92% Vax rate in my county (for 16+ yo's). My parents and DH and I have received our boosters. My college age kids wear masks outdoors, go figure, but I don't think they've been boosted yet. I have no idea if people are masking because I only leave the house to take walks outdoors. I don't mask outdoors, but I see others that do, and I feel embarrassed. I needed a few procedures and surgeries over the past few months, and there was a delay (about a week) because me and everyone else postponed medical screening for a year, and now we're all catching up. Since this pandemic began 2 years ago, I have yet to know anyone personally who has been sick with covid.

@Not_a_Number recommends black jack!

It depends on the college and it depends on your score.

Congratulations. I'm not well-versed in these things, but I heard anecdotally secondhand that Northwestern is particularly extreme in terms of the difference between ED and regular admissions. So good for your student, I hope he gets in!

I think taking DE courses at a well known school like E-R puts you on safer ground than taking courses at an unknown CC. Are these the same classes that regular undergraduates take? If so, I would make this abundantly clear in your course descriptions. He may be able to prep, but before you embark on this path, have you already located a site that will allow your student to test? Finding a school that will allow you to test was always hit or miss before the pandemic, and even this year it is still difficult to find a campus open to outsiders. Check this first, otherwise I think you are are fine with the E-R classes.

When you square both sides of an equation, you risk introducing extraneous solutions, so you need to test all your solutions in the original equation. Plugging in into the original equation we get the left hand side, and the right hand side, , so this is extraneous. Trying we get both sides of the original equation, , so this is our valid solution.

You can use whatever grading scale you prefer. There's a field on the Common App (or maybe a pulldown menu) to tell them what you use. I used +/- distinctions, but they are different from what you cited. I add 0.3 for a + and subtract 0.3 for a -. So B = 3 B+ = 3.3 B- = 2.7 But you can do whatever you prefer.

Good questions. You can represent ratios as fractions. "50 miles per hour" can be written as with the fraction bar replacing "per." Or in the context of pediatric medication dosing, on can write "20 milliliters per kilogram" as . I think of "per" as a synonym of "for every." It's similar to using "of" to represent multiplication. Have 2 of a quantity is akin to have 2 times a quantity.

I'll add that the Question Bank is really lovely. You can select problem topics, calculators or no, and generate nice worksheets with tons of practice problems and detailed solutions. It's terrific resource for prep.

I also scratched my head, isn't finding the derivative basically the first half of calculus? In answer to your question about preparing for the AP exam, I recommend going through the College Board audit so you can access their Question Bank and old exams. There are some idiosyncratic questions on the AP exam that you don't want to be parsing for the first time on the exam itself. There are lots more resources available once you get approved. If you select one of their sample syllabi, your approval will be automatic and within a few hours. If you submit your own syllabus...expect to wait several weeks or months for approval. I do this for my students who are using AoPS for calculus because the textbook doesn't have enough or the right kind of practice problems to ace the BC exam.

@VminusEplusFis2 From the Wikipedia article: The Feynman Lectures are considered to be one of the most sophisticated and comprehensive college-level introductions to physics.[5] Feynman himself stated in his original preface that he was “pessimistic” with regard to his success in reaching all of his students. The Feynman lectures were written “to maintain the interest of very enthusiastic and rather smart students coming out of high schools and into Caltech”. Feynman was targeting the lectures to students who, “at the end of two years of our previous course, [were] very discouraged because there were really very few grand, new, modern ideas presented to them”. As a result, some physics students find the lectures more valuable after they have obtained a good grasp of physics by studying more traditional texts, and the books are sometimes seen as more helpful for teachers than for students. And a link to the Feynman treatment of speed and acceleration.

Yes, I will use both interchangeably, "mile an hour" colloquially or with advanced students, but "miles per hour" in academic context, particularly with young students who are learning rate/time/distance for the first time. It isn't typical to see rate/time/distance taught in a writing curriculum, but I think it's a worthwhile endeavor because there are nice equivalences between English and mathematics, and the word "per" as an indication of a ratio is a good one. This is typically discussed in math or physics classes, but I welcome the English department to describe this continuity as well. If I am teaching a younger student about rate/time/distance, I might explain that people will often say "miles an hour" when they really mean "miles per hour" and explain the use of the word "per." The Feynman Lectures on Physics are based on Richard Feynman's lectures to CalTech students in the 1960s. I have not read Feynman, and did not use the Feynman Lectures to teach rate/time/distance to my own students. I'm fairly certain Prof. Feynman is not introducing CalTech students to time/rate/distance, but like I said I haven't read the book, so I could be wrong. I'm guessing CalTech undergraduates ought to have understood this concept long before they arrived on campus. (My Wikipedia article lists mechanics, but also radiation, heat, electromagnetism, quantum mechanics.)

This is not a quote from UHP, but from her teacher's guide. I am curious if anyone else is bothered by the use of "miles an hour" in a document decrying a lack of understanding of the concept. To my mind, "miles an hour" is not accurate. One should write "miles per hour" which is consistent with the idea of a ratio or a fraction. I had fun with a group of students explaining Galileo's dictum. If you are traveling in one space ship with no acceleration, and you see another space ship pass you by, you have no idea whether that space ship is traveling faster than you, or you are going faster than it, or perhaps you are traveling in opposite directions. Minds were blown that afternoon. I tried repeating it with another group of kids, and they just weren't getting it. 🤷‍♀️ I also enjoy describing how velocity can be negative or positive and layered on top of that you can have a negative or positive acceleration. It's all fun stuff.

