Leaving Cert Mathematics Notes

Free Leaving Cert Mathematics revision notes for Higher Level. Browse 28 topics and read online without an account.

28 topicsHigher LevelUpdated 5 Oct 2026

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Revise algebra, complex numbers, functions and financial mathematics, alongside calculus, trigonometry, probability and statistics. Work through topic explanations and diagrams at your own pace.

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Exam guideThis exam guide covers Leaving Certificate Mathematics at Higher Level for 2027.7 min read Algebra - CubicsTopic explanations.3 min read Algebra - Expressions & FactorisingAlgebra at Leaving Certificate Higher Level centres on manipulating polynomial and rational expressions with speed and precision.4 min read Algebra - InequalitiesSolving a linear inequality follows standard algebraic steps with one non-negotiable rule: if you multiply or divide across by a negative number, flip the…5 min read Algebra - QuadraticsIllustrated explanations.3 min read Algebra - Simultaneous EquationsIllustrated explanations.3 min read Algebra - Solving EquationsIllustrated explanations.3 min read Area & VolumeArea and volume, or mensuration, is about measuring shapes: how much space a flat figure covers, how much a solid holds, and how much surface it has.4 min read Complex NumbersA complex number is z = a + bi. To add or subtract, combine real and imaginary parts separately. To multiply, expand the brackets and replace i² with -1, e.g.5 min read Financial MathsCompound interest means you earn interest on both your starting principal and any interest that has accumulated in earlier periods.6 min read InductionMathematical induction is a method of proof that shows a statement is true for every natural number, without having to check them one at a time.3 min read Indices and LogsIndices and logarithms are fundamental tools for modelling growth and decay.4 min read Sequences & SeriesSequences and series are the mathematical language of patterns, covering everything from simple lists to complex financial growth.4 min read Co-Ordinate Geometry of the CircleIllustrated explanations, key terms and self-check questions.6 min read Co-Ordinate Geometry of the LineCo-ordinate geometry of the line is a core Paper 2 topic that describes geometric shapes using algebra.3 min read GeometryGeometry at Higher Level has two halves. The synthetic half uses axioms and theorems to perform formal deductions ('cuts') and proofs.4 min read Geometry - Constructions & ProofsSynthetic geometry at Leaving Certificate Higher Level moves from discovery to a formal, deductive system.7 min read Trigonometry - Functions & IdentitiesTrigonometry at Higher Level moves past simple triangles into the study of periodic functions, identities, and equations.3 min read Trigonometry - TrianglesTrigonometry for Leaving Certificate Higher Level focuses on the relationships between sides and angles in triangles.5 min read Differentiation - ApplicationsIllustrated explanations, key terms and self-check questions.6 min read Differentiation - RulesFor a straight line, the slope never changes. A curve is different because its steepness varies from point to point.5 min read FunctionsIllustrated explanations, key terms and self-check questions.6 min read IntegrationWhen you differentiate a function, you find its rate of change.6 min read ProbabilityIllustrated explanations, key terms and self-check questions.8 min read Statistics - Descriptive StatisticsDescriptive statistics focuses on organising, summarising, and making sense of numerical and categorical data.6 min read Statistics - Inferential StatisticsA population includes every single individual or item you want to study, whereas a sample is just a subgroup picked from that population.5 min read Statistics - Z ScoresThe normal curve is symmetric and bell-shaped.3 min read ProofsIllustrated explanations, key terms and self-check questions.50 min read

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