Applied Mathematics (H): A Paper That Mixes The Familiar With Challenging Curveballs

Leaving Certificate Applied Mathematics (H) Review

Reaction to 2024 Leaving Certificate Applied Mathematics (Higher Level) by Brendan Williamson, Applied Mathematics teacher at The Institute of Education.


  • Generous questions on new syllabus material but a few curveballs in questions based on the old syllabus. 
  • Minimal deviation from past papers, in particular the June and deferred 2023 papers. 

Opening the paper, students will be relieved to meet a question that could have been plucked from their textbooks. Question 1 was clear without any awkward spikes to worry about. Part (b) was nearly identical to the 2023 paper including part (ii) which tried to present as a curveball, but the underlying ideas were conventional. Part (c) on linear motion was more numerical than algebraic and so students will have been pleased as they ventured further into the exam. The first twist arrives in Q2, which is an ‘outside the box’ question. Students might struggle with part (a)(i)’s forces with a static hitch or the concept heavy (a)(ii). The algebra in the latter was straightforward but students needed to do some careful thinking before they could tackle it. This was balanced with a very nice part (b), a pulley question typical of previous papers.  

Question 3 (a) required the students to apply integration by parts to a rather contrived example, but thankfully the question removed any ambiguity in the desired method by clearly stipulating “by parts”. They would not do this in later questions, so the clarity is appreciated here. Part (b) was a standard question on an oblique collision with nicer numbers than usual. The second part of the (b) would be laborious for those only familiar with the old syllabus, but rather quick for those using the more modern course concepts. Question 4 was a collection of very approachable individual steps, first in circular motion and then differential equation but the act of collecting them under one umbrella scenario was unusual and potentially worrying for some.  

Question 5 (a) was completely typical but again offset by a (b) that was algebra heavy and messy so students might tie themselves in knots with unknowns. Question 6 was standard, and a good example of questions seen on both the June and deferred sittings in 2023. With such a new course, the deferred paper is an essential resource and students who went through it carefully will find this familiar. In contrast Q7 was reminiscent of the old course and could have appeared on any exam in the last 10 years. Interestingly, (b) on circular motion caused by friction has not appeared since 2006 and so would throw students focusing too much on past exam questions and not enough on covering the syllabus. 

Question8 (a) will have caused a moment of pause and concern from many as it requires the students to use “Bellman’s principle of Optimality”, but most will know this as “dynamic programming”. A student could work it out from the application and context, but most will be thrown by the odd choice of name. Interestingly, this question also contained the first appearance of students being asked to show understanding rather than application of concepts with relation to Bellman and Dijkstra. 

Question 9 shows that a definitive trend is emerging in how they examine second-order homogeneous and inhomogeneous equations. While this is only the third paper of the new syllabus, it is also the third appearance of this particular style of question. Finally, Question 10 was unusual in that project scheduling was not a whole question but ultimately this would pose little challenge to the students. The (b) of the question was not a carbon copy of previous years but the novelty was only surface level. The core mathematical ideas were well-worn for anyone who knew what was being asked. 

While there are definite challenges here, there is also enough choice and familiar questions that students should be able to fairly reflect their abilities with Applied Maths.