Institute of Education Study Notes

Friday, 22nd February, 2019

Academic Zone

Maths Paper 1 (H): A paper dominated by sequences and series

Reaction to Leaving Cert 2018 Maths Paper 1 (Higher Level) by Aidan Roantree, Senior Maths teacher at The Institute of Education.

A nice paper but challenging in a few places. This year’s higher level Maths Paper 1 was dominated by sequences and series, although algebra and calculus were also prominent. The sequences and series questions in particular were interesting, unusual and at first glance off putting, However, on investigation they turning into lovely questions. A students who entered the exam expecting to see familiar phraseology and wording everywhere would have been disappointed with these questions. However, those willing to investigate would have been rewarded.

Section A:

Question 1 was a very nice opener on aspects of algebra.

Question 2 continued the theme of algebra but combined it with sequences and series, but in a most creative way.

Question 3 was on calculus. This was a very doable question, once students realised that calculus was what was required.

As usual there was one question on complex numbers and this was Question 4. The much tipped Proof of De Moivre’s theorem appeared in Part A, and using it to calculate a power was Part B.

Question 5 was the second question to contain sequences and theories. Part A was a wonderfully clever, completely new problem for students who were willing to explore. A Recursion formula made an appearance in Part B, leading to a cyclic or periodic sequence. Although relatively easy, it would not suit students who had just learnt off formula.

Question 6 was an interesting mix of algebra, functions and calculus, but was very manageable.

Section B:

Question 7 returned to the topic much examined last year of natural log or exponential functions. The first couple of parts dealt with algebra. The next couple referred to graphs and finally there were parts on calculus, a by now very common mix.

Question 8 was the short question in Section B and revolved around the standard normal curve, or Gaussian Curve, with which students would be familiar from statistics. The approach this time however involved calculus and was set at a nice level.

The other long question in Section B was the third question to involve sequences and series. This originated from a sequence of patterns leading to a couple of geometric series. It was slightly challenging, but a very well-constructed question. The final Part D will separate those who will get a H1 from the rest.

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Aidan Roantree

About Aidan Roantree

Aidan Roantree is senior maths teacher at The Institute of Education, where he has been teaching maths and applied maths for 25 years. The author of 12 major maths books, Aidan is currently putting the finishing touches to a new series of text books, covering the new Project Maths syllabus.

View all posts by Aidan Roantree →

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