I'm still using the book that Momto6inIN linked with my students. 🙂 Besides modeling how to write great FRQ solutions, it also has a topical index that allows you to pull up FRQs on any specific topic that your student needs. I also used Barron's review guide (for MC practice) and a full released exam just before the real AP test in May.

It's difficult to give advice without really knowing your child 🙂 I'm a big fan, though, of not changing what's working well. So if Khan + Beast is working, I'd certainly keep going with that combo. As for when to move on to AoPS prealgebra, and which (if any) AoPS class to take, have you seen this advice from their site: What's Next after Beast Academy? Keep in mind that AoPS has a new self-paced option for prealgebra. Since your dd is on the young side, it might be a good way to transition into the online classes. She could still take advantage of teacher helps (like office hours and discussion boards and graded writing problems) while moving at a comfortable pace. AoPS Self-Paced Prealgebra Good luck!

Prayers that the chemo did its job & that the remainder of your treatment goes well 🙂

I've been using my Donvier half-pint for 30+ years. I think it's only available now used; the one I linked is still in the original packaging, though. This model makes a single cup serving at a time, and you only need to store the small inner cylinder in the freezer. Take it out, add your ingredients, turn the crank, and it's ready in 10-15 minutes. No mess! Lately I've been enjoying plain Greek yogurt with berries, but you can be as creative as you like.

I don't have a fluency test, but I also tutor high school math, and many of my kids are very weak on math facts. For those kids, I spend the last few minutes of every session playing the "24" game with them. I play the hardest level, and they choose the level they want to try. It seems to help with their fluency, especially in the case of my weakest kid. Listening in for more ideas!

Just catching up on the WTM boards tonight and saw this, lol. Here's a fresh link from the Barrons AP review book: (p.18 of the pdf) 4 Graphing calculator procedures needed on the AP Calculus exams

Praying for you!

My software developer son learned the basics of programming at about the same age as OP's son. For the middle school years, I let him have the freedom to build on that foundation and explore in a fun way. Believe me, I didn't put a lot of time into directing him, because he was wayyyyyy ahead of me already! I just supplied books and a few ideas. At the time, he loved playing a computer game called Chip's Challenge, so I challenged him to try to develop his own version of that game in one of the computer languages that he knew. It was quite a project, taking him the better part of middle school to perfect. Not only did he develop computer programming skills, but he grew especially in persistence and problem solving. He was really motivated to complete his other lessons so that he could run upstairs mid-afternoon and dig in. His sister was even recruited into the process as his art director! And I got free time in the late afternoon when nobody needed me. 🙂 We didn't even try AP classes with ds till he hit grade 10 (and he wasn't grade skipped)....AP CS AB (which was a harder version of the currently available AP CS A) was a cinch at that point. I'm glad we waited and had a stress-free experience. APs take more than knowledge; they take steady nerves, quick recall, good writing ability, and excellent time management. Ds was also a big-time USACO kid, but again not till grades 10-12. He made it to their highest level and just missed being picked for the summer training camp. He found that the free training problems on their website were great prep for their contests. Do they still have those available? None of this got him ANY credit for exempting class work at college (MIT). He started at the beginning in their computer science curriculum, and was right there alongside equally experienced & capable kids (which he loved!). He did tell me once that those USACO problems gave him a huge jump up on college CS work, though. And he's enjoying the life of a Silicon Valley software developer now. 🙂

Oh my gosh, where's that rolling on the floor laughing emoji? Scary flashbacks of middle school and those horrible belts... Yep, I'm old, too... 🤣

My daughter also wanted a more fun and literature rich 12th grade year after an intense year of PA Homeschooler AP English Language class in 11th grade. We decided we'd read together all those books which for some reason or other, we'd never gotten around to reading, but would be a shame to miss. The year started with How To Read Literature Like a Professor, which gave us a basis in analyzing literature. We then went on to read The Great Gatsby, The Awakening, The Bell Jar, Wuthering Heights, Beloved, Heart of Darkness, Macbeth, The Poisonwood Bible, The Glass Menagerie, a bunch of Chaim Potok, and a selection of short stories and poetry. I might be missing some, but I do remember that it was lots of fun!

My kids used Palma's REA review book, Excelability, and the test in the Official SAT subject test guide, as mentioned above. One other (free!) source for review are the released NLE exams online. The grammar questions and reading passages from Level 3/4 Poetry or Prose are great for SAT subject test study. Just skip the culture & history questions.

