A level H2 maths question spotting thoughts for AY2014
Yes this year's H2 Maths papers will be happening slightly earlier than usual, on two consecutive days 6 and 7 November 2014. Not that it would make any meaningful difference, because you the conscientious student (okay I am presuming that's the case) by now should be close to a hundred percent ready to do battle, otherwise ......... I don't really have to spell it out here do I?
Before I begin things proper, allow me to draw your attention to the ever so excessively cherished and erroneously worshipped mathematical formula booklet issued during every instance of a major assessment of one's junior college life - the MF15. It is neither your good friend nor trusted sidekick. It is only there to serve as an affirmation of sorts regarding recollection of things if your over tensed-up state of mind somewhat loses grip on some details of a particular math expression. It is not there to hold your hand every single step of the way.
Yet too many a time I have seen ineffective individuals desperately turning pages of the MF15 the minute he/she encounters an unfriendly looking trigonometry question. Or an intimidating integral screaming to be evaluated. Salvation, you say? More like utter confusion as eyes scan lines and lines of printed formulas. Confused as to whether to use a double angle manipulation, or the factor formulae. Or a common trigonometric identity. Or whatever. In the end, time slips by unforgivingly, and he/she is probably nowhere or perhaps just a wee bit somewhere closer to solving the problem. Sounds familiar? Are you one of these people described? Why can't you expend some effort to store all core formulas within your grey matter to avoid having to endure this agony time and again? It is not fatal to do a spot of memorization work, you have my assurance.
Okie dokes, let's now head over to the highlights of my (definitely not quite accurate) forecasts regarding what might possibly happen in this year's edition of the H2 A level Maths examination.
Applications of Differentiation
Call it a hunch if you so desire, aside from the rather commonplace parametric differentiation to obtain dy/dx, the question might also task a student to develop the underlying Cartesian equation from a set of parametric descriptions. And it isn't all too difficult. For example, if
Also, are you well versed in connected rates of change? I never fail to train my students to crack the following template problem (see immediate below) at top speed, do give it a try if you haven't chanced upon it thus far:
Applications of Integration
If you can perform parametric differentiation properly, please ensure you can do the same for parametric integration, which typically arises in area-under-curve and volumes of solids of revolution problems. A quick refresher:
Reconciling vectors with complex numbers? Yes it can happen, though I pray it doesn't, because it will almost certainly pummel the confidence of many. I for one have been thoroughly exhausted trying to explain to my charges the geometrical (and vector) implications of a polygon with none of its vertices being hinged at the origin when produced in an Argand digram, but somehow majority of them refuse to accept that the concept of vector addition/subtraction can be deployed in the topic of complex numbers. In their minds, vectors are vectors, while complex numbers are, well, just complex numbers. It is a "crime" to mix them both.
I have written a short piece detailing the process of computing various vertices of the above polygon-you can access it here. (see no.15 under supplements on the page)
Statistics
I have said it before: many embrace this section more than Pure Mathematics, and it isn't hard to see why. The GC (Graphic Calculator) does almost all the heavy lifting here, so the most likely reason behind you sinking (hopefully it doesn't happen though) is because you were less than meticulous in keying in the various commands. That said, I have noticed some struggling with using table constructs on the GC to capture the mode of a Binomial or Poisson distribution, so make sure you are adequately skilled in that department.
Oh, and consider an approximate distribution ONLY when the question explicitly requires you to do so. Discrete distributions (such as Binomial and Poisson) when approximated to that of continuous ones (such as the Normal distribution) require continuity correction, whilst that of a Non-normal to a Normal distribution via Central Limit Theorem (CLT) needs NO such modifications. Even at the present moment, I still see a small handful who absentmindedly pen in an unnecessary +/- 0.5 adjustment during the course of invoking CLT.
Lastly, as a friendly reminder, you don't want to be penalized over various definitions, so make sure you can provide a coherent explanation of the level of significance within a hypothesis testing story context, or what a p-value rendered by the GC truly means. Because however small the amount of marks being lost (unwittingly if you wish to argue), it could see you sliding from an A to a B grade.
I still have a couple more predictions floating in my head, that said this is as much as I can offer in a single post. Next stop: a very long, long holiday break. But before that, make sure you remain all sharp and alert for the most important set of written examinations of your 18 years of existence on planet Earth.
Good luck kids. Peace.