IB HL Calculus P3 May 2016: The Hardest IB Paper Ever?
IB HL Paper 3 Calculus May 2016 was a very poor paper. It was unduly difficult and missed off huge chunks of the syllabus. You can see question 5 posted above. (I work through the solution to this in the next post). This is so far off the syllabus as to be well into undergraduate maths. Indeed it wouldn’t look out of place in an end of first year or end of second year undergraduate calculus exam. So what’s it doing on a sixth form paper for 17-18 year olds? The examiners completely abandoned their remit to produce a test of the syllabus content – and instead decided that a one hour exam was the time to introduce extensions to that syllabus, whilst virtually ignoring all the core content of the course.
A breakdown of the questions
1) Maclaurin- on the syllabus. This was reasonable. As was using it to find the limit of a fraction. Part (c) requires use of Lagrange error – which students find difficult and forms a very small part of the course. If this was the upper level of the challenge in the paper then fair enough, but it was far from it.
2) Fundamental Theorem of Calculus – barely on the syllabus – and unpredictable in advance as to what is going to be asked on this. This has never been asked before on any paper, there is no guidance in the syllabus, there was no support in the specimen paper and most textbooks do not cover this in any detail. This seems like an all or nothing question – students will either get 7 or 0 on this question. Part (c) for an extra 3 marks seems completely superfluous.
3) Mean Value Theorem – a small part of the syllabus given dispropotionate exam question coverage because the examiners seem to like proof questions. This seems like an all or nothing question as well – if you get the concept then it’s 7 marks, if not it’ll likely be 0.
4) Differential equations – This question would have been much better if they had simply been given the integrating factor /separate variables question in part (b), leaving some extra marks to test something else on part (a) – perhaps Euler’s Method?
5) An insane extension to the syllabus which took the question well into undergraduate mathematics – and hid within it a “trap” to make students try to integrate a function that can’t actually be integrated. This really should have been nowhere near the exam. At 14 marks this accounted for nearly a quarter of the exam.
The syllabus is only 48 hours and all schools spend that time ploughing through limits and differentiability of functions, L’Hopital’s rule, Riemann sums, Rolle’s Theorem, standard differential equations, isoclines, slope fields, the squeeze theorem, absolute and conditional convergence, error bounds, indefinite integrals, the ratio test, power series, radius of convergence. All of these went pretty much unassessed. I would say that the exam tested around 15% of the syllabus content. Even the assessment of alternating series convergence was buried inside question 5 – making is effectively inaccessible to all students.
The result of this is that there will be a huge squash in the grade boundaries – perhaps as low as 50-60% for a Level 6 and 25-35% for a level 4. The last 20 marks on the paper will probably be completely useless – separating no students at all. This then produces huge unpredictability as dropping 4-5 marks might take from from a level 5 to level 3 or level 6 to level 4.
Teachers no longer have any confidence in the IB HL examiners
One of my fellow HL teachers posted this following the Calculus exam:
At various times throughout the year I joke with my students about how the HL Mathematics examiners must be like a group of comic book villains sitting in a lair, devising new ways to form cruel questions to make students suffer and this exam leads me to believe that this is not too far fetched of a concept.
And I would tend to agree. Who wants students to be demoralised with low scores and questions they can’t succeed on. Surely that should not be an aim when creating an exam!
I’ve taught the HL Calculus Option for the last 4 years – I think the course is a good one. It’s difficult but a rewarding syllabus which introduces some of the tools needed for undergraduate maths. However I no longer have any confidence in the IB or the IB examiners to produce a fair test to examine this content. Many other HL teachers feel the same way. So what choice is left? Abandon the Calculus option and start again from scratch with another option? Or continue to put our trust in the IB, when they continue to let teachers (and more importantly the students) down?