My daughter went through high school back when there were two AP Latin tests. Her high school years looked like this: grade 9 - Caesar (using Henle 2) grade 10 - AP Vergil grade 11 - AP Literature (Catullus & Cicero) grade 12 - independent study of Ovid and Horace As I recall, she really enjoyed both Ovid & Horace, so maybe your daughter would like Horace, too. She used these texts from Bolchazy Carducci: Horace: Selected Odes and Satire A Horace Workbook

Oh cool, thanks for the info! When I get home from traveling, I’m going to dig out my Dover catalog 🙂 i *still* have my whole collection of fun math books on the shelf that I started accumulating when my boy was little (including that cute Don Cohen spiral book)...and he’ll be 31 next week! And I may have a couple from when I was a little girl, too (but not telling my age, lol). Isn’t the Shanks et al precalc great? I even brought my copy on this trip...It’s been helpful with one of my better tutoring kids this year. 🙂

I agree with square_25. That sounds like a really cool calc book. I own about a gazillion math books, but i’m thinking that I need another one now, hmmm! Good luck and wishes for happy math adventures to your son 😀

Think about it this way: Since the ui >0, you know also that ui + 1 >0. You need to show that the infinite product (u1 +1 )*(u2 + 1)* (u3 + 1).... converges. But by the given inequality at the top of the problem, you know that each ui + 1 < exp(ui), so the product (u1 +1)*(u2 +1)*(u3 +1)...< exp(u1)*exp(u2)*exp(u3)....=exp (u1 + u2 + u3 + ...) by exponent rules. Since the infinite series u1 + u2 + u3 +.... converges (given), it has a sum S which is a positive real number. Then (u1 + 1)*(u2 + 1)*(u3 + 1)...< exp(S), showing that the infinite product converges. Hope that helps 🙂 I'll leave the proof of the converse to your son.

So thankful to hear this! You have been on my mind a lot lately ...I know how it feels to wait for those results.

As the mom of a full time AoPS employee, you are spot on!

One other quick thought: Take your nausea meds *before* you feel nauseous! I decided to tough it out the first week, and I went from feeling fine after the treatment to severe yuckiness in a heartbeat...After that I took my meds as soon as allowed after treatments, & I didn't have any more queasiness.

Praying for you that your treatments aren't too hard on you & bring you full healing.

What kind of calculator do you have? Sometimes there's a Mode button which brings up the settings menu (my TI 89). My TInspire has a Settings choice on the main page. I go there and choose Document Settings. I'm running out the door now, but i'll check in later.

Your daughter's calculator is set to radians instead of degrees. That's it! I tutor trig and that's a very common problem with my students.

Math Kangaroo: old papers

That's wonderful that things are moving quickly for you. Your husband's boss is a gem. My dh was told the same thing & it helped tremendously that year. Still sending positive thoughts and prayers your way.

Arcadia, I don't have any experience with getting a 2nd opinion for my BC, but my OBGYN directed to me to a surgeon & oncologist team that I had absolute faith in. If you don't, then by all means seek a 2nd opinion. Sending you hugs and lots of good wishes. I've survived stage 2b, grade 3, estrogen + BC after lumpectomy and chemo and radiation. There is lots of hope with modern treatments. If you have specific questions, I'm here for you, too.

I agree with everything here. My first thought was to recommend Patty Paper geometry, but after reading the examples of problems that gave him a hard time, I think he's beyond that. It sounds like he can already do the basics, but geometry tends to be difficult when you have a problem that integrates several ideas. It's like having a big toolbox & needing to know which tools to pull out for a given job. Sometimes only lots of experience in problem solving will do the trick. You might want to take a look at the original AoPS problem solving Vol 1. It sounds like he might be ready to tackle some of it. I've always thought that the geometry chapters were brilliantly done. In Ch 11.9, for instance, the authors give hints on how to tackle geometry problems that have you stumped...One of them is daijobu's hint of "drawing a line that isn't currently in the diagram." The text states that this is the "most difficult to master," and goes on to give more helps and problem solving practice. I still refer back to that chapter often in my teaching & learning. Your son might also enjoy going through the geometry problems in old AMC 8s and MathCounts (school handbook, past competition) papers. If you use apps with him, there's a cool MC trainer app (from AoPS), too. It's not strictly geometry, though.