Leaving Cert applied maths: New topics may have thrown some students

Students may have been thrown by new topics on the higher-level applied maths paper but there was also a good mix of the familiar.

Brendan Williamson, an applied mathematics teacher at the Institute of Education, said that question one, which focused on standard adjacency matrices was a nice, familiar introduction.

“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,” said Mr Williamson.

“This gentle start is instantly contrasted with a very tricky question two 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.

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“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. ”

Connected particles

Questions three and five, on connected particles, are often favoured by students looking for relatively easy marks, but the part (b)s in both these questions fell outside the norm, said Mr Williamson.

“Rather than allowing any choice, Q3(b) required students to use Prim’s algorithm, and it presented the information in a matrix, which has never happened on the paper before,” he said.

“Question 5 (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.”

There may have been disappointment for students here, he said.

“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.

Dynamic programming

Question six was 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,” said Mr Williamson.

“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 be standardised, so some may really struggle.

“This issue also arose in question 9(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.”

Projectiles

Question seven, which looked at projectiles that bounce, has not appeared as a topic since 2006 – but the concepts have been a key component of exams for years.

“Since the removal of inclines from the syllabus, students reviewing the relevant past papers will overlook this topic since the two often appeared together,” said Mr Williamson.

“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.”

Despite these challenges, Mr Williamson said that there were straightforward options, particularly in question 9(b) and question 10.

“If a student read through all 10 questions before selecting their favourite eight, they will realise that the end of the paper was good enough to offset some of the trickier elements in the middle,” Mr Williamson concluded.

The applied maths exam was scheduled at the same time as the religious education exam, and the Leaving Certificate 2025 is now formally over.