By "College Calculus and Physics" do you mean AP level? Or is there a specific calculus course or college level physics course like Light and Heat?

I'm just curious and not at all well informed on this topic. Doesn't the federal government issue bonds like all the time, every year? Or are there some years when no bonds are issued?

The thing is, a high SAT score is not very helpful because as you say it's easy to max it out. A kid with a math 780 could be anything from a student from a stable home who did his homework every night to an IMO kid like @Not_a_Number. Not that I know much about MIT, but I wouldn't say it's all about admitting students from stable homes. Thank you for owning up to liking the American system, because I also have affection for this system, despite its many, many flaws, with sports at the top of my list. I prefer it to, say, the Korean system of one exam and you are either in or out. We are a test-loving family, but one annual exam is too much for even my nerves. While less helpful exams like the SAT go away, I think there will always be contests and other opportunities like AMC, USACO, and even the National Mythology Exam for students who have an interest in whatever they truly enjoy.

This is my experience from a couple of years ago, so grain of salt. I'm pretty sure that everything on the Common App is reversible until you hit the final, final, submit button. The one where everything is complete and ready to be sent to colleges. Before that you can upload the transcript and see how it looks. I recall being disappointed that the CA added a wide margin to all my pdf's so I changed my margins to make it look more normal. I uploaded and deleted documents multiple times to see how things looked and how I could organize my documents in their fields. Also, know that the Common App customer service is quite good. They are responsive and helpful.

I also don't enjoy reading the transcripts. Part of it is I don't like to read long things online, and I wonder too if it may be easier if it were in 2 column format, I don't know. Just FYI, it won't take 1.5 hours to reread, lol, and turning off the student contributions makes it a bit easier, but not by much.

Yes, I'm a tutor, and so many students fit your son's description, I think AoPS has created a little niche for me. I'm like a human discussion board, but I answer questions in real time, and with a sense of humor thrown in. I also model skills like organized and clear mathematical writing. I help newbie students gets started with LaTex. In the example you provided with the line and parabola, if we find an solution or two, then before we enter the solution, I suggest we check it against the two original equations to show that it satisfies both. This last step serves 2 purposes: (1) Reminding us after all that algebra, of what we are actually trying to solve and why and what the geometric interpretation might be, and (2) reinforcing the importance of checking our work. I also conspicuously cross my fingers whenever a student enters her answer and clicks Submit. You can't be too careful when homework points are on the line. If it helps, the reading assignments are at the top of the weekly homework: I think the most committed students actually work through the textbook before lecture. They do all the problems and exercises, which enables them to participate more easily, and polish off the online homework. If it sounds like overkill, my daughters only did the textbook problems, and didn't do the AoPS online classes.

Parents call me for just this reason. 😉 I've seen discussion board threads about the writing problems that were a nightmare to parse. Multiple students posting to the same thread along with multiple TAs responding. Sometimes variables get changed in the process leading to more confusion, not less. Students post their solutions only to be redacted later. I think a lot of the TA hints are scripts as well, so I don't think the responses are very personal. I do exactly what you describe. I remind the students of what they learned that week. "Lecture this week was about similar triangles. Do you think similar triangles might be helpful here?" I know the transcript is available, but for younger students it can be a big ask to get them to reread the transcript. So I'll sometimes review the transcript with the student, or just make up my own practice problems. I agree I think using the textbook is a better option for most students.

I think transparency is illegal. https://theconversation.com/what-the-california-vote-to-keep-the-ban-on-affirmative-action-means-for-higher-education-149508

I agree with @Lori D. that awards in middle school aren't supposed to be included on a college app, but there are ways to sneak it in. I also like her idea of calling the classes Honors and then including something in the course description about honors designation awarded to students who achieve High Honors on the NGE. Another thing your student can if Greek or ancient languages or similar will continue to be a topic of interest in high school: he can mention his middle school awards in an essay or short answer part of his college app. Something along the lines of, "I was so pleased to be among the 5 people out of 2 million Greek students who earned High Honors on the NGE, that I was inspired to continue my studies in high school..." or something like that.

I write LoRs for my online students all the time. Even before the pandemic when I was meeting kids in person, I didn't really know them outside of class. I think teacher LoRs are speaking to a student's academic performance and interactions with the student. I think the Counselor Letter is really more about a student's personality and integrity and other soft characteristics.

^^^This this this. Exceptions are made for exceptional students, but one doesn't know if a student is exceptional until they apply. If it is truly onerous, I would write that the required info is in the Course Descriptions and School Profile. Maybe it is, maybe it isn't. I might also take a stab at approximating the information that was required, along the lines of @Farrar's suggestion. I can imagine some gal on the admissions committee looking over the homeschooling requirements and thinking to herself, "Wow, those requirements are really out of line and not helpful anyway." But if you've ever been part of a large org, you know that to get a front facing website changed requires meetings and approvals and TIME. Probably not worth the effort just to be nice to homeschoolers.