I am an English teacher and I would recommend this book to anyone who is studying for First Certificate, especially if they are studying alone. The cd provides practical examples of the grammar used in every chapter, together with the audio for the listening exam questions. Each chapter includes a exam question from the writing exam and a specimen essay for each question is included in the key. This is particularly important for students studying alone as many other books only provide suggestions for ideal essay answers, whereas this book gives you the entire essay, so you can see what the examiners expect.
The only drawback to this book is that it doesn't cover the speaking part of the exam - you will need to download a sample exam from the Cambridge website or perhaps buy a book of past exam papers so you can see the style of the exam.
With my students I also use the book
Cambridge Vocabulary for First Certificate with Answers and Audio CD. It's not as good value as this Cambridge Grammar book, as it's about the same price but only has 137 pages, but it does cover all the vocabulary expected for the exam.