2014 Applied Maths paper: ‘disgraceful’ or simply ‘testing’?

Update: A number of students have taken the time to write a considered responses in the ‘Comments’ section below, so please take the time to read it to get a student’s perspective.

You might also want to look at the relevant page on the boards.ie site where there is an ongoing debate about the fairness of the exam.

The leaving cert Applied Maths syllabus is just one page long. For each topic it’s not at all clear how to prepare students properly other than by looking at past questions. Therefore when a paper comes out that varies considerably from the usual format, it’s not surprising that students end up struggling to deal with it.

This is exactly what happened in June 2013. And again in June 2014.

But maybe Applied Maths isn’t meant to be a subject where students rely on past papers as a guide. Perhaps it should an ‘anything is fair game to appear on the paper’ approach. If that’s the case the only people it will suit will be the elite students. In which case it completely goes against the DES promotion of STEM subjects in recent years.

The real killer punch here is that this is the second year in a row where the Exams Commission has produced a nasty paper. Once is (just about) understandable; twice is a disgrace.

Giving feedback on these papers is difficult.
First impressions can be quite deceptive; it’s only when you sit down to do out the questions that you get a feel for their true level of difficulty. It doesn’t help that Applied Maths is the last exam on the Leaving Cert and many teachers will no longer be in the school to meet the students in person to get immediate feedback. I personally didn’t realise how bad last year’s paper was until I gave it out as revision to this year’s sixth years after Christmas. It was a bit late then to make any complaints. I’m not going to make the same mistake twice.
Apparently there is a new person setting the paper and perhaps he wishes to ‘put his own stamp’ on the paper. That would be understandable, but if only if it was done very gradually. The change in the Applied Maths paper over the past two years has been anything but gradual.

It is not outside the bounds of possibility that one person has the power to kill this subject completely. The numbers taking the subject have always been quite low; many teachers are teaching it outside normal school hours to no more than two or three students. Others who are teaching it in a school timetable have perhaps ten students and while a school could allow for this ‘luxury’ in the past, the insidious increase in the pupil-teacher ratio over the last few years has resulted in schools being forced to withdraw the subject from the normal timetable.
My own numbers are normally between ten and fifteen. In the last couple of years I have made a big effort to promote the subject including running ‘taster classes’ during lunchtime and coming in to their normal maths classes. This year 24 students have signed up to take the subject in fifth year. I’m now going to speak to all of them in the first week and ask them to think very carefully about going ahead with the subject. From a personal point of view it’s nice to say that I have a full class of students, but I’m not going to play with their futures just to massage my ego. In the past I have told interested students that they don’t need to be a genius at Maths to do Applied Maths; I’m now going to have to roll back on that one also.

Over the past two years the paper has been referred to as ‘challenging for the brighter students’. This is surely a euphemism. If the top students found it difficult then the C/B students would find it nothing short of a disaster. And as a colleague reminded me recently, when reviewing these papers there’s no point looking at it from the perspective of the A student – chances are they’ll still come out with an A regardless. But for the average student the consequences are likely to be much worse. For example two of my students (one a C student, the other a B student) simply gave up half way through. It was their seventh subject and they realised that it was going to end up as their worst result by a long shot. I could never condone a student leaving an exam early, and certainly not the Leaving Cert exam, but these are both conscientious students and I understand completely their frustration. I have contact details for each student and their parents and have sent them all an email apologising for the paper. While I didn’t set the paper, and nobody would ever think of blaming me, I do somehow feel responsible; should I have seen this coming? Should I have warned them in advance? Should I have discussed worse-case scenario with them? I certainly will do all this next year – it’s just unfortunate that it will have been a year too late for this year’s cohort.

I will also need to speak to my sixth years at the beginning of the year. Many of them do eight subjects in fifth year and drop one at the beginning of sixth year. I’d love to tell them that this year’s exam was ridiculously difficult and that the Exam Commission would never make the mistake of doing this twice. The fact of course is that they just have done it twice. And it has coincided with a new guy setting the paper. And there’s no indication that it will be any different next year. And then I’ll get them to review the evidence for themselves. At this stage we would have 5 questions covered to Leaving Cert Higher Level standard. The students simply need to look at the questions over the past ten years and see how the questions in 2013 and 2014 compare. I may be wrong, but my guess is that it won’t be pretty.
Again, it would be very dishonest to try and keep them in my class just to play the numbers game. I’ve no doubt I’ll lose some of them as a result. I can only hope that the number of students who jump ship won’t be too great.

