Leaving Cert applied maths: mix of old and new as final exams draw to a close

Despite a few curveballs there was little overall deviation from past papers

Today's higher-level applied maths paper contained generous questions based on new syllabus material. Photograph: Dara Mac Dónaill

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The higher-level applied maths paper contained generous questions based on new syllabus material, with a few curveballs in questions based on the old syllabus.

The paper was the last in this year’s Leaving Certificate, which has now concluded.

Brendan Williamson, an applied maths teacher at the Institute of Education, said that there was minimal deviation from past papers, in particular the June and deferred 2023 papers.

“Opening the paper, students will be relieved to see a question that could have been plucked from their textbooks,” he said.


“Question one 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 it as a curveball, but the underlying ideas were conventional.

“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.”

Mr Williamson said that question three required 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’,” he added.

“They would not do this in later questions, so the clarity is appreciated here.

“Question five (a) was completely typical but again offset by a part (b) that was algebra heavy and messy, so students might tie themselves in knots with unknowns.

“Question six 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.

“Question seven was reminiscent of the old course and could have appeared on any exam in the last ten years. A question 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,” Mr Williamson said.

“Question eight (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’.

“And question ten was unusual in that project scheduling was not a whole question, but ultimately this would pose little challenge to the students.”

Overall, Mr Williamson said, students would not be too thrown by the paper.

“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,” he said.