Reddit mentions of Grammar and Vocabulary for Advanced Book with Answers and Audio: Self-Study Grammar Reference and Practice

How to Teach Grammar

Teaching English Grammar: What to Teach and How to Teach it

Explaining English Grammar: A guide to explaining grammar for teachers of English as a second or foreign language. (Oxford Handbooks for Language Teachers)

Teaching Tenses: Ideas for Presenting and Practising Tenses in English

Grammar for English Language Teachers

Concept Questions and Time Lines

Grammar Practice Activities Paperback with CD-ROM: A Practical Guide for Teachers (Cambridge Handbooks for Language Teachers)

Grammar Games: Cognitive, Affective And Drama Activities For Efl Students

Teaching and Learning Grammar

Oxford Basics: Teaching Grammar

Oxford Practice Grammar

Oxford Learner's Grammar:: Grammar Builder

Natural Grammar

Just Grammar (2 levels)

Grammar and Vocabulary for Advanced Book with Answers and Audio: Self-Study Grammar Reference and Practice

Grammar and Vocabulary for First and First for Schools Book with Answers and Audio

Cambridge Grammar for IELTS

Cambridge Grammar for PET

Longman English Grammar Practice

Collins COBUILD English Grammar

A Practical English Grammar

Practical English Usage

Grammar Practice for Elementary/Pre-intermediate/Intermediate Students

I strongly recommend a prep book if you can afford it - not because it will teach you English (too late for that) but because it will give you tips and ideas on how to work through specific sections of the exam - passing CAE and CPE is as much about the language as it is about learning how to pass the exam. I like "Objective Advanced" but I suspect that any of the others will do.

Regardless of your choice of prep book (or skipping it), find as many questions and tests as possible. There are some online (make sure they are with the new format), there are some you can buy: The Advanced Trainer has 6 for example and is not that expensive. Grammar and Vocabulary for Advanced also contains exercises in the same format as they will be on the exam.

Find time and sit a few exams at home. Not "let me see the questions" or "oh, I need coffee" but follow the exact rules of the exam. When the time ends, stop. Don't cheat, do not listen to the things more than once and so on. Just... see what happens when you try to do it that way.

And just to get you started, there are a LOT of materials online. Here is a short collection:

Flo-Joe

Exam English

Cambridge English

English revealed - the free sections

Oxford's CAE Results online sections -
answers are downloadable for most sections

As for how hard it is - it depends on how much exposure you had had to the language. If you read/listen in English with ease, you should be fine.

A couple of small things about specific sections:

• Listening - if you miss something, just ignore it and keep listening or you will keep missing things.
  
  
• Writing - find someone to correct some of your writing between now and the exam. Find as many writing examples (both good and bad) and see why they are considered good (or bad).

PS I am trying to find the CGEL book, but all I have been able to find is this: https://www.amazon.co.uk/Grammar-Vocabulary-Advanced-Answers-Audio/dp/1107481112/ref=sr_1_fkmr0_1?ie=UTF8&qid=1541103990&sr=8-1-fkmr0&keywords=cgel+hewings+haines

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This isn't it, is it? Could you point me in the right direction? I must have this knowledge.