A few years ago we set up a discussion forum to help the many Applied Maths teachers who were working in almost complete isolation.
These are comments from three of those teachers (included with their permission):

Luckily I didn’t have a class doing the Applied Maths exam this year but this paper was an awful advertisement for students to do such a specialist subject. How many students would have got one full question correct or would have thought they got one correct?. Could the answers have been more uninspiring?

It was my first year teaching a highly motivated student applied maths in one year (repeat lc student). A massive effort was put in to preparing for the exam and my student is very diligent and hardworking. How is it then that she can get no reward when faced with a paper like that? In my opinion I thought it was a disgrace and my student came out visibly upset at the thought that her work throughout the year has gone to waste. Whilst the applied maths book is great it has no resemblance to 70 per cent of the questions asked in the 2014 paper. I’m raging to say the least.

I agree fully with the comments below. This was my first applied maths exam class and what a baptism of fire! I am very disappointed with the paper and my students were very upset with it. This negative reaction will filter through and our numbers will be adversely affected by this paper.

This was the report from The Irish Times:

Unfortunately for applied maths students, who were also sitting a morning paper, they were presented with a real challenge. “Strong students were really tested,” said Hilary Dorgan of the Institute of Education. “Students expecting a C grade may have left the exam thinking they had done very badly.”
The exam required a great deal of knowledge, aptitude, calmness and an ability to get through large amounts of data, according to Dorgan. The length of the paper may not have given students a chance to think about how to approach questions.

I don’t know Hilary Dorgan but his comments repeat what I alluded to earlier; if the strong students were really tested, how must the C grade students feel?

In contrast, this was the report in The Irish Examiner:

[The] subject spokesperson for the Association of Secondary Teachers Ireland (ASTI), said the higher level exam had some new features but the style and content were all welcome, with the opening question on linear motion featuring no underlying problems.

He said students might have been unnerved by the appearance of the more challenging elements in the first, rather than the second parts of questions on projectiles, particle dynamics and differential equations.

He said a question on collisions was set out in a way not seen before but students should have progressed well on it, and most should have been familiar with issues in a relative velocity question that looked very long at first.

I don’t know the ASTI spokesman either but it’s not likely that we’re going  to meet up anytime soon; we appear to inhabit different planets. Either that or he was guilty of the same offense as me – a quick browse through the paper giving the impression that it wasn’t too bad, whereas a more detailed analyses would reveal that it was anything but.




  1. An avid reader of your website who is extremely grateful for your in-depth tutorials, explanations, and solutions, I have, consistently, been an A1 student for the two year course, thanks to my wonderfully enthusiastic “Applied Mathematics” teacher in De La Salle College Waterford. Applied Mathematics was, and is, my favourite subject, the logical approach to the questions, the (clearly prior) consistency of the exam, the rewarding of a methodical approach over the correct mark, and the clear overlap of the Applied Mathematics course and the Physics course allow it to combine my love of Mathematics with my fervent interest in Physics. I repeated fifth year, clearly in error, for the purpose of swapping “Biology” with “Applied Mathematics” and “Chemistry” with “Design and Communication Graphics”. There was not an individual who was passionate for either Mathematics, or Applied Mathematics, that I would not have suggested partake in the course as it provides clear benefits in encouraging a logical approach to situations and an early jump, even if only slightly, on college material.

    This ‘logical approach’ is clearly no more. While I appreciate the department’s desire to make “Applied Mathematics” allign with “Project Mathematics” in presenting students with problems that must be tackled in a creative manner using the existing framework, their approach is completely misguided for four primary reasons; there has been no formal notification of this desire to present students with a paper that presents dynamic problems, the material we have to revise is completely inadequate for this approach and is unable to prepare students with such a proportion of borderline-useless questions/examples that always present the question in the same manner, the time limit of the examination which suits repetitive questioning but runs contrary to their new more ‘creative’ questions that drastically augments the difficulty by preventing the student from even thinking about what they’re doing, and the course’s rather narrow focus ensuring that the only way for them to encourage creative solutions is by presenting students with ‘tricks’ that rely merely upon the question’s presentation or duration rather than an inherent difficulty resulting in disingenuous questioning that’s designed to trick students rather than test their apptitude.

