Such a student would be fairly advanced in any case, having taken BC as a junior, or early enough to have a score to show.
Probably not the best example. Aside from the fact that “only” 1/3 of the test takers for this exam take it before senior year, Calc BC has one of the highest percentage of 5’s, with 40%+ f test takers earning that score. So if an applicant got an A in the class with a 2, the AO should wonder about grade inflation.
“So if an applicant got an A in the class with a 2, the AO should wonder about grade inflation.” Yes, but if the adcoms aren’t factoring in AP exam results when evaluating applicants, they would have no way to even wonder about grade inflation.
“Such a student would be fairly advanced in any case, having taken BC as a junior, or early enough to have a score to show.” But would you consider a student who took BC as a junior and received a 2 necessarily advanced? I know of kids who scored 1’s and 2’s on BC calc as juniors and are taking multivariable calc as seniors. Clearly these students have not mastered single variable calculus. How are they possibly able to succeed in a legitimate multivariable class?
Another user posed it as a hypothetical - I would not get caught up on a hypothetical. For starters, the hypothetical student should have a hypothetical GC to suggest that perhaps Caltech is not the school for him/her. 
Calculus BC also has a strong self-selection effect, where the strongest-in-math students are the ones who take it (as opposed to AB). That results in lots of 5 scores.
If I were that student I wouldn’t report the score at all.
@OHMomof2 ^But if AP exam scores are not a factor in admissions, what difference would it make whether the student reported his score or not?
Is this a high school (as opposed to college) multivariable calculus course? If so, it may be a watered down version.
But if students two grades ahead in math, theoretically top students in math, are earning scores of 1 or 2 (instead of 5), something is wrong. Either inappropriate acceleration in math, or poor quality teaching.
@ucbalumnus Yes, it is a high school course. But without AP scores, how would an adcom know the class was watered down? The transcript would have AP Calc BC: A in junior year and multivariable senior year. Scores of 1 and 2 are the norm for this class each year.
Look, they can look at everything they get told about. No one knows how much the weight each element. A kid who is applying to Harvard is likely to have excellent grades and excellent scores, including excellent AP scores. A kid from an inner city school who gets the first 4 anyone has gotten in that AP class and has a teacher saying this is the best kid I’ve ever had, is going to be looked at differently than one coming from a school where nearly everyone gets 4s and 5s on their AP tests.
FWIW many eons ago I got an A in AP Calc and a 2 on the exam. I don’t know what happened on that exam. I choked. I actually think I knew the material well enough.
A few years later (having forgotten all the calc I ever knew) I took Calc 1 as a self-paced course at Harvard. I got an A, finished the final exam before the half way mark and was asked to correct homework the following year. You don’t get second chances on AP tests - unlike the subject tests. If you are sick or distracted you are out of luck.
Caltech is probably not the best example here.
I suspect they do look at AP scores reported on the application for admissions purposes in math and sciences. I strongly suspect they would not want to subject a student to their math sequence if they got a 2 in AP Calc (which as others have stated is relatively rare because of the self-selection for who takes the course).
Given the usual distribution of scores on the AP Calc BC test, I suspect that most Caltech students got a 5, and that having taken it junior (or sophomore) year is not particularly rare at Caltech. Most of the students in my son’s freshman physics class at Caltech had previously taken multivariable (and retake it at a harder level the 3rd quarter of freshman year).
My son’s private school only had a few AP courses as they have their own honors curriculum. In addition, the campus was adjacent to our regional community college, so kids took regular college classes as part of the high school’s curriculum. Physics, for example, was only offered at the college.
My son had no AP classes and didn’t sit for any AP exams. He went to a Top 25 LAC so the lack of AP classes didn’t seem to be a problem in his case.
If the college application provides an opportunity to self-report AP scores, an admissions reader who sees an AP course listed in 11th grade or earlier but no AP score will probably assume that the AP score was low.
@ucbalumnus “Not sure why a student would consider math and science for engineering majors (i.e. mostly physics, plus some chemistry, or more chemistry for chemical engineering) to be a “death march”, since they are more about problem solving rather than memorization, and engineering majors are more likely to have liked math and science in high school.”
Perhaps you aren’t familiar with the phrase. Here are a few references:
https://www.designworldonline.com/the-math-and-science-death-march/?cn-reloaded=1
https://www.timeshighereducation.com/news/learning-how-to-learn-beyond-the-math-and-science-death-march/2019628.article
https://www.nytimes.com/2011/11/06/education/edlife/why-science-majors-change-their-mind-its-just-so-darn-hard.html See “the math-science death march.” in paragraph 3.
