I live in Australia and I will be doing my final high school mathematics test in 5 months from today. The test is about the following topics:
- Differentiation and Integration and their applications (Maxima/minima problems, volumes, motion [simple harmonic, projectile, circular and resisted motion], conical pendulum and banked tracks)
Complex numbers
Polynomials
Conic sections
Series and sequences, mathematical induction and analysis
Inequalities (similar to ones in IMO)
Circle geometry
Probability, combinatorics and binomial probability.
Here are some examples of past exam papers:
- http://www.boardofstudies.nsw.edu.au/hsc_exams/hsc2012exams/pdf_doc/2012-hsc-exam-maths-ext2.pdf
- http://www.boardofstudies.nsw.edu.au/hsc_exams/hsc2011exams/pdf_doc/2011-hsc-exam-mathematics-ext2.pdf
- http://www.boardofstudies.nsw.edu.au/hsc_exams/hsc2010exams/pdf_doc/2010-hsc-exam-mathematics-extension-2.pdf
The test starts of very easy then gradually gets harder. I'm confident that I can get most of the questions correct but timing is a problem as it is difficult to get the whole test done in the time allowed.
Many people, including my teacher, told me that the best way to prepare is to do as many of these papers as possible in timed conditions. Do you agree with that? The problem is that doing the same thing with slightly different questions over and over is very boring :(
Yes, it is the best way to get the highest mark on the test and yes it is very boring. At the very high percentiles, the ranks are decided by who did the most past papers, who saw the most familiar questions and who has practiced their speed - not necessarily by who has the most solid understanding of all the mathematical principles involved. With enough practice you should aim to get to the point where you don't even need to think about how to do the problems until Q8, everything before that is just writing down what comes to your mind as fast as you can.
Not saying is this the best way to learn or enjoy mathematics, but it is the best way to rank the highest on the tests. Unfortunately sometimes we all have to jump through some hoops.