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I'm supposed to start my preparation for the college admission math exam so I'm looking for a good explanatory/textbook/problem book which covers most of or all of precalculus topics with a hint of calculus on an advanced level. By that I mean it should not just explain a topic, give a few minor examples and take off. Rather it should go in depth and explain deeper things about that particular thing. Is there such a book?

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  • $\begingroup$ Ok in the first i meant shouldnt $\endgroup$ – diredragon Jan 9 '16 at 12:29
  • $\begingroup$ OK, I edited your question to match your comment. $\endgroup$ – Rory Daulton Jan 9 '16 at 12:30
  • $\begingroup$ What exams? Different exams cover different material at different levels of difficulty. $\endgroup$ – David Jan 9 '16 at 16:32
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Gelfand's Algebra, Trigonometry, Functions and Graphs.

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Calculus by Michael Spivak is one of the best textbooks I've ever seen. It provides leisurely explanations, a profusion of examples, a wide range of exercises and plenty of illustrations in an easy-going approach that enlightens difficult concepts and rewards effort.

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