Leaving Cert maths paper two: ‘overwhelmingly positive’ response from students

Students were pleased to find there were “no gremlins” to trip them up in Monday’s Leaving Cert higher level maths paper two, according to teachers.

“The consensus was overwhelmingly positive,” said Niall Duddy, maths teacher at Presentation College, Athenry and subject representative for the Association of Secondary Teachers Ireland (ASTI).

He said there were little hints thrown into questions, which meant it was very “user-friendly.”

“Any fears students had ahead of this paper this morning were completely unfounded. They were fearful about Monday considering Friday was so good – they thought it might be a reverse of last year but that didn’t turn out to be the way at all.

“Of course, there was the usual sting in the tail at the end of each question, which is what you would expect anyway,” he said.

Brian Scully, maths teacher at the Institute of Education, said the higher level paper was “an accessible sibling to paper one” with a “few novel moments to distinguish those confident in different contexts”.

Overall, he said there was a good mixture of questions that gradually increased the challenge of the paper.

There was a similar reaction from Stephen Begley, head of maths at Dundalk Grammar School and a subject expert with Studyclix, though he said section B of the paper was more challenging.

“Students would have found today’s paper two busier than Friday’s Paper one – but fair and doable,” he said.

Begley said many will have found the short questions in section A very standard and reasonable, while section B’s long questions put students through their paces.

“Looking at topics covered the regular features of statistics, probability, trigonometry, geometry, the circle and the line dominated the short questions, while longer questions were based on statistics, probability, the circle, geometry and trigonometry,” he said.

Begley said students would have been comfortable working through the short questions, while long questions required some careful reading and thinking.

“The opening question to the paper replicated a Junior Cycle style question on statistics and would have eased some nerves,” he said.

“Some standard probability questions followed in question 2, while no curve balls were thrown in trigonometry on question 3. For those who studied their constructions and proofs would have been delighted with a direct question 4, and the coordinate geometry questions on the line and the circle were rather decent and approachable.”

Scully also said the first question on stem leaf plots would have been familiar and recognisable as it drew from well-established material with the addition of unknown variables.

“The challenge was on the mechanical execution, not the comprehension. For example question 4 was a pure examination of curricular material rather than a test of its application,” Scully said.

“Later questions migrated to distinctly higher level-only concepts, but the progression was logical and offered the opportunity for those students striving for H2s and H1s to distinguish themselves.”

A trend that carried over from paper one, he says, was the mixing of topics.

“Many questions tested the mental agility of students as they bridged numerous aspects of the course: sometimes overtly, sometimes subtly,” he said.

“For example, probability appeared in many questions, frequently alongside a different topic. Most of the challenges posed in these questions would be reflective of term time preparations.”

Areas consistently perceived as challenging by students, like the notation and language of sets, were demanding in a manner that was familiar, he added.

“As such there were no additional gremlins thrown into this paper to upset the students or take this paper away from their expectations formed over their years of study,” Scully said.

The more challenging elements appeared in the less familiar moments.

Scully said the “ambiguous appearance of the sine rule and a novel question 9 might have worried some.”

The latter contained a unique diagram that required creative thinking and excellent understanding as it forced students to execute concepts in a context they will never have seen before.

“Yet, it was a trend that once students were brave enough to take that initial step into the question, their practice was rewarded by an emphasis on execution of concepts. Even the text heavy Question 10 was fair once you moved beyond the off-putting first impression.”

Begley agreed that the pace and intensity of the exam picked up in section B, where some “tricky bits were included to challenge students”.

“Question 7 on statistics and probability would have delighted many being similar in style to previous years. Question 8 put students through their paces for volume and geometry with a hint of calculus at the end, parts of which students may have found tricky. Questions were well prompted and if a student didn’t get one part it didn’t mean they were not able to tackle or complete subsequent parts,” he said.

Question 9, which was all about the circle and the line, required a “fair bit of careful thinking and application of their knowledge” he said.

“Really reading the questions, understanding the situation and visualising the scenarios was needed here,” he said.

“Closing the exam, Question 10 appeared with a rather busy and text loaded diagram and passage, but if students carefully read each question, it boiled down to a decent trigonometry question with some permutations at the end. Once again if a students could not complete one part to the question it did not disadvantage them in subsequent parts.”

Overall, he said the consensus was that section A was “quite nice”, while Section B was more challenging.

“At higher level we can expect some challenges and paper two had its fair and balanced amount of them,” he said.

“Overall, students should take comfort in the rather nice paper one from Friday alongside today’s paper and overall might agree that it was a fair, doable and approachable pair of exams.”

Niall Duddy said the consensus among students was that the final part of question 10 posed challenges.

“It was about a company making windscreen wipers, [had] a little bit at the end on traffic lights, which is probability and statistics, and given there was such an emphasis on trigonometry and geometry, it was a little sting thrown in at the end,” he said.

Overall, however, he said students were happy and very positive.

Ordinary level

The ordinary level maths paper, meanwhile, was “accessible” with no surprises, according to teachers.

Robert Chaney, maths teacher with Presentation Secondary School, Kilkenny, said there were “plenty of hints and scaffolded questions to lead the candidates”.

It was not without its challenge, though.

“There was a lot of probability which I suspect [some] candidates would have grumbled about. Probability is a topic many students just don’t like. Looking through the questions they were all very accessible apart from maybe one question or a part of the question (Q2) that would have stumped a lot of students,” said Chaney, a subject representative for the ASTI.

“It was about a pack of cards and the idea of picking cards and taking one card out, not putting it back in, taking another card out and working out the probability of that card being of a different colour and number. I would suspect that most students would have found it hard.”

He said the rest of the paper was “all very standard”.

“There was nothing that was significantly problematic in my opinion. A well-prepared student would have had no difficulty with this paper,” he said.

“There were a lot of instances where they told the student what to do, such as ‘use the theorem of Pythagoras to find …’ or ‘use the cosine rule to work out …’

“They were textbook questions. There was nothing that was in a format that was problematic for the students and there was no context that would have thrown the students.”

Jean Kelly, a maths teacher with the Institute of Education, said most students will feel their work paid off after an ordinary level paper with n

She said the questions drew from well-worn material that students will have covered countless times in the run up to their examinations.

Kelly said there were questions asked on “everything”, even the rarely-seen sets, which made its third appearance in 14 years.

“Despite the breadth of the material, the questions were snappy and neatly itemised so students could deal with each bit individually,” she said.

“While some parts were heavy in statistics and probability, students will be relieved that their archnemesis trigonometry made only a quick appearance.

Overall, she said the students sitting this paper knew exactly what they were being asked to do and should have left with a clear appraisal of how they performed, with many happy that they have secured what they need for their courses.

“All in all, a good resolution to their time with Leaving Cert ordinary level maths,” she said.

Stephen Begley, head of maths at Dundalk Grammar School and Studyclix subject expert, agreed that paper two was “welcoming, fair and doable paper for students”.

“Most students seemed quite content on leaving the exam hall on what was a candid exam at ordinary level,” he said.

“Most questions were presented that the opening parts of each were very doable, while later parts provided challenge. Given the choice afforded by post-pandemic arrangements, students would have been able to play to their strengths answering four of the five short questions and three of the four long questions, a certain advantage to students.”

“The paper closed with a volume question with a touch of converting units at the start. Students would have found this a very approachable and workable question given the formulas provided in their log tables.”

Overall, he said it was quite a “nice, fair and doable” [aper two for Leaving Cert ordinary level students.

“It really was a candid snapshot of what is covered on the course and I feel it had an excellent balance of accessibility and challenge for students,” Begley said.