Congratulations on receiving your offer to study Natural Sciences at Cambridge. It is important to prepare mathematically as thoroughly as possible in advance of your arrival in Cambridge.
It is strongly recommended that you work through the Mathematics for the Natural Sciences Workbook, which is intended for students coming to Cambridge to study the non-biological options of the Natural Sciences Tripos. The workbook contains questions based (roughly) on the core A-level syllabus. It should provide a useful set of revision problems for core mathematical skills; if some of the material is new to you, you are uncertain about it or you get stuck on any of the questions, then we strongly suggest that you refer to the NRICH website or an appropriate A–level textbook for support.
You will benefit from working through some of the rich scientific mathematics problems from stemNRICH on the NRICH website. Here you can find questions on mathematical biology, physics, chemistry, engineering and the most important areas of applied mathematics. You will also find supporting articles to help you to understand the important role that mathematics will play in your study of science. The style of mathematics and problem solving practised in stemNRICH and the selection of preparation problems will greatly aid your mathematical thinking in preparation for the Tripos, where problems are typically far more involved than those encountered at school.