The Most Common Topics on Higher Level Maths Papers

Calculus is the most common topic on Leaving Cert Higher Level maths. It appeared in 21 of the 22 Higher Level papers from 2015 to 2025, and it carries more questions and more marks than any other area. This post counts how often every topic appeared across those papers, and which of the two papers it appeared on. Our corpus stores every question from the past papers we have extracted, tagged with the topics it covers, so every number here is a count of the papers themselves.

The papers this post counts

Our maths corpus goes back to 2015 and runs to 2025. That is 22 Higher Level papers, Paper 1 and Paper 2 in each of the 11 years, holding 208 printed questions between them.

Every number below describes those 22 papers and nothing else. A count of what has happened is not a statement about what will happen.

How the topics are grouped

Each question in the corpus carries fine-grained tags such as tangent slope, de moivre's theorem or mid-interval mean. Across the 22 Higher Level papers there are 212 distinct tags, and 104 of them appear in only one paper. Counting at that grain tells you almost nothing.

So the tags are grouped into 12 topic areas, built out of the five strands in the official Leaving Certificate Mathematics syllabus. The syllabus strands are too broad to study from. Functions covers everything from reading a graph to integration, so each strand is split into the areas a student would revise separately.

A maths question usually belongs to more than one area. Of the 208 questions, 73 cover one area, 100 cover two, 29 cover three and 6 cover four. The counts below overlap for that reason, and the mark shares add to more than 100 percent.

Ten of the twelve areas appeared in every year

"Papers" counts how many of the 22 papers contained at least one question in that area. "Marks" is the marks printed on those questions, out of the 7,400 marks printed across all 22 papers.

Ten of the twelve areas appeared in all 11 years, on one paper or the other. Only Number & Arithmetic (7 years) and Financial Maths (6 years) missed any.

At this grain the question of what comes up most has a dull answer. Nearly everything comes up. The variation is in which paper an area landed on and how many marks it was worth when it did.

Which paper each area appeared on

The columns count years, out of 11 Paper 1s and 11 Paper 2s.

Complex numbers came up on every one of the 11 Paper 1s and on none of the 11 Paper 2s. Financial maths appeared 6 times, all on Paper 1. Going the other way, probability, statistics and coordinate geometry each appeared on all 11 Paper 2s, and probability appeared on a Paper 1 once in the 11 years.

Trigonometry and geometry are the areas that crossed over most. Trigonometry appeared on all 11 Paper 2s and on 8 of the 11 Paper 1s. Of its 9 Paper 1 questions, 6 also cover calculus and 3 also cover functions and graphs, so what crosses over is the trigonometric function rather than the triangle.

Calculus is on both papers and carries the most marks

Calculus appeared in 21 of the 22 papers, the exception being 2017 Paper 2. It covers 70 of the 208 questions and 2,800 of the 7,400 printed marks, which is more than any other area by both measures.

It also arrives mixed with something else more often than any other area. Of its 70 questions, 30 also cover functions and graphs, 16 also cover algebra, 14 also cover geometry and measurement, and 12 also cover coordinate geometry. A question asking for the equation of the tangent to a curve at a point is a calculus question and a coordinate geometry question at once.

That is the practical limit on studying by topic area. You can revise calculus on its own, and the exam will still hand it to you wrapped in something else. The SEC's Chief Examiner's Report for Leaving Certificate Mathematics makes the same point about the course, and asks teachers to give students practice at applying one strand to another (page 29).

Mathematics is not a list of discrete rules and definitions to be learned but rather a series of interconnected principles that can be understood and then applied in a wide variety of contexts. While compartmentalising knowledge may help keep it organised, it will restrict the ability to cope with unfamiliar questions, particularly those requiring the synthesis of knowledge and skills from several strands.

What appeared least often

Financial maths is the rarest area in the sample. It appeared in 6 of the 22 papers, as one question each time, on Paper 1 in 2015, 2017, 2020, 2023, 2024 and 2025. Number and arithmetic appeared in 8 of the 22 papers across 14 questions.

Neither count is a reason to skip the area. All twelve areas were on the 2025 papers, financial maths and number and arithmetic included, and a topic that has appeared in 6 of 22 papers has appeared. There are only six financial maths questions in the whole sample, so you can work through every one of them before you decide anything about it.

Short questions and long questions differ

Both papers run Section A, the shorter questions, and Section B, the longer contextual ones. Across the 22 papers there are 132 Section A questions and 76 Section B questions.

