Rusczyk R., Lehoczky S. The Art of Problem Solving. Volume 2. and Beyond

7th ed. — AoPS Incorporated, 2017. — 320 p. — (AoPS Competition Preparation). — ISBN: 978-0-9773045-8-5, 0977304582.A classic problem solving textbook for students in grades 9-12 who are preparing for advanced high school contests like the AMC 12, AIME, and the Harvard-MIT Mathematics Tournament.
The Art of Problem Solving, Volume 2, is the classic problem solving textbook used by many successful high school math teams and enrichment programs and have been an important building block for students who, like the authors, performed well enough on the American Mathematics Contest series to qualify for the Math Olympiad Summer Program which trains students for the United States International Math Olympiad team.
Volume 2 is appropriate for students who have mastered the problem solving fundamentals presented in Volume 1 and are ready for a greater challenge. Although the Art of Problem Solving is widely used by students preparing for mathematics competitions, the book is not just a collection of tricks. The emphasis on learning and understanding methods rather than memorizing formulas enables students to solve large classes of problems beyond those presented in the book.
Speaking of problems, the Art of Problem Solving, Volume 2, contains over 500 examples and exercises culled from such contests as the Mandelbrot Competition, the AMC tests, and ARML. Full solutions (not just answers!) are available for all the problems in the solution manual.Prove it!
Logarithms
Not just for right triangles
More triangles!
Cyclic quadrilaterals
Conics and polar coordinates
Polynomials
Functions
Taking it to the limit
Complex numbers
Vectors and matrices
Cross products and determinants
Analytic geometry
Equations and expressions
Inequalities
Combinatorics
Sequences and series
Counting in the twilight zone
Again and again
Probability
Find it and make it
Collinearity and concurrency
Geometry tidbits
Number theory
Diophantine equations
Graph theory
Parting shots