A Level H2 Maths question spotting thoughts for AY 2017

After exactly a decade of offering the 9740 H2 Maths curricula, JC2 Mathematics students this year shall constitute the first batch of A Level candidates being examined under the somewhat truncated 9758 H2 Maths syllabus which covers considerably lesser topics compared to its predecessor. Does that mean things will turn out to be much easier? Possible, though I ain't going to wager on that. This is because the actual A Level papers themselves in the past were already largely doable, and it is therefore unlikely a further downgrade in overall difficulty (of questions set) will come to pass given the education ministry's obvious intentions to adequately orientate youngsters in the rigorously demanding wilderness of STEM learning. A reduction in scope is compensated for by an enlargement in both depth and application of concepts taught, so if one is to expect anything, it would be that the problems might get a wee bit more intense. Cue: more critical thinking and improvisation involved. In this vein, allow me to present my main list of forecasts.

Complex Numbers

Hooray, the bulk dealing with De Moivre's Theorem and loci construction has been banished (to the Further Maths syllabus), as a consequence the student is left with very little content to internalize. That's the good news. The not so good news, is that he/she might perhaps be required to be more nimble in formulating solutions. To articulate this in a more concrete sense, examine the problem posed below-can you solve this set of simultaneous equations? Hint: consider multiplying both equations together, and then using the z=x+iy assignment.



Integration Techniques

Of late it has been observed that this particular integral (possessing both a linear factor in its numerator and square root of a quadratic polynomial in its denominator) is sort of making a resurgence:


Pretty please, with a cherry on top, make sure you know how to properly sort this out-till this day I still witness some of my students fumbling around on occasion despite my repeated attempts to communicate the proper manner of resolution to them. So here goes once again just in case:



Vectors

I seriously pray this is an anomaly, however apparently problems on calculating the shortest distance between two skew lines (technically not examinable within current syllabus) have been starting to surface in revision packages distributed to students in top-tier JCs, so it might be useful to thoroughly appreciate the solving process (you may wish to consult a detailed treatment I wrote HERE.) In any case, should such a problem arise, it must be packaged with various assisting pointers to nudge you in the right direction; that said it's better to be safe than sorry, so take the initiative to perform some reading up on your own first.


Functions

Officially the tiny segment concerning the restriction of a domain to enable the proper existence of a composite function isn't examined, but I am not absolutely convinced. I have encountered modified instances of this still terrorizing folks out there, so consider yourselves warned. Being also able to discern whether a function is even, ie f(-x)= f(x) or odd, ie f(-x) = -f(x) is climbing the popularity charts these days with a possible tie-in with calculating areas under graphs.....I think you get the drift.

By the way, since you are equipped with the knowledge to discover the range of a composite function fg(x), might you be able to extrapolate the logic employed in such a circumstance to similarly ascertain the range of a larger-sized composite function say fgh(x)? Food for thought.


Statistics

In all, much has been removed (including Poisson distribution, approximation via the normal distribution pathway, correlation/linear regression etc) ; since the only "newcomers" to the party are general random discrete variables, I'd say it is almost guaranteed this section will feature in a standalone problem. Naturally the ability to compute both the expectation and variance of a given probability distribution function is assumed, so kindly don't muck those up either. Beyond that, I wouldn't be too petrified (or nervous) about the non pure-maths portion of the paper.

And here we go, a reasonably detailed account of stuff to possibly anticipate what could come your way courtesy of yours sincerely. As I have always emphasized in previous years, this is merely a tabulation of personal predictions and should in no way serve as a wholesome replacement for your revision efforts. Leave nothing to chance, be doubly (best still, triply) prepared. At this point in time while I am drafting this, the H2 Maths papers are scheduled to happen in less than a month, hopefully you are almost already to do battle. God made you cool, so be cool. Remember a well deserved break awaits your weary soul soon enough.


Good luck kids. Peace.