Mathematics

Subject Content

The Mathematics syllabi are presented in the form of a core and a list of options.  It is envisaged that students would study the whole of the core and one option.

Higher Level Mathematics

Core
Algebra
Complex Numbers
Induction
Matrices
Coordinate Geometry of Line & Circle
Plane Vectors
Transformation Geometry
Trigonometry
Sequences & series
Functions
Differential Calculus
Integral Calculus
Discrete mathematics & statistics
Difference Equations

Options
Further Calculus & series
Further probability & statistics
Groups
Further Geometry

Ordinary Level & Ordinary Foundation Level Mathematics

Core
Arithmetic
Areas
Algebra
Complex Numbers
Synthetic Geometry-Theorems
Coordinate Geometry of the line and circle
Enlargements
Trigonometry
Finite sequences & series
Functions & graphs
Calculus
Discrete mathematics & statistics

Options
Further sequences & series
Further Geometry
Plane Vectors
Linear programming

Exam Structure

Higher and Ordinary Level Mathematics

There are two 2 hour papers.

Paper 1 Answer 6 out of 8 questions.

Paper 2 Section A.  Answer 5 out of 7 questions
              Section B.  Answer 1 out of 4 option questions.

Foundation Level Mathematics

There are two 2 hour papers.

Paper 1 Answer question 1 and 4 out of 6 other questions

Paper 2 Answer 6 out of 8 questions

Comment

Parents and students should be aware of the following when considering the study of Mathematics at Higher Level for the Leaving Certificate exam.

• The study of Mathematics at Higher Level is aimed at the more able Leaving Certificate student.
• The Higher Level syllabus is very long and time consuming.  It places significant demands on the Leaving Certificate student and requires a huge commitment in terms of time and effort.
• The material covered in Higher Level Mathematics is chosen for its intrinsic interest and general applicability, as well as its provision of concepts and techniques appropriate for future specialists in the field. However it may be assumed that some aims regarding the use of Mathematics in everyday life and work have been achieved at the Higher Junior Cert level and so the focus in Leaving Certificate Higher level is on deepening the understanding of Mathematical ideas and an appreciation of powerful concepts and methods. 
• There is a vast difference in the study of Mathematics at Higher Level for Junior Certificate and the Study of Mathematics at Higher Level for Leaving Certificate.

The Ordinary Level Mathematics course was designed to provide students with knowledge and techniques that they may need in the future. As well as equipping students with these important tools it offers students opportunities to deepen their understanding and appreciation of Mathematics.

Foundation Level Mathematics is available to any student who struggles with the Ordinary Level Mathematics syllabus. All students are expected to do Higher or Ordinary Level Mathematics in fifth year. If a student is experiencing considerable difficulty with the Ordinary level course, the teacher will discuss with the student and their parents the option of Foundation level Mathematics.

Bearing the above concerns in mind and not withstanding exceptional circumstances, a student must have achieved at least a grade (C) at Junior Certificate Higher Level, to be considered for admittance into a Higher Level Leaving Certificate class.