Mathematical Supplements

MATHEMATICALSUPPLEMENTS For H2 Math Students

MATHEMATICAL SUPPLEMENTS For H2 Math Students First Edition Yang Xu

A LETTER TO THE READER Hello, and thank you for picking up my book! I am Yang Xu from the 2021 VJC cohort, and I am really excited to share with you my journey with Mathematics! Math wasn't always my strongest subject, and I really struggled with it back in secondary school. I understand the frustration when concepts do not click despite the eort, and the disappointment at the marks lost to careless mistakes. But one thing Mathematics has taught me is that with the right mindset, appropriate guidance, and some practice, you can really start to see improvement, and even start enjoying math! Having gone through this journey myself, I rmly believe that everyone is capable of doing well in Mathematics, provided the eort and appropriate understanding of the subject. Mathematics is a subject of immense beauty, but only if you allow yourself to see it. In my humble opinion, the structure of the examined syllabus and the competitive nature of exams often overshadow the true elegance of math, making it easy to miss the profound connections between topics. Through this book, I hope to help you discover new insights and develop a deeper appreciation for math, especially for the examinable topics. But even if you don't come away with that appreciation right away, I still encourage you to keep an open mind and give your best eort. Remember, the true beauty of mathematics goes far beyond what I can express here. I urge you to continue exploring on your own if you're curious; there is truly so much more to discover! In this book, I have put together a non-exhaustive summary of the key ideas and conventional solving methods from the H2 Math syllabus. I've also included some personal tips, shortcuts, and insights that I found helpful as a student. These sections are designed to help refresh and review the H2 content while oering some new perspectives on familiar concepts. I have also dedicated a part towards the end of this book to exploring some interesting topics in the syllabus, though not explicitly taught. These concepts have personally helped me a lot in my math journey, but they're only the tip of the iceberg. I encourage you to dive deeper and explore more beyond what's presented here. Please note that this book is only supposed to serve as a supplement, not a 2

3 replacement of your school notes. Certain parts also require H2 knowledge that is not covered explicitly in this book. On a side note, I would also like to mention that Math concepts beyond the syllabus can also develop your critical thinking and problem-solving skills in H2 Math. After all, that is what you are being examined for. These topics either broaden your way of thinking, or provide valuable insights into H2 Math topics. For instance, learning about `Linear Algebra' has helped me to appreciate the interconnections between vectors, matrices, and systems of linear equations.