Pupils were relieved to encounter “no pitfalls” during Monday’s higher level maths Leaving Cert paper two, teachers have reported.
Niall Duddy, a maths instructor at Presentation College, Athenry and a subject representative for the Association of Secondary Teachers Ireland (ASTI), stated that the response was overwhelmingly favourable. He pointed out that the questions included small tips, making it quite “user-friendly”.
“Any concerns the students had about this paper this morning turned out to be entirely baseless. They were worried about Monday since Friday went so well – they thought it might be a repeat of last year but that wasn’t the case at all. He further added that as expected, the challenging part of each question was usually at the end.
Brian Scully, a maths teacher at the Institute of Education, characterised the higher level paper as “an open companion to paper one” with “a few unpredictable moments to differentiate those confident in varying scenarios”. He expressed that the paper had a balanced assortment of questions, gradually escalating in difficulty.
Similar feedback was given by Stephen Begley, head of maths at Dundalk Grammar School and subject expert with Studyclix, who did mention that the paper’s section B was more difficult.
“Students would have found today’s paper two denser than Friday’s paper one – but manageable and equitable,” Begley stated. He highlighted that many students found the short questions in section A to be usual and fair while the lengthy questions in section B put the students to the test.
“Regular topics such as statistics, probability, trigonometry, geometry, the circle, and the line dominated the short questions, whereas lengthy questions revolved around statistics, probability, the circle, geometry, and trigonometry,” he added.
Begley pointed out that while students would have been at ease working through the short questions, the long ones needed careful reading and contemplation.
“The initial question of the paper, replicating a Junior Cycle style question on statistics, would have assuaged some anxieties,” Begley noted. “Standard probability questions came next in question 2, while no surprises were presented in trigonometry on question 3. Students who had thoroughly studied their constructions and proofs would have been satisfied with a straightforward question 4, while the coordinate geometry questions concerning the line and the circle were pretty reasonable and approachable.”
Scully mentioned that the preliminary question on the stem leaf diagrams would have been widely identifiable since it was based on well-trodden material, augmented by unfamiliar components. He noted that the difficulty lay in the technical delivery rather than understanding the material itself. The fourth question, for instance, served as a pure examination of curriculum content rather than testing its application.
Subsequent questions transitioned to concepts aimed specifically at higher level thinking. Still, the sequence of questions was rational and provided an opportunity for those students aiming for high grades to excel. The blend of different topics characterises another trend that carried on from the first paper, according to Scully.
He went on to say that many questions were designed to test students’ cognitive flexibility, linking various components of the course in an evident or subtle way. He pointed out that probability featured in many queries, often alongside a different subject. He suggested that most of the challenges presented in these questions mirror the preparation students undergo during the term.
Topics deemed consistently difficult by students, such as sets notation and language, proved to be challenging in a recognisable way. Consequently, he asserted, there were no extra pitfalls in this paper that could unbalance students or deviate from the predictions they have made over their years of study.
According to Scully, the more critical challenges emerged in unfamiliar scenarios. He flagged that the vague presence of the sine rule and an original question might have caused some concern. The latter encompassed a one-of-a-kind diagram that demanded inventive thought and superior comprehension, obliging students to implement concepts they had never seen before.
Nonetheless, he noted, the trend was that as soon as students had the courage to plunge into the question, their effort was rewarded by focusing on the implementation of ideas. He added that the wordy question 10 was reasonable once students got past the initial intimidating impression.
Begley concurred that the exam’s pace and difficulty escalated in section B, containing some complex points designed to test students. He stated that question 7 on data and probability would have been a delight for many, as it was akin to styles seen in previous years. He concluded that question 8 challenged students with volume and geometry tasks, leading up to a touch of calculus at the end, some of which may have been tricky for students. He also noted that each query was adequately signposted, meaning that struggling with one aspect didn’t prevent students from attempting or finishing subsequent sections.
