Books for advanced high school students

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SUMMARY

This discussion focuses on recommended textbooks and problem books for advanced high school students in grades 9 and 10, specifically in the areas of Euclidean geometry, Algebra 1 and 2, and Trigonometry. Key titles mentioned include "Algebra" and "Trigonometry" by I. M. Gelfand, "Geometry Revisited" by H. S. M. Coxeter, and Kiselev's "Geometry" volumes I and II. These books are noted for their challenging problems that encourage critical thinking, making them suitable for students seeking more than basic formula application.

PREREQUISITES
  • Understanding of high school mathematics concepts, including Algebra 1 and 2.
  • Familiarity with Euclidean geometry principles.
  • Basic knowledge of trigonometric functions and proofs.
  • Ability to engage with problem-solving techniques beyond rote memorization.
NEXT STEPS
  • Explore "Geometry Revisited" by H. S. M. Coxeter for advanced geometric concepts.
  • Investigate Kiselev's "Geometry" for comprehensive coverage of both planar and 3D geometry.
  • Research additional materials published by the Mathematical Association of America (MAA) for adept high school students.
  • Look into problem sets specifically designed for Trigonometry proofs to enhance critical thinking skills.
USEFUL FOR

Advanced high school students, educators seeking challenging materials for their students, and anyone interested in enhancing their understanding of high school mathematics beyond basic concepts.

Geometrick
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Hi,

I'm looking for good textbooks or problem books for a 9 and 10th grade students. Maybe not as difficult as the AMC or IMO level math, but some problems that require some thought rather than just plug and chug formulas. For example, I want to find a good problem set for trig proofs, and some of the textbooks I am looking in only have a few problems or none of them are too hard (i.e. they involve 2 steps at most).

This is mainly for Euclidean geometry, Algebra 1 and 2 and Trig.
 
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Algebra, Trigonometry, are two books by Gelfand.

Geometry Revisited by Coxeter.

They are both hard and aimed at grades 9-10.
 
Kiselev's Geometry (both I and II) are good geometry books for both planar euclidean and 3D geometry.

They're both concise but they contain more details than the average joe high school math book.

http://www.sumizdat.org/

also you might want to look at books published by MAA. A lot of them are aimed towards adept high school students, and the materials are a tad bit harder, but are doable.
 

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