Leaving Cert Maths Paper 1 Topics: A Comprehensive Overview

On both the Higher and Ordinary Leaving Cert Maths syllabus, there are two final papers, Maths Paper 1 and Paper 2. Each paper is 2.5 hours long and looks almost identical from the front cover, but Maths Paper 1 tests completely different topics and skills than Paper 2. It’s important to know these differences before sitting the exam so that you’re aware of your strengths and weaknesses. Let’s take a look at the Maths Paper 1 topics so that you have an in-depth understanding of what’s going to come up on exam day.

Leaving Cert Syllabus: Maths Paper 1

The first thing you need to know is that Maths Paper 1 examines strands 3, 4, and 5 of the Leaving Cert Maths syllabus, so all of the Maths Paper 1 is based on these general topics. We break each of the strands down in detail in our Leaving Cert Maths Syllabus Simplified blog post, but for the purposes of this article, we’re giving a more general overview of what you need to know for Maths Paper 1.

Strand 3 is called the Number strand, Strand 4 the Algebra strand, and Strand 5 the Functions strand, and we’re going to explain what forms part of each in the next few sections.

Number Strand Topics

The Number Strand is divided into four different sections, and within each, there a number of different learning outcomes related to each. The table below showcases each of these sections with a list of the main subtopics, with those reserved for Higher Level marked in bold:

Note: These lists are by no means definitive. For a more detailed list of what you need to know, consult the syllabus!

Algebra Strand Topics

Maths Paper 1 is often thought of as the ‘Algebra Paper’. While it is not just algebra examined on Maths Paper 1, it does form a huge part of it, and the skills you develop from algebra are required to answer questions from many of the other strands.

Like the number strand, there are four sections:

Note: The Complex Numbers section also examines many of the topics from Number Systems, shown in the previous table!

If you struggle with algebra, you are not alone. It is the number one topic students struggle with across the board, from first to sixth year of secondary school. Luckily, at Breakthrough Maths, we boast some of the best algebra tutors in Ireland. Check out one of our tutors, Luke, breaking algebra down in 60 seconds below!

Luke is also teaching our 2-hour-long Exam Crash Courses – sign up now to hear the secrets of one of Ireland’s best maths tutors!

Functions Strand

Functions at Junior Cycle Level are so fun and simple. Sure, throw the few bits into the Casio and it’s all done for you.

Unfortunately, at Leaving Cert level, they do kick it up a notch with the addition of calculus (and if you’re struggling with that, you know where to look!)

The good news is that the Functions strand is only broken down into two parts:

Note: Again, these are not complete lists of what you need to know. Consult the syllabus to be 100% clear on what you need to have covered for the exam.

Proofs, Constructions, and Theorems

Even though Maths Paper 1 has nowhere near as much material to be learned off by heart as Paper 2, there are still a few things you need to be able to do on the day of the exam (especially if you are sitting it at Higher Level) that require a bit of memorization.

  • Proof that √2 is irrational
  • Construction of √2 and √3
  • Trapezoidal Rule (in the Log tables, but you need to know how to use it!)
  • Proof by Induction (i) Divisibility/Factors (ii) Series (iii) Inequality
  • Proof of the Sum of Geometric Series 
  • Proof of the Sum of Infinite Geometric Series Formula
  • Derivation of the Amortisation Formula
  • Binomial Theorem (again, in the Log tables)
  • Factor Theorem
  • Conjugate Root Theorem
  • Derivation of DeMoivre’s Theorem
  • Define Injective, Surjective, and Bijective functions
  • Completing the Square Formula
  • Differentiation by First Principles (i) Linear expressions (ii) Quadratic expressions
  • Poof that a line is tangent to a circle


Just to sum up all of the Maths Paper 1 topics one last time before we send you off to study them:

  • Complex numbers
  • Sequences and series
  • Indices & logs
  • Financial Maths
  • Length, area, and volume
  • Algebra
  • Functions
  • Calculus

If you are struggling with any of the above topics, know that we will be covering them in our Exam Crash course, where we will provide detailed notes, as well as exam predictions to help you smash Maths Paper 1 (and Paper 2)!

T.J – CEO of Breakthrough Maths.

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