating and solving linear first-order difference equations. Students explore recursive sequences and their long-term behaviour.
Solving homogeneous and non-homogeneous second-order difference equations. Students use characteristic equations to find explicit formulas for sequences.
Applying difference equations to real-world scenarios like predator-prey models, population dynamics, and loan amortisation schedules.