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[quote=pettifogger][quote=Anonymous]OP.  We have been doing AOPS's Contest Math for Middle School (small paperback) after the intro series.  It was a good book to practice, but DC is sick of it (we repeated the missed questions up to 4 times).  Then, I randomly purchased from Amazon Learn or Review Trigonometry Essential Skills, but it is too easy.

DC is not math genius, and we are not that interested in pushing for the contest math direction.  DC recently took AMC8 at school though.

I looked at the AOPS's Intermediate Algebra book, and it seems too difficult/unnecessary.  Alcumus is recommended, and we will do, but I am looking for a next book to work on.

Is AOPS's precalculus book a bad idea (wondering this book may be easier than Intermediate Algebra?), or do you recommend just repeat Intro to Algebra book for a second round?
 
   
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While starting to learn the beginning of AoPS Precalc would not be a bad idea, I would personally not recommend it until they have a very good grasp of algebra. Despite its smaller size, the precalc book has more difficult material than Intermediate algebra (for the most part). The book is very different from a typical K12 precalculus book. It essentially teaches three topics in great depth, connecting them all together: 1) Trigonometry in the first third of the book, 2) Complex Numbers in the second part of the book, and 3) Fundamentals of Linear algebra (vectors, matrices in both 2D and 3D) as well as a final chapter on solving tough geometry problems using vectors and other tools learned in the book. Some of the problems (not all) can be very difficult, and a few have appeared in past high school Olympiads such as the USAMO, etc.

I think the most important principle is that your DC should enjoy math (CMMS is a lovely little book, but I don't think it was a great idea to have made them repeat problems they missed 4 times, as that is not a recipe for enjoyment...) One way to do that is to solve lots of interesting problems at an untimed and relaxed pace. A few ways that could be done is by perusing the AoPS site and cherry picking problems that look interesting to them (i.e from the past AMC 8 or even AMC 10 questions) or perhaps via playing Alcumus (which itself contains a very large collection of problems, many from past contests).

Earlier in this thread I have recommended for you Anna Burago's Mathematical Circle Diaries. If your DC finished the Intro series, Year 2 (the second book in the two book series) would be more appropriate. It contains many interesting problems organized by various topics, that are excellently curated, similar to AoPS. It introduces students to some difficult ideas that most don't see until a discrete math course in college (i.e Pigeonhole Principle, Invariants, Parity, Combinatorics, Graph Theory, etc) via approachable problems aimed at advanced middle schoolers. Some of these topics are really very lovely, but sadly AoPS did not include them in their books (other than perhaps in their Intermediate Counting and Probability book, which is an amazing but challenging book, on par with their Precalculus or Calculus book).[/quote]

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