Recommendations for High School Students
The Introduction Series of our Art of Problem Solving curriculum is a complete curriculum for
outstanding math students in grades 6-10. The texts also give
students a solid foundation for success in programs such as the American Mathematics Competitions,
and help them develop the problem solving skills they'll need at top colleges and in highly competitive careers.
Click on a book's title for more information.
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 | By Richard Rusczyk A thorough
introduction for students in grades 6-9 to algebra topics such as linear equations,
ratios, quadratic equations, special factorizations, complex numbers, graphing
linear and quadratic equations, linear and quadratic inequalities, functions,
polynomials, exponents and logarithms, absolute value, sequences and series,
and more! Text: 656 pages. Solutions: 312 pages. | Introduction to Algebra: Textbook and Solutions Manual | $59.00 | |
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 | By David Patrick A thorough introduction for students in grades 7-10 to counting and probability topics such as permutations, combinations, Pascal's triangle, geometric probability, basic combinatorial identities, the Binomial Theorem, and more. Text: 256 pages. Solutions: 120 pages. | Introduction to Counting and Probability: Textbook and Solutions Manual | $42.00 | |
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 | By Mathew Crawford A thorough
introduction for students in grades 7-10 to topics in number theory such as
primes & composites, multiples & divisors, prime factorization and
its uses, simple Diophantine equations, base numbers, modular arithmetic,
divisibility rules, linear congruences, how to develop number sense, and more. Text: 336 pages. Solutions: 144 pages. | Introduction to Number Theory: Textbook & Solutions Manual | $47.00 | |
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 | By Richard Rusczyk A full course in challenging geometry for students in grades 7-10, including topics such as similar
triangles, congruent triangles, quadrilaterals, polygons, circles, funky
areas, power of a point, three-dimensional geometry, transformations, introductory trigonometry, and
more. Text: 557 pages. Solutions: 226 pages. | Introduction to Geometry: Textbook & Solutions Manual | $57.00 | |
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Our
classic Art of Problem Solving Volume 1: the Basics has been used by students getting started in
high school math competitions for over 16 years.
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 | By Sandor Lehoczky and Richard Rusczyk A classic problem solving textbook for students in grades 7-10 who are preparing for contests like MATHCOUNTS and the AMC 8/10/12. Text: 288 pages. Solutions: 144 pages. | Volume 1: Textbook and Solutions Manual | $42.00 | |
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Students who have completed our Introduction Series of texts, or who have finished Algebra 2 in a standard curriculum, are ready for our
advanced high school texts, which complete the Art of Problem Solving curriculum through calculus.
Click on a book's title for more information.
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 | By Richard Rusczyk and Mathew Crawford A comprehensive textbook covering Algebra 2 and topics in Precalculus. This book is the follow-up to the acclaimed Introduction to Algebra textbook. In addition to offering standard Algebra 2 and Precalculus curriculum, the text includes advanced topics such as those problem solving strategies required for success on the AMC and AIME competitions. Text: 720 pages. Solutions: 336 pages. | Intermediate Algebra: Textbook & Solutions Manual | $64.00 | |
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 | By David Patrick An intermediate textbook in counting and probability for students in grades 9-12, containing topics such as inclusion-exclusion, recursion, conditional probability, generating functions, graph theory, and more. Text: 400 pages. Solutions: 208 pages | Introduction to Counting and Probability: Textbook and Solutions Manual | $42.00 | |
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 | By Richard Rusczyk A comprehensive textbook covering precalculus topics. Specific topics covered include trigonometry, complex numbers, vectors, and matrices. Includes many problems from the AIME and USAMO competitions. Text: 528 pages. Solutions: 272 pages. | Precalculus: Textbook & Solutions Manual | $53.00 | |
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 | By David Patrick A comprehensive textbook covering single-variable calculus. Specific topics covered include limits, continuity, derivatives, integrals, power series, plane curves, and differential equations. Text: 336 pages. Solutions: 128 pages. | Calculus: Textbook & Solutions Manual | $49.00 | |
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Our classic Art of Problem Solving Volume 2: and Beyond has been used by students preparing for advanced high
school contests such as the AMC 12, the AIME, and ARML for over 16 years.
