Leaving Cert maths paper 2: Students seeking H1s or H2s find paper particularly challenging

Higher-level maths students who were anxious about their performance in paper one did not find comfort in paper two, but ordinary-level students will be pleased, teachers have said.

Aidan Roantree, a maths teacher at the Institute of Education, said that students looking for H1s and H2s will have found the paper particularly challenging, especially towards the end.

“The paper continued the same mixture of the familiar and the quirky, but on a larger scale with more of both,” he said.

“The question setter is consciously creating papers that are unlike previous years by adding novel questions that would have been hard to prepare for,” Mr Roantree said.

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“Upon opening the paper, students will have felt an initial confidence boost to get them going. Section A’s Q1, Q, 2, Q3 offered a reassuring and familiar start to the paper. This will have allowed students to accrue marks before venturing into the trickier sections.

“At Q4, the quirkier aspects of the paper emerged with questions that were evocative of pre-2015 statistics: interquartile ranges, averages, and later stratified sampling in Q10.

Section B followed a similar pattern with approachable opening questions followed by mounting difficulty.

In particular, Q9’s part C was a very challenging probability question which would have tested the abilities of even the highest achievers.

“Indeed this paper contained some of the hardest questions on either paper, so students will leave the exam with a sense of having really pushed themselves,” Mr Roantree said.

Niall Duddy, ASTI subject representative for maths and a teacher at Presentation College Athenry in Co Galway, agreed that higher-level paper two was more testing than paper one.

“But students didn’t say they couldn’t do it, and paper two is traditionally the trickier of the two,” he said.

“On the plus side, it was user-friendly and contained hints here and there, such as where to use sine and cosine.

“The topics were quite focused, except for the trigonometry question which included some algebra; this is part of a recent trend of amalgamating the topics on the papers.

“Questions on statistics and probability would be familiar. Some students didn’t like the look of question eight, which included a 3-D problem, but the question itself wasn’t unusual.

“Overall, my students felt that while it was trickier, it was doable.”

Similarly, Stephen Begley, head of maths at Dundalk Grammar School, Co. Louth and a Studyclix subject expert was more upbeat about the higher level paper.

He described it as “a very fair and decent paper, though it did have some curve balls to get students thinking”.

While the higher level will always contain some challenge, Mr Begley said the questions did not mix topics, and provided good guidance and direction to students on how to start their answers.

“Those who prepared for a typical paper 2 would have been content with this paper which enabled students to showcase their knowledge of the usual core topics in a range of questions. Whilst not without challenging parts of course, the examiner was generous with their questioning style which contained clear instruction and even provided formulas or methods at times,” he said.

“As a tale of two halves, the two maths papers were well balanced in terms of difficulty, with neither being dominated by challenge. All in all, it’s been a pretty good, fair, and accessible set of exams for Leaving Cert higher level maths students in 2025.”

Ordinary level

On the ordinary-level exam, Jean Kelly, a maths teacher at the Institute of Education, said that students who felt uncertain about their performance on paper one will have been relieved.

“Gone are the questions that jump around topics or hide aspects behind the language of the question,” she said.

“The paper was snappy, cutting right to the point and unified in the topics examined. Question one was focused on statistics, Q2 on trigonometry, Q3 on the circle. This helped students stay focused on the task and feel like they are being helpfully scaffolded as the questions got harder. This feeling of momentum will help them get through the paper and feel much more assured in their performance.”

The paper was heavy on statistics, probability and trigonometry, with area and volume having a lesser presence than in previous years, which was likely due to a surprise appearance on paper one, Ms Kelly said.

“While there were enough challenging pieces on the paper to distinguish those striving for the O1, even those who struggle to pass will find themselves in a good position,” she said.

“The paper was often helpful, either through tips or by combining topics into a useful grouping. For example, the appearance of constructions in section B was new, but the helpful pairing of dilations and area and volume helped ease students through the material.

“While paper one needed students to constantly, even anxiously reread the questions, there was a nice snappiness to this paper. Students who had the fundamentals were able to quickly get their marks without fuss and frustration,” said Ms Kelly.

Mr Duddy said the ordinary-level topics were laid out clearly and that the paper was user-friendly with lots of helpful hints.

Similarly, Mr Begley said the ordinary level paper presented a “very typical and manageable” set of questions spanning the usual suspects of trigonometry, coordinate geometry, statistics, probability and area and volume.

“Whilst the tail end of questions were not without their stings, the opening parts provided good space for students to gather marks,” he said. “Overall, students could play to their strengths topic wise in this rather fair and approachable Paper 2.”