(HSC Maths Extension 1 ) Jacqui from Dux College runs through the common ‘birthday problem’, which asks you to show that “In a group of 23 randomly chosen people, the probability that at least 2 people share the same birthday is greater than 50%”. If you try to plug your numbers directly into your calculator, you’ll find the numbers are too big. You first need to cancel out some terms before using your calculator!
HSC maths and sciences are structured and assessed in a fundamentally different way. These differences require different approaches in studying both types of subjects, in order to secure a top band in each. In this short article, we will look at the main differences between HSC maths and sciences, and give you some insight as to how each type of subject ought to be approached.
Study year 11 and 12 maths topics together
The syllabi of HSC mathematics is integrally linked with the preliminary (year 11) syllabus. This applies to all levels of HSC maths, from General to Extension 2. There is no sudden identifiable transition between preliminary topics and HSC topics. In contrast to HSC sciences (such as Chemistry and Physics), their syllabi are clearly split into preliminary topics and HSC topics.
In mathematics, topics you learn in your preliminary year, or even going back to year 10 (e.g. the sine and cosine rule are sometimes used in year 12, even in Extension 2) are unavoidable when you need to study for HSC topics. For example, we all need to know how coordinate geometry works, and how to find the equation of normals and tangents, before we can understand the Conics topic in Extension 2, or parametrics in Extension 1. The key point here is that there is no clear distinction between year 11 and year 12, for mathematics.
One approach to maths tutoring or teaching at schools is to teach topics according to their relationship with each other, instead of whether the actual syllabus categorises them as preliminary or HSC topics. For example, we can teach year 11 Extension 1 probability, up to the harder permutations and combinations normally studied in year 12. This approach in studying is also advantageous, as it helps you consolidate and group relevant topics together.
An extreme example that may work for some is the anecdote of a private maths tutor that is reputed to teach year 7 geometry, then for the entire year, progress to harder and harder geometry topics, finishing off with Extension 2 style circle geometry. While we can see this approach may work for some students, the extreme case is not recommended for most students. Instead, we recommend students to study the relatable preliminary and HSC topics together. For example, the reason why the Fitzpatrick series of books (the yellow book for 2 unit, the green book for 3 unit, and the pink book for 4 unit) is split according to 2, 3 and 4 unit reflects this fact about HSC mathematics. The writer did not choose to split his books according to preliminary and HSC as he correctly identifies that it is more convenient and advantageous to student learning by making them learn year 11 and 12 topics together, where they are very related.
Recommended approach for HSC sciences
HSC sciences, unlike mathematics, have topics that are clearly divided as preliminary and HSC topics. For example, in Preliminary Physics, you learn about waves and communications devices in The World Communicates, resistors and using Ohm’s law in Electrical Energy in the Home, vector addition and movement in Moving About, and some basic astrophysics in The Cosmic Engine. Now, if we look closely at the topics taught in the Preliminary year, and compare them to the HSC topics, there is very little direct overlap. The main value in Preliminary Physics is for students to gain a solid grasp on the physical principles that are relevant to the HSC.
For example, in The World Communicates, knowledge of waves and how they propagate is important to many topics in the HSC. However, knowledge of mobile phones, fax machines, GPS and CD/DVD technology is irrelevant to the HSC. So the point here is: understand the physical principles (waves, electrical resistance, Ohm’s law, vector addition, forces, momentum etc) but don’t pay too much attention to the specifics (e.g. you’ll never be asked to calculate the resistance of a circuit in a HSC question, and you don’t need to know about Red Giants / White Dwarves if your school does not do the Astrophysics option module).
Ideal approach to studying HSC Physics and Chemistry
The ideal approach here is to learn the preliminary course as usual, paying close attention to the physical principles that are involved with the content. However, remember that you will not be tested in your HSC year on the specifics of the preliminary course. For example, you will not be required to know how to calculate resistance in series and parallel circuits in the HSC Physics course. In fact, the HSC assessments and exams will only test what is in the year 12 HSC syllabus. Therefore, you will definitely need to know the specifics of each dot-point in the HSC syllabus, but not the specifics of the preliminary syllabus.
A good approach is to start your learning early. Cover the preliminary topics as quickly as you can, (with the help of Chemistry tutoring or Physics tutoring, or from your school teachers) and move onto the HSC topics as quickly as you can. This leaves you with the maximum amount of time to study the content that is directly relevant to your HSC. Remember, only the content of the year 12 syllabi will be examined, so use this fact to your advantage when studying HSC sciences!