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 | By Richard Rusczyk and Sandor Lehoczky 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. Text: 320 pages. Solutions: 184 pages. | Volume 2: Textbook and Solutions Manual | $45.00 | |
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We carry several books of problems from the American Mathematics Competitions (AMC). Below are the three
most recently published collections of AMC problems.
Click on a book's title for more information.
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 | By David Wells and J. Douglas Faires Past problems with complete solutions from the American Mathematics Competitions 12 (AMC 12), which is one of the first tests in the series of contests that determines the United States International Math Olympiad team. This book includes all AMC 12 tests from 2001-2007. 230 pages. | Contest Problem Book IX | $49.95 | |
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 | By J. Douglas Faires and David Wells Past problems with complete solutions from the American Mathematics Competitions 10 (AMC 10), which is one of the first tests in the series of contests that determines the United States International Math Olympiad team. This book includes all AMC 10 tests from 2000-2007. 212 pages. | Contest Problem Book VIII | $49.95 | |
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 | By Harold Reiter Past problems with complete solutions from the American Mathematics Contests (AMC 10 and AMC 12), which is the first test in the series of contests that determines the United States International Math Olympiad team. This book includes tests from 1995-2000, including the 50th Anniversary AHSME issued in 1999. 183 pages. | Contest Problem Book VII | $49.95 | |
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Click here for more books from the AMC.
We also carry collections of problems from The Mandelbrot Competition, which is excellent preparation for the AMC and AIME tests.
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 | By Sam Vandervelde Past problems
with complete solutions from The Mandelbrot Competition 2002-09.
Contains problems that are excellent practice for the American Mathematics
Competitions, as well as excellent problems for students first learning
how to tackle challenging proof problems. 180 pages. | Mandelbrot Morsels | $25.00 | |
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 | By Sam Vandervelde Past problems
with complete solutions from years 1995-2002 of The Mandelbrot Competition.
Contains problems that are excellent practice for the American Mathematics
Competitions, as well as excellent problems for students first learning
how to tackle challenging proof problems. 148 pages. | The Mandelbrot Problem Book | $23.00 | |
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 | By Sam Vandervelde Past problems
with complete solutions from the first five years (1990-95) of The Mandelbrot Competition.
Contains problems that are excellent practice for the American Mathematics
Competitions, as well as excellent problems for students first learning
how to tackle challenging proof problems. 112 pages. | The First Five Years | $20.00 | |
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We offer one compilation of middle school and beginning high school contests from the UK.
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 | By UK Mathematics Trust This 188-page book contains problems and solutions for 10 Junior Challenges (1997-2006), 10 Intermediate Challenges (1997-2006) and 9 Senior Challenges (1997-2005) in the United Kingdom. These tests correspond roughly to the AMC 8, AMC 10, and AMC 12, respectively. 188 pages. | UKMT Ten Years of Mathematical Challenges: 1997 to 2006 | $24.95 | |
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The Art of Problem Solving textbooks listed above for study after Algebra 2 all contain material useful for students getting started with high school math olympiads. Click here for more information on these texts.
Below are several books we offer for high school olympiad preparation from other sources.
Click on a book's title for more information.
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 | By Titu Andreescu and Gabriel Dospinescu A series
of articles paired with collections of problems, designed
for students preparing for high-level high school contests such as national
olymipads. 554 pages. | Problems from the Book | $69.95 | |
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 | By Geoff Smith A Mathematical Olympiad Primer includes a survey of tactics and strategies useful for advanced problem solving, as well as the British Math Olympiad problems and solutions from 1996 through 2006. Suitable for students just starting on the high school olympiad level. 178 pages. | UKMT A Mathematical Olympiad Primer | $24.95 | |
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 | By A D Gardiner and C J Bradley This geometry text offers beginning and advanced geometric problem solving tactics, as well as numerous practice problems. The book is most appropriate for experienced geometers who are learning how to take on more challenging geometry problems, such as those offered at the high school olympiad level. 264 pages. | UKMT Plane Euclidean Geometry: Theory and Problems | $24.95 | |
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