by Aisling Kenny
The 2026 Leaving Certificate Higher Level Mathematics Paper 1 was a fair, balanced, and accessible examination. Overall, students were very pleased with the paper, particularly with Section A, which contained familiar topics and straightforward questions that allowed candidates to build confidence early on.
Question 1 opened with basic algebraic techniques, providing an approachable start and helping students settle into the examination. Question 2 featured a recurring decimal expressed as a fraction, a topic that has not appeared for some time, alongside some straightforward financial mathematics. Question 3 consisted of a combination of differentiation and integration, covering standard applications of both topics.
In Question 4, parts (a) and (b) involved typical complex number problems. Part (c), however, offered a slightly different challenge, requiring students to determine a possible set of numbers that satisfied given conditions. Question 5 was relatively routine, featuring elementary set theory and a straightforward logarithms question. Question 6 included a proof by induction involving inequalities, a factorial equation, and, in part (c), required students to construct a geometric sequence that met specified conditions. Overall, Section A was both accessible and student-friendly.
Section B produced more challenges than Section A. Question 7 centred on a volume function and included standard differentiation techniques, as well as a typical rates-of-change problem. Question 8 focused on exponential functions, while Question 9 examined sequences and series. Although both questions were relatively lengthy and wordy, the mathematical content was approachable, and students generally responded positively to them.
Question 10 assessed students’ understanding of functions and derivatives in a more innovative and less conventional manner. While it required careful thought, it remained fair and allowed well-prepared students to demonstrate a strong understanding of the topic.
In conclusion, this was a well-constructed paper that struck an effective balance between accessibility and challenge. Students generally left the examination feeling satisfied with their performance, though they found itex long and challenging.
