A level H2 maths question spotting thoughts for AY2012
Last year's papers delivered a nasty surprise in the form of 2 questions which were truly old-school style. Many teachers were caught off-guard, me included. It would seem that examination setters are favoring a return to the 90s, when the old Further Maths standard was in place over here in Singapore. Back then a completely different style of problem solving techniques were imparted, skills which H2 mathematics students are neither taught nor exposed to. So, should anyone be overly concerned? I would say no, not at least for the present moment. While it is rather likely the papers will contain an increasing quantity of F-maths flavored question structures,majority of the problems issued would still remain as common place ones. Which means it is highly advisable students attempt and be well acquainted with previous editions of the A Level H2 math examination papers (and yes that includes the tremendously easy 2010 ones).
For regular items on the menu, you can refer to writings of mine in previous years to capture the essence of what to expect in general, therefore I won't waste time reproducing these here.
Instead, I will touch upon what I have mentioned earlier with regards to the board embracing ancient stuff, as this is where things are clearly filed in the "unpredictable" cabinet. And most students fear the unpredictable, however small/trivial a portion of the big picture they occupy. I cannot say for certain my forecasts will be dead-on accurate, but hopefully they can help provide some measure of confidence. Here goes my set of anticipatory advice:
1. Complex Numbers
Binomial series expansion coupled with trigonometry could be rigorously implemented within a complex numbers question. Take a look at this problem (Q1 on the page) and study it thoroughly. I have been getting my students to repeatedly solve this bad-ass here, telling them: " It could save your life." (Not to be taken literally of course).
2. Binomial/Poisson Distributions
You can discover the mode of both distributions very easily with the use of the graphic calculator, but what if the setters desire to make your beloved GC redundant? And how can this be achieved? View this problem (Q10 which deals with Binomial distribution on the page) to get a better understanding of what I am talking about. Should a Poisson distribution be tested instead,here is the modified formula: P(X=k+1)/P(X=k) = λ / (k+1) , where λ denotes the Poisson parameter.
What could happen here? The usage of the R-formula could pop out and bite you, in the form of an integral waiting to be evaluated. View this document I wrote for my supplementary site to learn more. And if you must know, the R-formula isn't present in the current version of the MF15.
For solving first order differential equations, while you were taught the variables separable and substitution techniques, there is actually one more within the family, called the integrating factor method. While its relevance lies outside the core syllabus, an existing question could be modified and adapted based on exam requirements. To attain a better appreciation of things, examine the handout on this page (see no. 3 under Supplements).
This concludes the discussion (there is only so much I can share within a single page), hopefully I have helped addressed some pressing doubts. Study hard and stay healthy for this very last lap. All the best for your A levels kids. Peace.