    The introduction of the “Project Mathematics” course is something that has been controversial, to say the least, with students and teachers alike, but one thing that is abundantly clear is that, at the very least, we are very well aware of what is on the syllabus, with adequate material to prepare ourselves even if we are unable to predict what the questions we will encounter may be. The same cannot be said for this seemingly new “Applied Mathematics” course that has been furtively slid into the existing framework without any projected valid reason. “Fundamental Applied Mathematics” by Oliver Murphy is, to be quite blunt, useless in the face of this new shapeshifting golemn. The questions that are asked are, generally, presented in a consistent, repetitive fashion, and while an alteration in the number of variables and what you are trying to find may increase or decrease the challenge the questions present to the students, they are, at the very least, consistent. The layout of the questions are typical, the diagrams are similar, what you’re being asked to find tends to vary between a few items at best, and the duration they take to complete is proportional to the competence of the students’ proficiency at mathematics. For past “Applied Mathematics” papers, this book is absolutely perfect, resembling the examinations and providing a wide selection of potential things that may be encountered by students. Now? It’s worthless, as it bares a mere resemblence to the type of questions that we are now encountering. This would not be an issue if past papers were sufficient preparation material, but they quite simply, having done back to 1980 with my class, are not adequate, and it’s absurd. Where have we ever been presented with a Relative Velocity question possessing a table as we were presented with this year? Where have we seen a pulley system like that of the “a” part in question four which was clearly designed to trick students into misreading the question rather than challenge their knowledge? The simple answer is that the past papers are useful in improving the students’ mathematical ability and perhaps providing a vague idea of how to approach this new style of questioning, but ultimately they, too, are inadequate at preparing us for these dynamic questions, which were introduced without the students having any awareness of their introduction. What has been done with “Applied Mathematics” is nothing short of scandalous, and is akin to what would happen if the old “Mathematics” course had, one year, suddenly, been presented in “Project Mathematics”‘s manner without any prior warning; how can students prepare for an examination without even the slightest idea of what they should actually be preparing for, dynamic questions or the previously methodical repetitivity, with material of questionable merit and relevance? How can I justifiably recommend my friends, siblings, and relatives preparing for the Leaving Certificate to study a subject that I had been consistently acing only to come out with a B, at best (and this is speculation on my part, but I am absolutely certain that I did not get my expected grade this year which will have an absolutely massive impact upon the points that I expected to acquire and, almost certainly, will not be able to study “Mathematics” as I had intended because I chose to follow my passion and proficiency for “Applied Maths” rather than do “Biology”), knowing that they might not be as passionate and could leave it with a low grade or, worse, a failure? Two people in my class, consistent B and C students, walked out of the exam prior to the end. These students were no slackers, but in the face of this crucible I empathised with their empty gaze and defeated trudging out of the examination centre.

    They didn’t have much time to trudge out of the centre, however, as the examination is only two and a half hours long, in which we are expected to get six questions done. In past papers, I consistently managed to complete seven questions, (Questions 1-6 and Question 10). This year? I managed six, leaving two parts relatively incomplete and one small part being misinterpretted (Q6b(ii)), not even attempting question four because of the layout designed to deceive. There is simply no time to both think about the problem, and solve the problem, when there are deliberate time sinks (Question 5 immediately springs to mind) and bizarre presentations, If the examination had been increased to a three hour examination, perhaps the dynamic questions could be ignored as we would at least have time to think about what we’re doing, but in the present state it is simply a farce and the transition from one style of questioning to another is nonsensical without changes to the timing of the paper, the material provided, and purposely deceiving questioning presentation.

