Other Study Materials

"Official" Material: Textbooks and Lecture Notes

Although I have identified past papers as superior, there is still a place for other study materials. Textbooks and lecture notes are a great way to help you understand concepts in more detail, since they usually provide examples and in-depth explanations which you probably wouldn’t find elsewhere.

Many large-scale examinations are based entirely on material contained within an official textbook. You can use the official textbook as your main point of reference while building up your bank of model answers from past papers, since it is guaranteed to contain the information you need.

Furthermore, exercises in official textbooks very much mimic the style of question you are likely to encounter in an exam. Aside from past paper questions, these exercises are the best way for you to practise.

If you are a university student, textbooks can present more of a challenge. There is usually much less direct correspondence between university courses and textbooks compared with those at high school. You will generally have to rely on lecture notes provided by your lecturers and multiple textbooks.

When choosing which topics to study at university, my decisions were heavily influenced by the quality of lecture notes provided. This is because learning from lecture notes is much, much faster than learning from textbooks. Unlike textbooks, lecture notes tend to be much more closely aligned with exams.

Although textbooks are the highest-quality references available for most subjects, learning from them is an extremely slow process. Textbooks contain a lot of additional material beyond what you need. It takes a long time to sift through to the material that is relevant to you. Or you will just have to settle for learning a lot of unnecessary information.

Either method is inefficient, like fishing in a lake full of fish that you don’t want. Whether you use a line or a trawler, you will pick up lots of unwanted catch amongst the fish you are actually interested in.

The Internet

When I was studying for my Mathematics (and Further Mathematics) A-Level, I found a set of “cheat sheets” online that a teacher had created precisely for students taking their Mathematics A-Level exams. All essential information for each module had been condensed onto one or two pages.

This was not an official resource. However, it was extremely helpful whenever I needed to look over concepts I hadn’t remembered or understood properly while doing past papers. In fact, I didn’t touch my textbooks again.

It won't always be easy to find a concise, complete set of notes like this, but the lesson is the same: any resource that provides a shortcut to your preparation is a true gift. Take advantage of them.

Many universities and individual academics publish videos or other resources online and make these available for free. During my university years, some of the lecture slides we were given were terribly unclear or incomplete. For one of the not-so-well-documented topics I took in my final year, I learned all of the material from a set of videos which a professor from a different university had created.

This was a very engaging way to learn when I wasn’t busy with past papers, and it added some welcome variety to my preparation.


Students often shy away from contacting teachers and lecturers during the exam period. If you are stuck on a particular concept or some aspect of the subject is unclear, who better than an expert to help you improve your understanding? Rather than waste hours struggling alone, simply send a quick email explaining your problem and read the response. I asked tons of questions both at school and in my final year at university. The teachers, lecturers, and supervisors I had contacted were always happy to help.

Discussing exam material with your peers is also hugely beneficial. One exceptionally gifted individual at university was always particularly generous in explaining ideas to me. It is hard to overstate the advantage of being friends with a genius who can also articulate concepts in a clear manner.

Don’t forget that your understanding and knowledge will also be strengthened by helping other students who might be struggling. Nothing forces you to clarify your grasp of a subject like trying to teach it.