A level H2 maths question spotting thoughts for AY2011
Last year’s H2 maths examinations turned out to be surprisingly easy, which means there might be “unwanted excitement/ challenges” in store for candidates this year ( though I pray it won‘t be the case). In such an instance, I have recalibrated
my predictions for specific star topics; I shall also put up question templates to help you (the student) better understand what I am talking about. Here goes:
A master number series strategically segmented into a collection of miniature sequences within brackets have been wildly popular of late in many school preliminary exam papers, but have yet to surface at all in the past 2 editions of the A levels. In the sample template below (Q1), make sure you master the technique to efficiently extract the necessary clues needed to construct expressions for the various designated terms.
2. Binomial Series Expansion
I wish to draw attention towards the very typical ending of such a question structure, where a numerical substitution is to be made in order to derive an approximate value for a surd. While in most cases this substitution is handed to you, this year you might have to figure it out for yourself. (See Q2).
Two concepts (either one or both) might take center stage this time; the first one being calculating the shortest distance between two parallel planes and the second one which involves setting up specific conditions within abstract plane equations (where certain components of the scalar product or Cartesian form is unknown) such that three planes ultimately do not intersect at a point (see Q3 part (iv) ).
If the (applications of) integration problem were to deal the student a shocker, my wager would be on area approximation via the rectangle rule ( see Q4). A similar variant has been solved which you can view here. For Maclaurin’s Series, I just wish to remind the student to exercise care when dealing with small angle approximations. For instance, no expression was taught in terms of rewriting sec x directly when x is small, so convert sec x into 1/(cos x) before applying the relevant formula.
5. Complex Numbers
To clearly illustrate what I am driving at, it would be best to use a worked example . Check this one out and make sure you know how to deftly manipulate the various constituents of a nth degree polynomial equation.
This part of the paper typically involves routine GC work which most students manage pretty well. The only questions which might spring nasty twists would be hypothesis testing (where you have to conduct standardization in order to solve for unknown parameters based on pre specified conclusions) and linear regression ( memorise the various complicated looking mathematical formulas for the regression line equations and product moment correlation coefficient- they might just save your life). Have a glance at this worked example to scare yourself into action.
And this concludes the main bulk of my guesses for the upcoming 2011 H2 maths papers-as usual I will add this disclaimer: predictions are just predictions, nothing more. Bear in mind that only hard work and maintaining a calm disposition during the actual examinations will truly bring about greater chances of success. Good luck kids.