Reaction to 2025 Leaving Certificate Applied Mathematics (Higher Level) by Brendan Williamson, Applied Mathematics teacher at The Institute of Education.
- Topics making their debuts will throw some, but the calm students would be able to navigate effectively.
As is typical of the Applied Math exam, Question 1 was a nice introduction. It was a standard adjacency matrices question which will be familiar to everyone. While the mention of “period of a particle” in part (a) might throw some students, most will have been able to approach the circular motion question. This gentle start is instantly contrasted with a very tricky Question 2 on differential equations. This question deviated from the normal by being both fully on a single topic and requiring students to reproduce a particularly challenging proof. Indeed, the later sections of the question contained an oddly subtle shift in how gravity is handled that will put some out. While the nuts and bolts of the mathematics were fine, the overall approach would certainly have deterred many.
For most students they will be drawn to the much nicer Questions 3 and 5 on connected particles, an area often favoured by students looking for relatively easy marks. The Part (b)s in both these questions fall outside the norm though. Rather than allowing any choice, Q3(b) required students to use Prim’s algorithm and presented the information in a matrix, which has never happened on the paper before. Q5 (b) was peculiar in the purity of its mathematics – normally the Applied Maths exam structures the questions around real world scenarios but this question on abstract vectors was simple and straight to the point. While students should be aware that not every topic gets examined the absence of project scheduling, a major part of the course and typically one full question, will have been both jarring and disappointing.
The most striking moment for many students will have been Q6 on dynamic programming, a new addition to the course. This topic has four elements that can be examined but unfortunately the hardest aspect, equipment replacement and maintenance, appeared. Since this has only been part of the course since 2022, the most effective manner in which teachers and students should approach it is yet to standardized, so some may really struggle. This issue also arose in Q9(a) as the necessary depth of a student’s grasp of displacement time graphs and the amount of class time to allocate was not previously clear. Both of these questions will provide helpful insights for teachers in future years but for the current cadre in the exam hall they will be disquieting.
Teacher insight and guidance really was crucial for this exam, none more so than in Q7(b) on projectiles that bounce. A question exactly like this has not appeared since 2006 but the concepts has been a key component of exams for years. However since the removal of inclines from the syllabus, students reviewing the relevant past papers will overlook this topic since the two often appeared together. A good teacher would have been sure to reintegrate the bounce calculations back into the course, but a student who was focused on past papers alone will find themselves worried.
But the paper was not entirely challenging and contained many palette cleansers for those who kept calm and remembered their training. Q9 (b) and Q10 were nice and straightforward, as if copied and pasted from previous exams. If a student read through all 10 questions before selecting their favourite 8 they will realise that the end of the paper was good enough to offset some of the trickier elements in the middle.