Precalculus is part of the acclaimed Art of Problem Solving curriculum designed to challenge high-performing middle and high school students. Precalculus covers trigonometry, complex numbers, vectors, and matrices. It includes nearly 1000 problems, ranging from routine exercises to extremely challenging problems drawn from major mathematics competitions such as the American Invitational Mathematics Exam and the USA Mathematical Olympiad. Almost half of the problems have full, detailed solutions in the text, and the rest have full solutions in the accompanying Solutions Manual.

As with all of the books in Art of Problem Solving's Introduction and Intermediate series, Precalculus is structured to inspire the reader to explore and develop new ideas. Each section starts with problems, so the student has a chance to solve them without help before proceeding. The text then includes solutions to these problems, through which new techniques are taught. Important facts and powerful problem solving approaches are highlighted throughout the text.

Richard Rusczyk is the founder of the Art of Problem Solving website and is the author or co-author of 6 Art of Problem Solving textbooks. He was a national MATHCOUNTS participant in 1985, a three-time participant in the Math Olympiad Summer Program, a perfect AIME scorer in 1989, and a USA Mathematical Olympiad winner.

The solutions are co-authored by Naoki Sato. He is a curriculum developer and the director of WOOT at Art of Problem Solving. He won first place in the 1993 Canadian Mathematical Olympiad and is a 2-time medalist at the International Mathematical Olympiad. He has been Deputy Leader of the Canadian IMO team three times.

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Pre-Test: Students should be able to complete most or all of the pre-test before beginning this book.

Post-Test: Students who can comfortably solve most or all of the problems on the post-test will likely find this book to be mostly review.

the Art of Problem Solving, Volume 2: and Beyond Click for more information

Intermediate Counting & Probability Click for more information

Intermediate Algebra Click for more information

Precalculus
Introduction and evaluation of trigonometric functions, trigonometric identities, complex numbers, exponential form of complex numbers, De Moivre's Theorem, geometric representation of complex numbers, roots of unity, applications of complex numbers to geometry, two-dimensional and three-dimensional vectors and matrices, determinants, dot and cross product, applications of vectors and matrices to geometry.
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