IE · Subject guide
Mathematics
Leaving Certificate Mathematics (NCCA specification), Higher and Ordinary Level, with the SEC examination.
01 · Overview
Mathematics
Leaving Certificate Mathematics (NCCA specification), Higher and Ordinary Level, with the SEC examination.
- Subject guide
- Leaving Certificate
- Topics mapped
- 21
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
Strand 1.1 Counting
Systematically listing and counting the possible outcomes of experiments as the groundwork for probability.
- 02
Strand 1.2 Concepts of Probability
Understanding probability as the relative frequency or theoretical likelihood of events, including the use of fair and biased situations.
- 03
Strand 1.3 Outcomes of Random Processes
Calculating probabilities for single and combined random events, including expected value and the rules for combining events.
- 04
Strand 1.4 Statistical Reasoning with an Aim to Becoming a Statistically Aware Consumer
Engaging critically with statistics encountered in everyday life and evaluating how data and statistical claims are presented.
- 05
Strand 1.5 Finding, Collecting and Organising Data
Designing data investigations and gathering, classifying and organising primary and secondary data appropriately.
- 06
Strand 1.6 Representing Data Graphically and Numerically
Displaying data with suitable charts and graphs and summarising it using measures of centre and spread.
- 07
Strand 1.7 Analysing, Interpreting and Drawing Conclusions from Data
Drawing valid inferences from data, recognising sampling variability and acknowledging the limitations of conclusions.
- 08
Strand 2.1 Synthetic Geometry
Working with formal geometric definitions, axioms, theorems, proofs and constructions in the Euclidean tradition.
- 09
Strand 2.2 Co-ordinate Geometry
Using the Cartesian plane to analyse lines and circles algebraically, including distance, slope, equations and intersections.
- 10
Strand 2.3 Trigonometry
Solving problems involving angles, lengths and areas using trigonometric ratios, identities and the sine and cosine rules.
- 11
Strand 2.4 Transformation Geometry, Enlargements
Investigating transformations of figures, with particular attention to enlargements and the effects of scale factor.
- 12
Strand 3.1 Number Systems
Extending fluency across natural numbers, integers, rationals, reals and complex numbers and reasoning about their properties.
- 13
Strand 3.2 Indices
Manipulating expressions involving integer, rational and other indices and applying the laws of exponents.
- 14
Strand 3.3 Arithmetic
Applying numerical and proportional reasoning to real contexts including financial mathematics, ratio, rates and error.
- 15
Strand 3.4 Length, Area and Volume
Calculating perimeters, areas and volumes of two- and three-dimensional shapes and applying these in practical problems.
- 16
Strand 4.1 Expressions
Generating, representing and manipulating algebraic expressions, formulae and patterns, including factorising and rearranging.
- 17
Strand 4.2 Solving Equations
Solving linear, quadratic, simultaneous and other equations and forming equations to model situations.
- 18
Strand 4.3 Inequalities
Solving and representing linear and quadratic inequalities and interpreting their solution sets.
- 19
Strand 4.4 Complex Numbers
Performing operations on complex numbers and representing them on the Argand diagram, including their geometric meaning.
- 20
Strand 5.1 Functions
Understanding functions, their domain, range and graphs, and using different families of functions to model relationships.
- 21
Strand 5.2 Calculus
Using differentiation and integration to analyse rates of change, slopes, maxima and minima, and areas.
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.