    Deceiving presentation is putting it lightly, however. Who can honestly say that Question 4’s intial part was genuinely designed to test students’ understanding of the material, and not trick them into perceiving it as a typical pulley system? In Question 6, bii, how is a student meant to deduce how they want us to interpret the question; does the string get caught on the peg and the radius of the circle halves, does the string pass over the peg and we alter the height to the height of the peg on the existing circle, or does it mean to find the tension when the string ends up hitting the and the ball hangs below it? Ultimately, I interpretted it in the third manner, assuming that they would encourage us to use our existing answer, but now, I am unsure if this is what they wanted, and if they were looking for one of the other interpretations. The aforementioned Relative Velocity a part has never, to my knowledge (certainly not in the recent past), been presented in such a manner.before, and if the table was not enough to throw students off, the examiner so kindly decided to put thirty minutes between for X, Y, and Z, just so there was even more room for error. Question 5’s b part was rather fine upon first viewing, but as soon as you commence you realise just how time-consuming this absurd question actually is, presenting students with an array of places to make an error. The Question 1’s b part was somwhat nice upon first inspection, but the maximum velocity of the car on the slope was a bizarre addition that is certainly not common, and definitely not something that could have been prepared for prior to the examination without scouring the course for niggly areas.

    And, ultimately, this brings me to one large assumption that I’ve made throughout this response; that they have altered “Applied Mathematics”‘s examination style to try and allign with “Project Mathematics”. There is no validity to this assumption. Why? Because the department has not actually told us what on earth is going on. Are students meant to expect this level of difficulty from now on or is this akin to the spotting of a unicorn and this style of questioning, two-years-in-a-row, is two incredibly unlikely circumstances occuring consecutively (which, given the rarity of two misjudgings in a row, I see as less probable)? If some comment was made, at least we could get some perspective on what is actually occuring (but surely there is no way the department will confess to a grave error which directly impacted upon the futures of many students, it’s much preferable to adjust the marking scheme towards a curve and pretend all’s well that end’s well).

    Were I to go back two years with the knowledge of the crucible that awaited in 2014’s paper, I would slap myself silly at the prospective of repeating to do my favourite subject. I, obviously, cannot do this, but what I can do is prevent other students from making the same mistake, putting time and effort into a subject and getting a grade that is completely unproportional to one’s apptitude, effort, or commitment. Those in my class who expected As are now expecting low Bs or Cs at best (myself included). Those who were expecting Bs are expecting to scrape a pass. Those who had been getting Cs are worshipping any deity they can dedicate themselves to between now and the date when we receive our results in sheer hope that they actually passed the guillotine that was presented to us this year. You have mentioned in your post on Boards.ie that you were seeking students in the C-B range to comment, and to provide their interpretation of the paper. It, therefore, may seem odd that I am replying, having consistently received As throughout the two years that I have studied the course. Today, however, I am no A student, I’m quite clearly in this range having been absolutely bewildered by what was presented. If one or two questions were unusual in their appearance, there would not have been much issue, but when four or five of the most commonly answered questions are completely irregular there is a fundamental flaw. If you wish to make the course more substantial, please, I beg of you, increase the amount of calculus that we must learn which will have a direct benefit in university, should we wish to attend, while counteracting the great quell that has occured in the “Project Mathematics” course. If you insist on putting in oddly framed questions, at least alter the material, timelimit, and syllabus to reflect this desire so students actually know to expect this and teachers can cover a wider range of topics. This was already a subject with a minimal uptake. One would expect that the department would wish to broaden its appeal rather than starve off the few mathematical hopefuls that dare to tackle a subject perceived by many to be merciless as it is ‘even harder maths’ (to quote a family member explaining the subject to a relative who emigrated), but perhaps the preception of the majority is, indeed, correct, and the department wishes to eliminate the subject entirely and funnel the few interested students into more ‘traditional’ subjects like “Accounting”, “Biology”, “Chemistry”, “Economics”, “Geography”, or “History”, because if this pattern continues, the already niche subject is going to have an even more limited appeal as all but the most stubbornly enthusiastic students cower elsewhere from the paper’s scorn.

    1. On question 6 b (ii), I think that there are at least two occasions when the particle is at the same height as the peg. First, as the particle is released from above the peg, it is at the same height as the peg before it ever reaches the vertical. Second, after the string contacts the peg, the particle will swing up to the same height as the peg again.

  2. Thanks Adam, that’s quite a considered reply.

    There is also a discussion on this on boards.ie – go to page 10 or so in the link below to see what others have to say.

    I think if the subject is going to develop we need to have a open discussion about where to go from here, and that discussion should hear the voices of teachers, students, examiners, employers, parents and third level folk.

