A level H2 maths question spotting thoughts for AY2010

Another year zips by, and it is less than a month away from the A levels as I compose this to share my thoughts and expectations for the upcoming H2 maths examinations. I believe most of you students out there are already in battle mode and putting finishing touches to your revision, but are still, to a large extent, fearful of the unknown or afraid that Murphy's Law might just pay you an unwelcome visit during this critical period of your academic lives. I recognise from experience that a systematic formulation and compilation of forecasts (at least for maths) is helpful for the state of mind as it gives one direction and security (hopefully insurance) , so as with the previous year, I shall put forth my humble thoughts on what the menu might look like for AY2010.

Majority of the syllabus and all key topics (namely complex numbers, statistics, calculus and vectors) will inevitably be examined, so I shan't be repetitive by drawing up a similar reference list categorised according to topic as I have done for AY2009. ( You can read my piece titled “ A level H2 maths question spotting thoughts for AY2009” filed under Examination advice/ recommendations, but with the adjusted mindset that anything is possible-what didn't come true last year may well just be at the doorstep this time.) I would add in new specific nuggets of personal predictions at a later stage, but please allow me to first highlight the single most important development in the H2 maths papers.

During the early “guinea pig” years (2007-2009) , we teachers and tutors were groping in the dark attempting to fashion intelligent guesses regarding the flavour and style of the exams. However, a certain trend has been observed to emerge, that being a growing mix of questions with seemingly strange contexts which demand the candidate to not only be capable of identifying the underlying concepts being tested, but also to employ deft, flexible thinking in the solving process. This was especially true for last year's A levels. For example, a question meant to test one's understanding of the system of linear equations was cleverly disguised as an innocent polynomial-like question. I could vividly recall one of my former charges remarking that she was “dumbstruck” when she first encountered it. Another which took many by surprise was one which combined functions, periodicity and integration ( view worked problem here). The two mentioned above were so prominently peculiar that various versions/interpretations of them were incorporated into tests and exercises for the current batch of JC2 students. Would anything remotely close to these two odd-duck question structures be making a reappearance? I hardly reckon so. Then what is the moral of the story? Well, brace yourselves for the unexpected and be mentally prepared to think out of the box-I believe that there may be at least 4 or 5 instances of questions with exceptionally strange profiles surfacing in this year's papers. But no matter how weird things get, just bear in mind that you are still simply being examined for your knowledge of the core syllabus, so in any case, you shouldn't be straying too far or pushing the boundaries.

With that out of the way, we shall focus on the main bulk of the papers. For the pure maths portion, topics such as binomial expansion, partial fractions and inequalities are rooted in rigidity, typically leaving setters little room to get too creative, so make sure you do well for those parts.On the other hand, I wish to draw your attention to applications of integration, in particular volume integrals. My hunch is that if the question gets “colorful”, it would be because the axis of revolution is no longer the traditional x or y axis, but perhaps some other location, eg the line x=2. Ensure that you have a firm grasp of the “strip theory” so that the correct formulation is made. Please be equally mindful of vectors, especially the notion of 3 planes intersecting one another. While I pray that it will be a straightfoward determination of the common point/line of intersection, I personally feel that its likely that things may get nasty ( to obtain a clearer picture of what I am trying to say, you can view Q5 and Q8 of Vectors also filed under The Question Locker). In addition, go brush up on how to properly construct a differential equation that models the situation described in the question-this item has been absent for the past 2 years. And not to mention, your integration skills as well, since the resolution of any DE clearly involves calculus.

Up next, statistics. Well, note that there is rarely a question that purely tests binomial, poisson and normal distributions separately, since one distribution could be manifested within another. If you can smoothly manoeuvre between the big 3, then I do not forsee any major issues arising from these parts. Central limit theorem is a permanent occurence, so as I have emphasized it in my 2009 predictions, I shall do so again here-be clear about its underlying mechanism. If you were to quiz me as to which statistics question would be spectacular this year, I would have to say linear regression. How so? Simply by providing an incomplete data table and enforcing certain conditions such that the student is left with no choice but to utilise the primitive least squares regression line equations instead of the graphic calculator. Some of you may claim thats why the MF15 exists for a reason, but I can assure you, in my little experiment conducted not too long ago, despite allowing my students full access to the formula sheets ( A typical lesson with me usually means no peeking at the MF15), many fumbled and failed to produce any relevant workings-this is because the formulas are not listed in their entirety. There are 4-5 different expressions to compute the gradient b of the line of y on x, but only one is given in the booklet.

I shall end my post here-hopefully you will find my advice helpful when planning your revision strategies. I am no fortune teller, so exercise judgment and sensibility when reading my opinions. No matter what, leave nothing to chance and make sure you are fully prepared. Study hard kids, and GOOD LUCK.