Leaving Cert Exam - Topics on Each Paper

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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

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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