  3. I have to say that I don’t agree with the majority of what Adam has said. I’ve commented on boards.ie as well but I want to reply to what was said here. Again, I stress that I am not an A student, I’m a mid B student and a really good exam for me would yield a B1. Our class never covered Q6, so I have no comment on that question, it may indeed have been horrible. Q2 is where my opinion differs most from Adams. Yes, there has never been a table before. And yes, the half hour intervals made the question awkward. However, I don’t see why this evoked such a strong reaction. I found the question to actually be very straightforward, once you got the positions of the boats at one time. It required a calmness in approach, at first, I saw the question and grimaced, but once I actually considered what was asked for two minutes, it was fine. You just needed to be quite careful. Saying that questions like this are unacceptable since we’ve never had a table before, is in my opinion, absolutely ridiculous. An applied maths student aiming for an A should be well able to adapt to a slightly strange question. Once the leg work was done,this question was very basic.

    Q1: Part A should not have been a surprise, it’s fairly straigforward. Part B ii was unusual, I’m still not fully sure if my answer is correct. I realised that the car couldn’t really have an acceleration, as then it wouldn’t have a maximum speed, and the question wasn’t bad from then on. I can understand complaints with this question to a certain extent.

    Q4: Part a was certainly different. Again, I think peoples’ reactions have been extreme. Although I had never seen a system like it, the only approach that made any sense was to give one acceleration twice the other. We simply couldn’t solve the question if the accelerations and tensions were completely random and not connected to each other. I accept that this was an off-putting question, but by no means unacceptable. Part B was basically as standard as they come.

    Q5: Part B of question 5 was incredibly time consuming. It was a different approach than normal. However, again, if you took your time and were careful with your algebra, then this question was actually easier than normal, in my opinion.

    Q3: I found this question to be absolutely ordinary. For part B, some people seemed shocked by the fact that the particle struck the inclined plane moving horizontally. I really don’t understand why, I’ve done several questions like that in past papers and in the Applied Maths book. If you look at what we were asked to prove, it’s quite similar to q3 2004 in terms of algebra.

    Q8: Part a is always fine. Part B was by no means unusually hard. Finding the period of oscillations was actually easier than it might’ve been,since finding the moment of inertia was quite simple. Part 2 is hard, undoubtedly. Just understanding the wording of the question was difficult, and I think this is unfair and unnecessary. Saying this, I’ve always struggled with this question, and I feel like most people who planned on doing q8 (I didn’t) would have been able to deal with all of the q.

    Q10: Part A was quite typical. Part B was also fairly typical, the second part was challenging, but at least part 3 was attemptable without getting part 2, and this is fair.

    So, to sum up, Q2,3,5,8 and 10 were pretty much standard in terms of real difficulty, once you adjusted to the strange layout. This is 5 out of 6 questions. I thought q1 and 4 were genuinely strange, unexpected and difficult. I didn’t go near qs 6,7 or 9, so I don’t know what they’re like. However, most people do q1-5 and 10, and 4 out of 6 of these qs were nowhere near as hard as they could’ve been. Maybe this exam just suited me for some reason, as I seem to be in a minority with my opinion. However, if I’m really honest, peoples’ reactions to this exam make no sense to me. Did they sit the same paper as I did? Because I did roughly as well as I expected, whereas others are saying they went in aiming for an A and will now be happy with a C.

    I’m not trying to anger anyone or show off in any way (I definitely didn’t get an A), but I just want to show that I disagree with most peoples’ reactions to this exam.

  4. I have to agree with most of the opinions expressed by students this year in that the paper we were presented with was unconventional, unprecedented and ultimately unfair. I was a consistent A1 student for two years who went into the exam with all 10 topics prepared and felt quite confident. I left the exam in tears.

    I by no means believe that Applied Maths papers should be totally predictable. In fact, a large amount of what is being tested is a student’s ability to apply knowledge of a topic to an unseen question, and I completely understand that. However, I fully support the view that questions this year were not set to challenge students, but to trick them, and there is a massive difference between the two.

    While the marking scheme may be adjusted, while the A1 rate may stay the same, while we all may ultimately be rewarded in the end, there is little consideration given to the students who sat the exam. I for one, will have a hard time forgetting that paper, letting go of the worry, and I am dreading opening my envelope on August 13th.

    Simply put, I feel that my work over the two years paired with my love and aptitude for Applied Maths was not given the chance to be displayed in the exam. I am disappointed and upset, and while I’m still not ruling out the possibility of getting an A, I know I won’t have shown my best work, along with many other students this year.

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