Some areas sit mostly in one section. Of algebra's 47 questions, 34 are in Section A. All 12 complex numbers questions are in Section A. Calculus goes the other way, with 40 of its 70 questions in Section B, including at least one in all 11 years.

Section B questions also mix more areas. A Section B question covers 2.30 topic areas on average, against 1.58 for a Section A question. The long questions are where the strands get combined.

The papers changed shape in 2021

The 2015 to 2020 papers each printed 300 marks across 9 questions. The 2021 to 2025 papers print 380 marks across 10 questions. The extra questions are choice, added as an assessment adjustment for disruption to learning during Covid. The Exam Material Archive flags the papers from 2021 onwards as adjusted and notes that they do not necessarily follow the structure of papers from other years.

Those adjustments have not been withdrawn. The Department of Education confirmed on Wednesday 5 November 2025 that they stay for the 2026 Leaving Cert. The same statement says Leaving Cert 2027 students will have them in maths as well, until the revised specifications arrive under Senior Cycle Redevelopment.

The adjustment matters for reading the mark shares above. The 7,400 figure counts marks printed on the paper, not marks any one candidate answered, and from 2021 a candidate answers fewer questions than the paper contains. Where the extra choice makes an area easier to avoid, its share of printed marks overstates what it was worth to a student who skipped it.

Frequency is history, not a forecast

None of this predicts a paper. The whole syllabus is examinable every year, so a topic appearing in 21 papers running places no constraint on the 22nd.

The most recent Chief Examiner's Report for Leaving Certificate Mathematics tells teachers and students to cover the full syllabus, and warns about leaning on the papers themselves (page 28).

Close to the time of examination, questions from past and sample examination papers provided by the State Examinations Commission should be used for practice. However, examination papers should not be relied on excessively during any extended period of learning, as this might unnecessarily restrict the range of student learning and limit candidates' ability to deal with questions set in unfamiliar contexts.

That report is from 2015, and one line of it has since changed. It gives "there is no choice on any of the examination papers" as the reason to cover everything, which the adjusted papers have softened. The SEC has not produced Chief Examiners' Reports since 2019, so there is no newer one for maths.

The way this data goes wrong is when a low count is read as permission to drop something. Financial maths appeared in 6 of 22 papers here. If it appears in your year and you skipped it, the count did you harm.

What the counts do describe is your own preparation. You have been practising off these same 22 papers, so the areas that are thin in the table are the areas you have had the fewest chances to meet. Financial maths gave you 6 questions and 255 marks of practice material. Calculus gave you 70 questions and 2,800 marks. That gap is in your revision whether or not it is in next June's paper.

What to do with it

Take one area and work its questions across several years in sequence, the way the past paper study method describes. Closed book, then marked against the scheme. Calculus has 70 questions in the sample spread over both papers and both sections, so several attempts show you more of its range than one does.

Pick the area you have done least of. The counts above also tell you which areas keep turning up together. Pairing calculus with functions and graphs, or trigonometry with calculus on Paper 1, matches the way they arrive on the paper. If you are weighing up the level itself, there is a separate post on dropping to Ordinary Level.

FAQ

What is the most common topic on Leaving Cert Higher Level maths? In the 22 Higher Level papers from 2015 to 2025, calculus appeared in 21 of them, covering 70 of the 208 questions. Ten of the twelve topic areas appeared in every one of the 11 years.

What comes up on maths Paper 1? In those 11 years, algebra, functions and graphs, sequences and series, and complex numbers each appeared on all 11 Paper 1s. Calculus did too. Financial maths appeared on 6 of them and on no Paper 2.

What comes up on maths Paper 2? Probability, statistics, coordinate geometry, trigonometry and geometry each appeared on all 11 Paper 2s in the sample. Calculus appeared on 10 of the 11.

Can I use this to predict what will come up? No. Everything on the syllabus is examinable in any year, and the SEC's Chief Examiner's Report tells teachers and students to cover the full syllabus. Use the counts to find the topics you have practised least, not to decide what to leave out.

Why do the mark shares add to more than 100 percent? Because 135 of the 208 questions cover more than one topic area, and a question's marks are counted under each area it covers.

Every question behind these numbers is on the Leaving Cert maths topic pages, grouped by area and by year, with the marking scheme beside each one. Each area also has a free PDF pack at Higher or Ordinary Level, with no account needed. Start from the past paper finder if you want a full paper instead.