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Leaving Certificate Mathematics (NCCA specification), Higher and Ordinary Level, with the SEC examination.
Overview
Leaving Certificate Mathematics (NCCA specification), Higher and Ordinary Level, with the SEC examination.
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.
Systematically listing and counting the possible outcomes of experiments as the groundwork for probability.
Understanding probability as the relative frequency or theoretical likelihood of events, including the use of fair and biased situations.
Calculating probabilities for single and combined random events, including expected value and the rules for combining events.
Engaging critically with statistics encountered in everyday life and evaluating how data and statistical claims are presented.
Designing data investigations and gathering, classifying and organising primary and secondary data appropriately.
Displaying data with suitable charts and graphs and summarising it using measures of centre and spread.
Drawing valid inferences from data, recognising sampling variability and acknowledging the limitations of conclusions.
Working with formal geometric definitions, axioms, theorems, proofs and constructions in the Euclidean tradition.
Using the Cartesian plane to analyse lines and circles algebraically, including distance, slope, equations and intersections.
Solving problems involving angles, lengths and areas using trigonometric ratios, identities and the sine and cosine rules.
Investigating transformations of figures, with particular attention to enlargements and the effects of scale factor.
Extending fluency across natural numbers, integers, rationals, reals and complex numbers and reasoning about their properties.
Manipulating expressions involving integer, rational and other indices and applying the laws of exponents.
Applying numerical and proportional reasoning to real contexts including financial mathematics, ratio, rates and error.
Calculating perimeters, areas and volumes of two- and three-dimensional shapes and applying these in practical problems.
Generating, representing and manipulating algebraic expressions, formulae and patterns, including factorising and rearranging.
Solving linear, quadratic, simultaneous and other equations and forming equations to model situations.
Solving and representing linear and quadratic inequalities and interpreting their solution sets.
Performing operations on complex numbers and representing them on the Argand diagram, including their geometric meaning.
Understanding functions, their domain, range and graphs, and using different families of functions to model relationships.
Using differentiation and integration to analyse rates of change, slopes, maxima and minima, and areas.
Where this subject applies
These pathways and regions are explicitly connected to the subject in the curriculum.
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.
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.
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Public references
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