@ucbalumnus “However, it is true that the end goal of engineering education is to prepare students for engineering design and related work, and some students may prefer a curriculum organized to introduce engineering design earlier, rather than the more traditional arrangement of natural science then engineering science then engineering design that is mainly based on prerequisite sequencing.”
While students might prefer it, the standards for engineering courses require the calc, diff.eq., physics, chemistry, organic chemistry, and thermo. You could take an intro version, but it won’t meet the standards and you will have to take it again after you finish the math and science sequence. Given that most successful engineering students are already adding a 5th year to graduate, that would make it worse.
Additionally, engineering majors nationally drop the major at a rate of about 60%. At a top school like UMich, for example, the most failed course is Calc II (a required engineering course). That suggests to me that an applicant who has a demonstrated ability to succeed in Calculus is a plus for admissions. It would be interesting to see the difference in the drop rate between students who begin with a 5 in BC Calc, and 5 in Physics C and students who have not taken those courses in high school. I suspect it makes a significant difference in success rates at the college level.
Better safe than sorry
I’m sure colleges consider everything they see on an app, including AP scores. But for all the reasons mentioned - primarily that most students will have few in time for senior year - I do not believe they are a factor of much significance.
@ucbalumnus “Not sure why a student would consider math and science for engineering majors (i.e. mostly physics, plus some chemistry, or more chemistry for chemical engineering) to be a “death march”, since they are more about problem solving rather than memorization, and engineering majors are more likely to have liked math and science in high school.”
Perhaps you aren’t familiar with this phrase. Here is an example:
@ucbalumnus “However, it is true that the end goal of engineering education is to prepare students for engineering design and related work, and some students may prefer a curriculum organized to introduce engineering design earlier, rather than the more traditional arrangement of natural science then engineering science then engineering design that is mainly based on prerequisite sequencing.”
While students might prefer it, the standards for engineering courses require the calc, diff.eq., physics, chemistry, organic chemistry, and thermo. You could take an intro version, but it won’t meet the standards and you will have to take it again after you finish the math and science sequence. Given that most successful engineering students are already adding a 5th year to graduate, that would make it worse.
Additionally, engineering majors nationally drop the major at a rate of about 60%. At a top school like UMich, for example, the most failed course is Calc II (a required engineering course). That suggests to me that an applicant who has a demonstrated ability to succeed in Calculus is a plus for admissions. It would be interesting to see the difference in the drop rate between students who begin with a 5 in BC Calc, and 5 in Physics C and students who have not taken those courses in high school. I suspect it makes a significant difference in success rates at the college level.
True, the prerequisite structure makes the traditional arrangement “optimal” in that respect. However, many colleges now are trying to incorporate design work earlier in the engineering curricula, presumably to keep students more interested and let them see how learning the prerequisite natural science and engineering science is important.
Most students generally take more than 4 academic years to graduate, so engineering is not that unusual in this respect. Engineering students may average slightly longer due to curricular difficulty, but length of time to graduation is mostly correlated to admission selectivity.
However, a top school is likely to retain a far higher percentage of engineering frosh to graduation with engineering degrees than the average-selectivity school. Even a course that is “most failed” may not have that high a failure rate. https://gradeguide.com/course/MATH/116/ indicates that only 2% of Michigan MATH 116 (calculus 2) students earned E (F) grades. An additional 5% earned D+/D/D- grades, and an additional 4% earned C- grades. Even with the most expansive non-pre-med definition of “failing” (C- to E), that means that only 11% “failed”. (Note: Michigan engineering requires C grades and a 2.0 GPA to declare major.)
Engineering is different though. At most colleges, their average students can’t get admitted to it. The high drop rate and extra year are occuring after selecting a much stronger group of students to participate.
I do think they could integrate the second year courses with engineering courses more. For example, instead of first taking orgo and then taking polymers engineering, a program could offer two polymers science and engineering courses that integrate theory and practice. This would allow students to more immediately understand why they need to know this material.
“Most” may only be in the context of capacity limited popular state flagships that are commonly discussed on these forums. At these schools, students are generally capable, though some of the have artificially high attrition due to weed out policies (e.g. Wisconsin, Purdue, and some others, but not Michigan).
Many colleges are much less selective, and are not more selective for engineering majors. Examples include many CSUs like SFSU, CSULA, CSUSac, CSUN, etc. In other states, there are schools like FIU, UTEP, UTSA, etc. Some forum favorites like Alabama (Tuscaloosa and Huntsville) also fall into this category.