楼主，我给你朋友推荐2本书，专门给中学生数学竞赛用的。书不仅仅有理论部分（比如各种theorum, principles, etc)，还讲解了几百道以前Mathcount/AMC8/AMC10 的考题。你让孩子先把理论搞懂了，然后看题和答案，看用哪个理论解题最好最快，举一反三。数学竞赛嘛，多刷题，尤其是以前的考题，很重要。

Geometry Problems For Math Competitions

https://www.amazon.com/Geometry-Problems-Math-Competitions-Jerry/dp/B09NRHHQHL/ref=sr_1_1?crid=1921WD6J224UZ&keywords=solving+geometry+problems+jerry+gu&qid=1704397969&sprefix=solving+geometry+problems+jerry+gu%2Caps%2C102&sr=8-1

A Guide to Probability and Counting

https://www.amazon.com/Guide-Probability-Counting-Jerry-Gu/dp/B0CC4K5FVB/ref=sr_1_2?dib=eyJ2IjoiMSJ9.nD0KhONOv9N8cHCfuuWCywI5wK-8vW2BZ8jyI24A26oQAWXvjWoQjNz4FP47gnss.tlLJbKcHAF7Vn4iwBgfyli_iWgfguAS68DHZsB2Xs20&dib_tag=se&qid=1708282525&refinements=p_27%3AJerry+Gu&s=books&sr=1-2&text=Jerry+Gu