Introduction
Most JC students will take mathematics, even Arts stream students, as it is the most common contrasting subject taken. Building on the foundation you’ve made in O Level Elementary Math and Additional Math, you’ll go on to learn more complicated concepts across roughly 16 chapters, depending on how your school counts it. H2 Math is divided into 2 parts: Pure Math (roughly 10 chapters) and Statistics (6 chapters). Some chapters will be more familiar than others. A lot of secondary school skills in Differentiation and Integration are repeated in the A level syllabus, with some additions here and there, so don’t forget your secondary school stuff! Other topics like Functions and Sequences & Series will be less familiar.
Examination Structure
You’ll take two (intense) 3-hour papers. It's 45 minutes more than your Additional Math papers, but the time really passes quite fast! The first few questions in each paper are shorter, simpler and worth less marks. The length, difficulty, and marks of the questions increases towards the end.
Differences from Secondary School
Personally, I found H2 Math a notch higher in terms of difficulty compared to E and A Math, because the questions in secondary school tended to be very repetitive and muggable. The JC statistics topics will also be pretty new to students. Most students find Statistics to be easier, apart from the Permutations and Combinations chapter. Fret not though, with sufficient practice you’ll get the hang of it! You’ll also be using this new, expensive and really powerful calculator called the Graphing Calculator (GC), the controls for which students might initially find unfamiliar. I encourage students to learn a bit of the basics of using GC from online sources, just to make your transition smoother, though this isn’t 100% necessary (make sure you’re learning how to use the model that you’re going to buy).
Paper 1 will solely test Pure Mathematics topics, whereas Paper 2 tests both Pure Math and Statistics, in two separate sections. Style of questioning for Pure math questions in P2 are largely similar to those in P1. I’ve not come across many questions that mix Statistics and Pure Math topics together, but Cambridge is fond of mixing Pure Mathematics topics, and mixing Statistics topics.
Exam and Study Tips
** The exam format for H2 Math is pretty self-explanatory and straightforward, hence this document will not go into too much detail about it. Instead, it will provide tips on scoring for H2 Math.
Parts of the following extracts are adapted from http://jccrashcourses.com/, and their PCME Study Guide.
The best way to study Math is to do consistent practices (very obvious point, but this is especially crucial for Math!). It's easy to forget past topics even if you mastered them previously. Do full timed practice papers on top of just topical exercises because it trains you to handle multiple topics at once and lets you revise previous topics. Note that making notes may help you gain a better understanding of the topics, but will not improve your grade unless you actually do questions. It’s useful to make your own summary / formula sheets for all the topics because you’re going to need to refer to them constantly, but compared to content-heavy subjects like Biology or Geography, notes for Math are far less crucial than doing actual practices.
Another equally important thing is to learn from your mistakes via spending time reviewing your past practices. Even if you managed to get the answers, it's worth looking at the suggested solutions because chances are there are shorter and more efficient methods out there, especially for concept-heavy topics like P&C, Probability, or Vectors. Over time, you'll get more proficient at using these more efficient methods, and you can save a lot of valuable time.
Get yourself a copy of MF26 for reference (a formula sheet that you can find online) during your study sessions, and be very familiar with what is inside there. You'll save time without having to flip around aimlessly during exams because you know exactly what is in there and where it is, and you can also lighten your memory load so you can focus on memorising other formulae not found inside. Also, get proficient at using your GC. Too many people neglect their GCs and prefer to use their Scientific calculators, and consequently miss out on many features that the GC provides. There are so many shortcuts that you can take with your GC, especially for topics like Vectors, graphing, and stats, and you can even do cool things like checking your answers for integration. Some students force themselves to use only the GC for all calculator-work to master it as quickly as possible. You don’t need to do the same, but start paying more attention to any tips and tricks that your tutor shares, and work on getting proficient at using the GC.
Master your fundamental skills. These are so crucial because they will be used time and time again, and you only need to master them once since you will be using them so often that they quickly become second nature. Some examples include:
Manipulation of equations and inequalities: factorisation, cross-multiplication method, polynomial expansion or long division, BODMAS, crossing out common terms, partial fractions, flipping of inequality signs;
Basic trigonometry: Toa-Cah-Soh and their corresponding graphs, key identities outside of MF26, effects of A and B in AsinBx; solving for angles using A-S-T-C quadrants; appreciating why -sinx = sin(-x) etc;
Basics of quadratic equations (Ax2 + Bx + C): discriminant, number and nature of roots, strictly positive / negative functions, stationary points;
Geometry: recognition of similar triangles, alternate angles, formulae for volume and surface area of common shapes.
These basic skills are especially important because in H2 Math you’re dealing with much, much tougher concepts, so if you’re struggling with any of these, it will impede your understanding of the new concepts and make things even more difficult than they already are. Whenever you encounter any of your weak points in your practices, spend some time working on them by consulting your tutors or friends.
As a good exam habit, check your final answers after you’re done with the paper. There are different efficient ways of checking for different topics, so for instance instead of checking through each and every step, you can just plug your final values into any available formulae to check if the results tally. Refer to the general tips provided for H2 Mathematics in the document under Academic Resources: Mathematics_HCI_Pure Math Learning Points_Ho Song Yee
Regarding carelessness:
Form a habit of constantly checking your work each time you complete a question - use the GC functions to help you for the topics that can be checked with the GC (it is thus important to familiarise yourself with the GC). Familiarise yourself with MF26 too.
Pay attention to make sure that you have answered all parts of the question. Students often miss out parts of a question especially if it’s long.
Some questions ask you to express your answer in a specific form. If this is followed up with the phrase: “where a, b and c are constants to be determined”, this signals that you must include a=_, b=_, c=_ in your final answer.
Be aware of the units they give you; sometimes they are inconsistent. For instance, some quantities given in question are in km while others are in m, so be sure your working does not conflate the two, and conversion may be necessary
Tips on Using the GC
You can refer to this website which provides a brief introduction on how to use the GC for H2 Math. https://mathdistinction.com/category/1-h2-maths-tips-9758/ti-84-plus-techniques/
Unfortunately I can’t find many websites or videos online that do a comprehensive crash course which introduces the various functions of the GC, but don’t worry too much as your Math tutors will guide you along. All the best for H2 Math!
Contributed by Ho Song Yee (HCI ‘20)Edited by Judith Ko
Additional information adapted from http://jccrashcourses.com/