A Level H2 Maths question spotting thoughts for AY 2015

I am not going to wager on Singapore's Golden Jubilee having a positive knock-on effect on this year's A Level exams (the two maths papers happen a week apart starting 5 November next month). Would they be much easier compared to past editions? I hardly reckon so. What about being extremely unforgiving on the flip side? Nah, I won't lose sleep over it. That said, with less than 20 days to go as I am drafting this, I pray most of you students are pretty much done with your past year paper packages and are attempting one final intensive review of the 9740 syllabus.

My educated guess for what's in store for candidates this year: most questions would be run-of-the-mill, so whether one scores in those boils down largely to one's propensity to carelessness. Read each line carefully, and assume nothing. Presentation matters, so does legibility of handwriting. Check your work once. Check your work yet another time. Then again, it is almost certain a small handful of problems will be slightly more steeped in difficulty to differentiate between the A graders and the rest of the cohort. This is where I make myself relevant by introducing some of my personal predictions and recommendations to attain that extra "edge". Here goes:

Functions

The notion of periodicity embedded in piece-wise continuous functions caught many by surprise when it first occurred in the 2009 papers; since then it has been featured umpteen times in numerous school examinations. Just when things seem to get boring, the f(x)=f(x+n) design was of late modified by some rather enterprising teachers. Check the following out:

How would you sketch f(x)? While the integrity of its periodicity is somewhat maintained, each cycle peaks at different amplitudes. This is how it looks like:

What about a slight tweak to the definition?

Give yourself a pat on the back if you can obtain the graph of this odd function below:

Calculus

Proving basic integration and differentiation results may seem naturally straightforward, so I was rather taken aback when some of my more competent charges fumbled at performing such derivations. So much for rote learning. Here are some examples:

Implicit differentiation is another concept which still bothers more than just a few. When I detailed the process with regards to computing the second order derivative for a set of parametric equations, there was more indigestion observed than expected. Take a look at this:

Vectors

Do you know how to compute the shortest distance between a point and a line without employing the vector product concept? Here is an actual problem for you to contemplate (pay special attention to the final part):

While one must know how to decide if two lines are skew, what about finding the shortest distance between two skew lines? Yes this concept is not examined under the current syllabus, however a problem with pointers can always be designed to get around this. Its about preparing for the worst and hoping for the best. You may wish to consult this post I previously wrote (skip straight to the end).

Statistics

This section of the second paper is typically the easiest to score in, yet also the one where students can spectacularly flounder because of their epic carelessness whilst punching buttons. As I have said to my students for the 1304569206th time: you are what you key (into your GC). Meticulous saves the day, "can't be too bothered" ruins it.

If there's one thing I wish to draw your attention to, it would be dealing with unknown mean and variance quantities of a Normal distribution. Study the problem below carefully and decide how you would approach it. Hint: Portraying the various information on a standard normal Z curve would help loads.

I could go on forever, but time is a luxury at this juncture and I do have to return to tending to my students. Hopefully the above which I have articulated will provide you with sufficient food for thought.

The haze has returned, and I have personally seen more individuals falling ill because of it. So do always try to stay indoors, drink lots of water and get plenty of rest. Having a clear head during any examination is absolutely critical, more so when you are attempting Maths papers.

Good luck kids. Peace.