The ninth query in the exam paper, centred around the concepts of a circle and a line, necessitated a considerable amount of strategic contemplation and implementation of students’ understanding, according to the examiner. Students needed to pay close attention to every detail of the questions and grasp the scenarios.
In the examination’s conclusion, the tenth question emerged, laden with an intricate diagram and a detailed explanation. Nonetheless, the whole question essentially distilled down to a fairly straightforward task on trigonometry, featuring a few permutations at the conclusion. Should a student fall short of answering a portion of this question, it wouldn’t hinder them on the following segments, as per the examiner’s reports.
Broadly speaking, he found section A to be regarded as “quite nice”, while section B presented more of a challenge. The examiner noted that the prospect of challenges is expected at a higher level, and he believed that paper two offered a balanced number of such hurdles. Students should take solace in the comparatively pleasant first paper and today’s counterpart, enjoying the serene and manageable pair of tests.
Niall Duddy reported that students widely agreed that the final segment of the tenth problem brought some difficulties. That part was based on a windscreen wiper producing company and ended with a portion on traffic lights, pertaining to probability and statistics. Given the exam’s heavy focus on trigonometry and geometry, this last segment emerged as an unexpectedly sharp twist.
However, overall, he stated that the students seemed quite content and tremendously optimistic.
As for the ordinary level maths paper, teachers claimed that it was “accessible”, devoid of any surprising elements. Maths teacher Robert Chaney from Presentation Secondary School, Kilkenny, mentioned that there were “ample hints and scaffolded queries directing the candidates”. However, this did not mean the paper was without its fair share of difficulties.
Notably, a heavy focus on probability is a domain many students exhibit a dislike towards, which might have caused some candidates’ dissatisfaction. All things considered, the questions seemed quite attainable for the students, with possibly one or a part of a question (Q2), that could have potentially puzzled numerous students, according to Chaney, a subject representative for the ASTI.
The original text discussed a probability exercise involving a deck of cards where students picked and removed cards, determining the probability of drawing cards of unique colours and numbers. The assumption was made that this task could have been challenging for most pupils. However, the remainder of the examination paper was deemed average.
There was a consensus that the paper didn’t pose any significant problems. It was suggested that students who revised thoroughly wouldn’t have encountered any issues with the paper. The students were specifically directed in several places on how to utilise mathematical theories like Pythagoras or the cosine rule.
These were described as textbook questions with no unusual formats or contexts that could have confused the students. Jean Kelly, a mathematics teacher at the Institute of Education, opined that most pupils likely felt a sense of achievement after completing an ordinary level paper.
The questions were based on familiar topics that students would have revised repeatedly before the exams. Questions included a range of topics, even the rarely included sets, which had appeared for the third time in 14 years.
Even though the paper covered a wide range of topics, the questions were concise and neatly categorised, allowing students to tackle each part independently. While certain questions leaned heavily on statistics and probability, students were reportedly relieved that the ever-dreaded trigonometry only made a brief appearance.
In summary, Kelly believed that students who attempted this paper knew exactly what was expected of them. They should have emerged with a clear understanding of their performance, and many would be satisfied that they achieved the grades needed for their chosen courses.
Stephen Begley, head of maths at Dundalk Grammar School and a Studyclix subject expert, concurred that the second paper was a “cordial, fair, and manageable task for students”. He noted that many students seemed quite satisfied as they exited the exam hall, characterising the ordinary level exam as straightforward.
Begley commented that the initiation segments of most tasks posed were highly manageable, while the concluding parts offered a bit of a test. The flexibility offered by post-pandemic changes would have granted pupils the chance to exploit their aptitude, tackling four out of five minor queries and three out of four major ones, proving favourable to them.
He concluded by saying that the exam wrapped up with a volume-related task initiated by the conversion of units. With the equations provided in their logarithm tables, students would have deemed this task quite comprehensive and executable.
In summary, Begley stated that the second paper for Leaving Cert ordinary level pupils was generally “pleasing, just and manageable”. He added that it was a truthful representation of the course content, offering an ideal blend of simplicity and challenge for the students.