The Mathematics Workbook is available on-line here: https://www.maths.cam.ac.uk/undergraduate-admissions/workbook.pdf. You should work through this and can go over any problems when you get here. A paper copy of the workbook will be sent to you in mid-August.
Courses in Part IA: http://www.maths.cam.ac.uk/system/files/iacourses.pdf
Kevin Houston, How to think like a Mathematician - A companion to undergraduate Mathematics, Cambridge University Press.
M. R. Spiegel, Vector Analysis and an Introduction to Tensor Analysis, Schaum’s Outline Series. It is extremely important that you familiarize yourself with the material in Chapters I to 4 in particular.
R. P. Feynman, Lectures in Physics, Addison-Wesley, Volume I: Chapters 1 to 17 and 21 to 25. Volume II: Chapters 1, 8, 12 and 18. This book is an excellent introduction to Physics. It is especially recommended for students who did not study Physics at school or college. The material in Volume II is more advanced and will be necessary knowledge during the second year at Cambridge.
M. Spivak, Calculus, Benjamin. A good introduction which is aimed slightly above A level (or equivalent) and concentrates on techniques.
S. Lipschutz and M. Lipson, Schaum’s Outline of Linear Algebra, Schaum’s Outline Series. Provides a good introduction to the subject.