Leaving Cert Maths Paper 2 Topics: A Comprehensive Overview

There are two final exam papers on both the Higher and Ordinary Leaving Cert Maths syllabusMaths Paper 1 and Maths Paper 2. Both are 2.5 hours long, but Maths Paper 2 tests completely different topics and skills than Paper 1 (which we broke down in this blog). It’s important to know the differences before sitting the exam to know where your strengths and weaknesses lie. Let’s take a look at the Maths Paper 2 topics , so you have an in-depth understanding of what’s going to come up on exam day.

Leaving Cert Syllabus: Maths Paper 2

The first thing you need to know is that Maths Paper 2 examines strands 1 (Statistics and Probability) and 2 (Geometry and Trigonometry) of the Leaving Cert Maths syllabus, so all of the Maths Paper 2 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 2.

Statistics And Probability Strand

Statistics and Probability is probably the most intense strand in terms of just how much you need to know. There aren’t any shortcuts either, because it makes up roughly half of Maths Paper 2, so you need to know your stuff.

Below we have a table, broken up by subtopics, of the main things you need to know for the Statistics and Probability sections of Maths Paper 2. Anything in bold font is for Higher Level only.

Note: This is not a definitive list of everything you need to know for the exam. Consult the syllabus to make sure you have everything covered!

If this list intimidates you, or if the step-up from JC Statistics has proved to be too much of a challenge, book in with Breakthrough Maths – Statistics is one of the main topics we cover for Senior Cycle students, and our lessons make the whole thing way more interesting!

Geometry And Trigonometry Strand

Geometry and Trigonometry is not as content-heavy as the previous strand, but instead comes with the addition of a lot of material that needs to be learned by heart, especially at Higher Level.

Note: Depending on what level you sit the exam at, the list of things you need to know from Synthetic Geometry will vary. Consult the syllabus to be sure.

YOU WILL ALSO NEED KNOWLEDGE OF LENGTH, AREA, AND VOLUME FROM THE NUMBER STRAND (which is mostly a Paper 1 topic, but will be relevant to Maths Paper 2 for some questions).

Proofs, Constructions, And Theorems

Maths Paper 2 has a significant volume of material that, to put it quite simply, needs to be learned by heart.

  • Definition of statistical terms: Stratified, Cluster, Quota
  • Terms to describe the distribution of data: Symmetrical, Positive Skew, Negative Skew, Uniform, Bimodal, Multimodal
  • Empirical Rule
  • Percentile Rank Formula
  • Construction of 95% confidence intervals
  • Calculation of p-values
  • Basic Probability Formulae: Mutually Exclusive Events, Addition Rule (Non-mutually Exclusive Events), Multiplication Rule (Independent Events), Conditional Probability
  • Bernoulli Trials
  • Constructions 1-21 (+ 22 for Higher Level)
  • Definition of geometric terms: theorem, proof, axiom, corollary, implies, converse, is equivalent to, if and only if, proof by contradiction
  • Proof of Theorems 11-13
  • Derivation of trigonometric formulae 1-7 and 9

Additionally, you’re going to need to know a couple of functions on your calculator so that you can generate the following (with the help of your Log tables):

  • Binomial coefficient (for permutations and combinations)
  • Correlation coefficient
  • Standard deviation


Just to sum up all of the Maths Paper 2 topics one last time before we send you off to study them:

  • Sets
  • Probability
  • Statistics
  • Geometry
  • Co-ordinate Geometry
  • Trigonometry

TJ— CEO of Breakthrough Maths.

Need help in Maths? Contact the Breakthrough Maths team here.

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