Leaving Cert Exam - Topics on Each Paper

Paper 1

Number
3.1 Number Systems
  • Irrational Numbers
  • Complex Numbers (also 4.4)
  • Induction
  • Limits
  • Patterns, Sequence and Series
3.2 Indices (and Logs)
3.3 Arithmetic (Financial Maths)

Algebra
4.1 Expressions
  • Add, Subtract, Multiply, Divide
  • Factorising Expressions
  • Simplify Rational Algebraic Expressions
  • Binomial Theorem
4.2 Solving Equations
  • Linear Equations
  • Quadratic Equations
  • Simultaneous Equations 
  • Cubic Equations
  • Index Equations
  • Exponential Equations
4.3 Inequalities
  • Linear Inequalities
  • Quadratic Inequalities
  • Rational Inequalities
  • Modulus Inequalities
4.4 Complex Numbers (also in 3.1)
  • Add, Subtract, Multiply, Divide
  • Conjugate Roots
  • Argand Diagram
  • Polar Form
  • De Moivre's Theorem for Expansions, Roots, Trigonometric Proofs
  • Prove DeMoivre's Theorem

Functions
5.1 Functions
  • Graph Cubic, Exponential, Logarithmic & Trigonometric Functions
  • Injective, Surjective and Bijective
  • Inverse of Function
  • Quadratics in Complete Square Form
  • Limits and Continuity of Functions
5.2 Calculus
Differentiation
  • First Principles
  • Differentiation by Rule
  • Rates of Change
  • Max & Min

Integration
  • Anti-differentiation
  • Average Value
  • Area Bounded by Curves

Paper 2

Probability & Statistics
1.1 Counting
  • Permutations & Combinations
1.2 Concepts of Probability
  • Mutually Exclusive
  • Independent Events
  • Addition & Multiplication Rules
1.3 Outcomes of Random Processes
  • Bernoulli Trials
  • Normal Distribution
1.4 Statistical Reasoning
1.5 Collecting & Organising Data
1.6 Representing Data
  • Graphs
  • Mean & Standard Deviation
  • Correlation
1.7 Analysing Data
  • Margin of Error
  • Hypothesis Testing

Geometry & Trigonometry
2.1 Synthetic Geometry
  • Constructions
  • Theorems
2.2 Co-ordinate Geometry
  • Line
  • Circle
2.3 Trigonometry
  • SOH CAH TOA & Pythagoras
  • Sine and Cosine Rules
  • Sectors and Arcs
  • 3D Problems
  • Graphs
  • Trigonometric Equations
  • Derive 8 Trigonometric Formulae
  • Apply Formulae (Solve Identities)
2.4 Transformations & Enlargements

Number
3.4 Length, Area and Volume
  • Polygons
  • Nets
  • Composite Shape Problems
  • Trapezoidal Rule
*Note: It is possible that some elements of may come up in either paper e.g. Area and Volume could form part of a question in Paper 1
Structure of the Examination 
(Department Circular S82/2013)

The examinations at Higher level and at Ordinary level will each consist of two written papers, each carrying 300 marks. 

Paper 1 will test the material in Strand 3, Strand 4, and Strand 5 of the new syllabus. There will be two sections on the paper, as follows: 

o Section A: Concepts and Skills 150 marks 
o Section B: Contexts and Applications 150 marks 
  
Paper 2 will test the material in Strand 1 and Strand 2 of the new syllabus, along with material from 
Section 3.4 in Strand 3: Length, Area and Volume. There will be two sections on the paper, as 
follows: 

o Section A: Concepts and Skills 150 marks 
o Section B: Contexts and Applications 150 marks