The 2026 Leaving Certificate Mathematics Papers

As I mentioned a few days ago, examinations for the 2026 school Leaving Certificate are under way. One of the interesting things about the Irish system is that the examination papers are put up online immediately after the examinations. Students took their first paper in Mathematics (either Ordinary or Higher level) on Friday and the second was this morning. There has been some reaction in the news here and here.

Anyway, I thought I’d share the Mathematics papers here so you can see what you think of them.

Here are the two Higher Mathematics papers:

LC003ALP100EVDownload LC003ALP200EV (2)Download

The Ordinary Level papers are here:

LC003GLP100EV (2)Download LC003GLP200EV (1)Download

They look reasonable to me. The thing that strikes me about them is that they are much more structured than the A-level mathematics examinations I took way back in 1981.

Comments are welcome through the box below.

#HigherMathematics #LeavingCertificate #mathematics

That Scottish Higher Maths Paper 1…

Talking of Examinations, I saw an article on the BBC website about a recent Higher Maths paper in Scotland which has generated complaints and a petition because it was allegedly unfair. The introduction to the petition states:

This is not a complaint that the paper was too hard. Students expect to be challenged. The problem is that the 2026 Higher Maths Paper 1 used language and phrasing that was confusing, ambiguous, and inconsistent with every past paper students had revised from. Questions were not simply difficult — they were worded in ways that made it genuinely unclear what was being asked.

Past SQA Higher Maths papers have followed a recognisable style: clear command words, standard notation, and questions that test understanding rather than the ability to decode unusual phrasing. The 2026 Paper 1 departed from this in ways that penalised well-prepared students simply because the wording did not match the conventions they had been taught to expect.

Numerous other news outlets have covered the story too. It is frustrating that most of the pieces focus on what people said about the paper but don’t actually include a link to the paper itself, making it impossible to make your own mind up.

So you can make your own mind up here is a scan of the actual paper (obtained from here):

2026_Higher_Maths_Paper_1_ScanDownload

Bear in mind that the Scottish examination system is not the same as in England & Wales – the “Highers” are not as advanced as A-levels and are more similar to the Irish Leaving Certificate.

My opinion, for what it’s worth having neither taught nor studied in the Scottish system, is that there is nothing out of the ordinary with this paper. There is a lot to do in just 75 minutes – for 12 questions that’s just over 6 minutes a question. I don’t like examinations that are speed tests.

That said, the questions look well structured and the “command words” are without exception on the list here. Some questions are easy and others harder: I think Question 12 is the most difficult, but I think that’s intentional – to stretch the stronger students. The only thing I would quibble with is the wording of 11(a) (ii):

The second sentence is redundant. How can one possibly “explain why” without giving “a reason”? The reason is basically that the quadratic remaining after you have taken out the factor (x+2) does not factorize.

I looked at the 2025 Paper 1 and it seems a similar level, though the questions are phrased in a terser fashion. Here it is for reference:

NH_Mathematics_Paper1-Non-calculator_2025Download

There may well be context that I’m missing, however, so I’d welcome comments on the diffculty and/or fairness through the box below.

#Examinations #HigherMathematics #mathematics #ScottishHighers

Measure And Derivative A Unified Approach by G.E. Shilov; B.L. Gurevich

This volume is intended as a textbook for students of
mathematics and physics, at the graduate or advanced
undergraduate level. It should also be intelligible to
readers with a good background in advanced calculus
and sufficient “mathematical maturity.”
The phrase “unified approach” in the title of the book
refers to the consistent use of the Daniell scheme, which
starts from the concept of an elementary integral defined
(axiomatically) on a family of elementary functions. In
the Introduction we explain in detail why we prefer
this approach to others, in particular to the Lebesgue-
Radon-Frechet approach, which starts from axiomatic
measure theory.

Revised English Edition
Translated and Edited by Richard A. Silverman

You can get the book here and here.

#1966 #derivative #higherMathematics #integral #lebesgueIntegral #LeviSTheorem #mathematics #measureTheory #physics #RiemannIntegral #sovietLiterature #StieltjesIntegral #theoryOfIntegral

The 2025 Leaving Certificate Mathematics Papers

As I mentioned a few days ago, examinations for the 2025 school Leaving Certificate are under way. One of the interesting things about the Irish system is that the examination papers are put up online immediately after the examinations. Students took their first paper in Mathematics (either Ordinary or Higher level) on Friday (yesterday), and there has been some reaction.

Anyway, I thought I’d share the papers here so you can see what you think. Paper 2 is on Monday 9th June, so I’ll add those papers then.

LC003GLP100EVDownload LC003ALP100EVDownload

They look reasonable to me. The thing that strikes me about them is that they are much more structured than the A-level mathematics examinations I took way back in 1981.

Comments are welcome through the box below.

Update: As promised here are the Papers 2:

LC003GLP200EVDownload LC003ALP200EVDownload

Reaction to Paper 2 of Higher Mathematics is that it was more challenging than Paper 1.

#HigherMathematics #LeavingCertificate #mathematics

2015-2021 A/L Higher Mathematics past papers in pdf
#HigherMathematics
#PastPapers
#ExamsReminder

Visit our website to learn more
https://www.examsreminder.com/2022/03/al-higher-mathematics-past-papers.html

2015-2021 A/L Higher Mathematics past papers

Download 2015-2021 A/L Higher Mathematics past papers in pdf for free, higher mathematics past papers and marking scheme, Higher Mathematics papers