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

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 鈥榦utside the box鈥� question. Students might struggle with part (a)(i)鈥檚 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.听听

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 鈥渂y parts鈥�. 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.听听

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.听

Question8 (a) will have caused a moment of pause and concern from many as it requires the students to use 鈥淏ellman鈥檚 principle of Optimality鈥�, but most will know this as 鈥渄ynamic programming鈥�. 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.听

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.听

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.听

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• A new syllabus combining elements of the old and new course in a way that required students to know the full breadth of the course.
• Some questions were very similar to the sample paper, while others offered new and unexpected twists.

This was the first year of the new Applied Maths syllabus which not only changed the topics covered but the way students approached revision and the composition of questions. Students could no longer focus on only a handful of topics at the expense of the rest, assured that that would be sufficient. The modern paper mixes topics together in way that requires a strong grasp of all elements.

Question 1 offered a nice introduction to the paper. It bore a similarity to the sample paper and the instructions were generous in their clarity 鈥� being told to use integration by parts is a useful piece of guidance. Question 2 started with Dijkstra鈥檚 algorithm, which is a rather standard and expected element of the course. The underlying mechanics of the question was clear and familiar, but students would likely have preferred fewer points and smaller numbers for ease. As it stands, the questions were manageable but time-consuming, a trait that would be found elsewhere on the paper. Part (b) on collisions was reminiscent of questions from the old syllabus but trimmed to accommodate the modern timing of the exam.

Question 3 was a tough question and will likely be skipped by most students. It drew on a topic from the old syllabus (circular motion) but the particulars of the question were novel and complicated the matter, such that a generally unpopular topic became even more unpalatable. Question 4 looked like it might follow suit, with its mention of 鈥渂uoyancy鈥� evoking the topic of hydrostatics. However, this was a vocabulary issue rather than a mathematical one, so anyone breaking down the question鈥檚 information would be able to parse out the core concepts. While Question 3鈥檚 circular motion was off putting, the linear motion of Question 4(b) was particularly manageable but arithmetic heavy, again requiring students to mechanistically work through the task.

The final half of the paper was a fine balance of familiarity and challenge. Questions 6 and 9 were very similar to the sample papers, so students who had worked on them will likely be relieved. The former question asked about second order inhomogeneous difference equations, which might cause some moments of pause but, as with every challenge on this paper, when considered as part of an ensemble shouldn鈥檛 cause much trouble.

Pleasingly, Question 7 offered students the choice between Prim or Kruskal鈥檚 algorithm. The later stages of the question offered a curveball that might have spooked some, as it required a more common sense approach than strictly methodological approach. Students wondering where dot products would make their debut found them in Question 8 on projectiles (not the anticipated collisions). What was expected was the first order difference equation of Question 10. The latter part of this question saw a return to circular motion and, while the algebra may have spooked students, the mechanics of this question were similar to those in previous years, unlike its counterpart in Question 3.

Overall, this was a fair but challenging paper that fused material into a new way of examining Applied Maths. Students would have found some questions much more time-consuming than others and the consideration of which questions to answer was much more involved than previous years. There were lots of opportunities for students to earn marks, in particular for those aiming for the H3/4 will find lots on the table. The top scorers will be those who could draw on the full range of the course.

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In 1998, Oliver was the first winner of the Victor Graham Perpetual Trophy for achievement in Applied Mathematics, awarded by the 91制片厂 for Numerical and Computational Analysis. In 2005, he was appointed as the first Chairman of the newly-formed Irish Applied Maths Teachers鈥� Association (IAMTA). So, As you can see, Oliver is highly regarded for his Applied Maths work and we look forward to seeing his book in classrooms across the country.

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