My school has very old pre-calculus books that are not in the best of shape. We also have calculus textbooks that we are not the biggest fans of.
I am wondering if anyone knows of a textbook that combines these two subjects into one - this way we may only need to order one new textbook instead of two separate ones.
If you're willing to consider a foreign book, you might look at something like Mathematics: The Core Course for A-Level (1981) by Bostock and Chandler, or one of its earlier or later incarnations.
This is a book for the 16-18 age range in England. In the preface, the authors write: "With the varied nature of O-level courses, the starting point for an A-level text presents problems. We have started most topics from the beginning, assuming only a very basic mathematical knowledge." In other words, before the introduction of a national curriculum in the mid-1980s, there was so much inconsistency in what knowledge 16-year-olds could be expected to have that the authors thought it wisest to start quite low.
The chapter headings are as follows: Algebraic Relationships, Algebraic Topics, Functions, Coordinate Geometry I, Differentiation I, Trigonometric Functions, Trigonometric Identities, Differentiation II, Integration, Coordinate Geometry II, Curve Sketching, Vectors and Three Dimensional Coordinate Geometry, Complex Numbers, Permutations and Combinations, Series, Solution of Equations, Numerical Applications.
Generally, the level is similar to what would be expected in a calculus class in the U.S., but at this level in the U.K. there is much less focus on integration technique. Some of this is in the sequel, Further Pure Mathematics, which also addresses a wide variety of other topics.