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Absolutely!
This strategy helped me and so many of my students and friends keep track of their weaknesses. It also keeps you grounded because when you look back at that book and all of the errors you made, it helps to ensure you don't get too cocky 😃
I recommend to dedicate a workbook to your mistakes (because you will no doubt make more than you count throughout the year). Its good to even write down the questions that you made a silly error for because it helps for several reasons:
1) If you are making the same silly error across multiple questions, this book will help you notice the pattern. What you may think is 'silly' may in fact be a hole in your knowledge or poor technique
2) Rewriting a question that you know you should have received full marks for is painful, annoying and time consuming. While it may not seem fun, it can be useful because you should be less likely to make the same mistake and have to repeat this process.
As for staying ahead, I recommend to only stay one or two chapters ahead. Any more and you may begin to sacrifice your understanding of the topic your school is covering (which is bad for your SACs). This is because your understanding really comes from doing constant practice questions, so when you work ahead, make sure you stay in touch with past topics.
I hope this helps 🙂