Leaving Cert maths paper 2: ‘More challenging’ than first paper

The second higher-level maths paper was more challenging for students than paper one, with another surprising no-show for financial maths on both the ordinary and higher paper, teachers have said.

"Today's higher level maths paper two was definitely more tasking than paper one," said Studyclix.ie expert teacher Alan Boal of Royal and Prior Comprehensive School in Raphoe, Co Donegal. "A thorough competency of probability and statistics was required especially as they made up half of the long questions. Trigonometry made up the remaining half of the long questions with the students' favourite of trigonometric graphs thrown in for good measure."

Eamonn Toland, founder of TheMathsTutor.ie, agreed that students will have found a trigonometry-heavy paper two more challenging.

“Section A was particularly challenging and the probability Question 1 about picking players for a soccer team may have confused some students,” he said. “There was a lot of emphasis on giving proofs. The geometric proof question (6) had a difficult part (b). On the other hand there were some relatively straightforward coordinate geometry questions. Section B was more forgiving and students that knew their trigonometry would have scored well here.”

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Aidan Roantree, senior maths teacher at the Institute of Education in Dublin, said that there were some isolated tricky parts, but students had enough choice to avoid questions they were not comfortable with. "With the choice available to them this year, students could have avoided probability and statistics altogether," he said.

Mr Toland said that the ordinary level paper was accessible overall. “But it was a little more challenging in places for students, especially if they had omitted coordinate geometry from their revision plans. Students who knew their basic concepts would have scored well as any contextual questions didn’t disguise the required mathematics in any complicated way. Financial maths has once again failed to feature in Paper 1 or Paper 2, which many teachers and students will find disappointing.”

Jean Kelly, a maths teacher at the Institute of Education in Dublin, said that the ordinary level questions were clear and precise. "There was enough scaffolding to walk students clearly through each part of each question. For the first time ever there was a long question on coordinate geometry of the line."

Mr Toland said that both higher and ordinary level students had a greater choice of questions this year and only had to complete six questions instead of the usual nine. “Some of the questions were a little longer than those set in previous years, while others were of a similar length. The overall effect was that students would have benefitted from quite a bit of extra time to complete each question.”

Try this at home: Leaving Cert maths paper 2

In a particular population 15 per cent of the people are left footed. A soccer team of 11 players, including 1 goalkeeper, is picked at random from the population. (a) Find the probability that there is exactly one left footed player on the team. Give your answer correct to three decimal places.

(b) Find the probability that less than three players on the team are left footed. Give your answer correct to two decimal places.

(c) The goalkeeper is left footed. Find the probability that at least eight of the remainder of the team are right footed. Give your answer correct to two decimal places.