A level H2 maths question spotting thoughts for AY2009

The first H2 math paper commences on November 10, 2009-that is less than 3 weeks away as I am penning this. Hopefully all of you are getting along fine with your preparations. At this stage,I have added question spotting into the teaching curriculum for most of my students, priming them to anticipate certain specific types of questions that could possibly surface in this year's A Levels. For the benefit of all out there, I have decided to compile a synopsis of my predictions:

1. AP/GP

The problem could involve relating three terms within an AP to that within a GP eg 1st, 3rd and 8th terms of an AP correspond to the 5th, 9th and 19th terms of the GP. Further information may be furnished, and students could be required to solve for the values of those terms or certain attributes of the series, eg common ratio.

The problem could also involve 3 consecutive terms within an AP, their sum is given and when the value of one these terms is modified, these 3 terms get transformed into those of a GP; the student is required to find those terms.

Bank compound interest problems have always been popular, and they function on the fundamentals of a GP series, so students may want to be mindful of that as well.

2. Binomial Theorem

Call it my gut instinct, but somehow I feel that finding the general term of a binomial series expansion would be on the cards this year.

3. Calculus

Typically anything goes, but with regards to applications of differentiation, students may want to pay attention to rates of change, especially in contexts which involve conical structures, eg inverted cones leaking water, inverted cone within upright cone etc.

Questions involving minimising cost while keeping a certain characteristic of that object being made at a constant value,(eg finding minimal amount of material required to produce an item of a desired volume V to optimize cost considerations etc)have made regular appearances of late, so brush up on these ones too.

In addition, students may wish to take notice of less popular formulas involving cotx, cosec x and their respective identities/derivatives. The last thing you really need is to realise you need to integrate cosecx with respect to x in an area question, but can only slam the graphic calculator against your head for not having committed the formula to memory.

A Maclaurin's series expansion question is quite likely to make an appearance; such expansions are mostly manageable and all you have to do is to be very careful. However, you may want to bear in mind that these questions typically possess extensions which seek the deduction of the series expansion for some other strange looking function. Usually such deductions will require the employment of differentiation or integration of the original series, so that's my tip for you.

4. Vectors

Main concepts involving finding shortest distance to and/or foot of perpendicular to a plane from a fixed point and angles between lines/planes are likely to rear their heads. My forecasts for the vector questions would include finding the line of intersection between two planes,where a common point lying on both planes are known, and the direction vector of the line of intersection can be obtained through the vector product of the two normals to the separate planes.

In addition, students may also wish to pay attention to understanding the mechanics of obtaining the equation of a line reflected in a certain given plane.

5. Complex numbers

Well, most would agree with me this is one of the most COMPLEX topics they have ever came across. My hunch is that students may be required to express high order degree polynomials in terms of a composition of separate quadratic factors,

eg z^7-1=(z^2-2z*cos(2*pi/7)+1)....................

Another possible question structure would involve a geometrical shape (eg square or triangle) where certain vertices of that shape are assigned specific complex numbers in Argand space, and it is required of the student to compute the complex numbers representing the unknown vertices of the shape. This can be achieved through the multiplication of another complex number to create the scaling and rotation effect of traversing from one vertex to another. If your jaw is slack and mouth wide open in confusion, start by referring to the section in your notes which explores the consequences of multiplying a complex number by i. (a common factor that rotates the original complex number by 90 degrees anticlockwise)

6. Statistics

The concepts of E(aX+b) and Var(aX+b) existed a long time ago in the old C maths syllabus, but of late it has popped up once again in the preliminary examinations of quite a few JCs. So do go flip through your notes on those stuff once again and be very crystal clear on these ideas.

Combining the concepts of pricing and a specific related attribute of the entity which is normally distributed (eg a durian costs \$x/kg and its weight follows a normal distribution of mean A kg and standard deviation B kg ==> pricing distribution of durian is normally distributed with mean \$Ax and standard deviation \$Bx) has appeared umpteen times in numerous examination papers, so it would be wise to ensure you are well acquainted with this.

Central limit theorem remains an enigma to most students and hence many tend to abuse it. Make sure you understand its mechanics and basis of employment thoroughly; while keywords like mean and average within the question could suggest the investigation of the distribution of the sample mean, it is important that you know when to bring CLT into the picture -a large sample size doesn't necessarily warrant its usage. ( You could refer to my posting-random thoughts on dreaded mathematical concepts 4 for some inspiration)

The usual works-regression, hypothesis testing, permutation and combination blah blah blah blah will definitely surface, so I shall not pretend to be a clairvoyant with regards to these topics.

So there you go-my predictions for the 2009 A levels H2 maths. Of course I have more detailed forecasts on many other topics, but this is as much as I can provide in a condensed post. Remember, they are JUST predictions, so do not take a gambler's stance and merely conduct revision based on my above few recommendations.

All the best to everyone.

Study hard kids, and GOOD LUCK.