Just keep in mind that the UCs do not give financial aid to nonresidents. I think out-of-state cost of attendance is around 65k-ish though perhaps it varies by campus.

Loyola Chicago has a beautiful, cold campus and the NPC gave us a price around 40k (21k merit estimate off 60k COA, when I ran it last spring; that may be outdated by now). I'm not sure how reliable the NPC merit estimate is, but my sense is that bigger scholarships are not uncommon.

The comparison of a homeschooler's transcript to a private Christian high school's transcript may not be super helpful because these high schools have relationships with the colleges. The colleges have particular rigor expectations for the students they select and some familiarity with the high school's rigor even for regular, non-AP classes. (Private high schools do vary in rigor.) Homeschooling is outside that box but I imagine less frame of reference for the admissions officer. With the disclaimer that I am truly just guessing, I'd think there are plenty of kids with few APs from private religious high schools applying to mid-tier Christian colleges, though maybe it depends on what you mean by "mid-tier." My kids attend a fairly rigorous Jesuit high school where many students apply to mid-tier Catholic colleges at every level of student - these colleges will be reaches for some students, matches for many, and strong students use these colleges as safeties. In this high school, strong students will have 6-8 APs and only a handful of students will have more than that. The rest may have few APs or even no APs - it varies quite a bit. More guessing: from our kids' high school, 3 APs would probably be sufficient for most mid-tiers, but it really depends on the particular colleges. The published stats, especially acceptance rates, at many of the Catholic colleges can be a bit deceptive. SCU is an obvious example that I would not consider to be mid-tier any more - in spite of a 50% published acceptance rate and >60% in our high school's Naviance, most of the acceptances to SCU from this high school are strong students who would have more than 3 APs. Perhaps USD, LMU, Providence College, Loyola Chicago, Loyola Maryland would be better examples as mid-tier and my guess is 3 APs from this high school may be enough for students considering these colleges as matches (ACT middle 50 percentiles for enrolled students is 26-30 for all of these colleges, although their acceptance rates vary from 50 to 75%). My dd will be applying to 2-3 from that group as low matches/safeties; she will have 7 APs total (3 junior yr, 4 senior yr). A Christian but-not-super-religious mid-tier that comes to mind is TCU. I know someone there who probably had around 3 APs from a public high school. Loves it.

Just open a parent practice account. https://www.commonapp.org/whats-appening/college-counseling/whats-common-app-practice-account

Next summer, just do a practice test to see how close he might be. That would be the best approximation. https://collegereadiness.collegeboard.org/psat-nmsqt-psat-10/practice/full-length-practice-tests I'm not positive, but I think the second practice test was the 2016 administration. If you decide he should prep, use SAT prep. In our house, ACT and SAT results are not comparable (i.e. the concordance is not helpful) due to personal strengths and weaknesses that render the ACT unsuitable (speed). As far as comparing PSAT and SAT, in theory, a student should receive the same numerical score on both tests if they were taken on the same day. I'll never understand the point of the lower ceiling on the PSAT, but College Board set up this system so that students would see growth in the form of score increases between the time of the PSAT fall junior year and the time that they typically would take the SAT the following spring or fall. NMSQT relies on the Selection Index instead of the four-digit PSAT score. To calculate the SI, add together the subscores for reading, writing and math (each out of 38 total possible), and then double.

What an admissions officer will infer from a graded AP course without a self-reported test score is an open question. That would be really interesting to ask an admissions officer someday if I ever get the opportunity to do so anonymously. From what I have read, this varies by school - some super-selective schools care, others do not. I have a hard time imagining that a great deal of attention is paid to data points that are not present in the short time an app gets read, but we are not looking at extremely selective, HYPS-level schools. One anecdotal example I read about was U Chicago, where a person claiming to be a former admissions officer said they care about missing AP scores, but that person worked there >5 yrs ago, and since then the school has changed its written testing policies for SAT/ACT. Their new test-optional policy surely has its share of a need to read between the lines, but it is premised on the idea of reporting what the student feels is representative. A homeschooled AP course may make reporting much more important; I have not looked at homeschooler app requirements. Incidentally, over the summer, a lot more colleges changed their regular, non-homeschooler testing requirements to allow self-reporting of SAT/ACT scores in the app - seems much more common than it was even a year ago. (The Common App includes the ability to self-report an AP test, taken or planned to take, the date, the subject and the score. The student can include as many or as few as they wish. Tip: the Common App allows you to open a parent "practice" account that allows you to see all of this.)

Maybe just ask for a copy of the transcript. At my kids' school, the transcript reports two semester grades for a year-long class (which I thought was typical). I agree -call or email guidance. You don't have to say which class you're thinking about.

One of the possible ways is by placement test. What other way are you thinking about that isn't offered? I was under the impression that at most colleges, a math placement test is to be expected, unless the student has AP credit. Shouldn't the student who took calc in high school be able to pass the placement test (that is likely precalc content)?

I had it all mixed up; my apologies. https://pre-ap.collegeboard.org/frequently-asked-questions

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Mind if I ask what colleges asked for AP scores to be sent from College Board? I was under the impression that no colleges require an official AP score report for admission purposes, but only later, for placement and credit.

Look better for admissions? My understanding is that scores are self-reported on the common app. It's unclear to me whether officially-sent AP scores are even seen by admissions or are sent directly to the registrar's office for credit and placement. When self-reporting, a low score can be omitted, looking as if the student didn't take the test, or took it and scored poorly - colleges are not going to know which was the case. While I've seen some people suggest that the college will assume the worst (low score), intuitively I imagine that app readers aren't devoting time to conjecture on whether the test wasn't taken or whether the score was low, but simply moving on as there's no data point - too little time. Some colleges award credit for a 3. I'd suggest taking the test to see what happens.

There is wide variation in competitiveness by school https://admissions.illinois.edu/Apply/Freshman/profile

I believe MIT only has EA, nonrestrictive.

nevermind - I see it discussed over at CC