Reddit reviews An Introduction to the Mathematics of Finance: A Deterministic Approach
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Used Book in Good Condition
Good luck. For CT1 I suggest doing a lot of past papers (this goes for any of the CT exams tbh) and perhaps this textbook: http://www.amazon.co.uk/Introduction-Mathematics-Finance-Stephen-Garrett/dp/0080982409
I'm sure you can find older editions of that one for much cheaper, but old editions may lack some of the material from the later chapters on financial derivatives (futures, forwards, swaps and options etc)
A month is also a tall order, but CT1 is quite simple, so it's manageable if you allocate time well.