Should I take Calculus 2 my freshman year of college?

[Asker321]

I self-studied Calculus 1 (AP Calc AB) in my sophomore year of high school and I got a 4 on the AP exam.

I took the class Calculus 2 (AP Calc BC) in my junior year of high school. I did not take the exam at the end of the year.

I didn't take any math in my senior year of high school.

Because I passed the AP exam for Calc AB, I cannot get any credit from taking Calculus 1.

If I were to take Calculus 1 my first semester, I will have to take 2 math courses my next semester (Discrete Mathematics and Calculus 2).

I think that would be more difficult, so I'm not sure if it's the best decision.

Should I go straight to Calculus 2 my first semester instead?

 

[Buzz Bloom]

If you are looking forward to a non-academic career in Applied math, Calc 2 is on that path, and Discrete Math is probably not. If you look towards an academic career in Pure math, you will probably need both.

 

[symbolipoint]

I self-studied Calculus 1 (AP Calc AB) in my sophomore year of high school and I got a 4 on the AP exam.

I took the class Calculus 2 (AP Calc BC) in my junior year of high school. I did not take the exam at the end of the year.

I didn't take any math in my senior year of high school.

Because I passed the AP exam for Calc AB, I cannot get any credit from taking Calculus 1.

If I were to take Calculus 1 my first semester, I will have to take 2 math courses my next semester (Discrete Mathematics and Calculus 2).

I think that would be more difficult, so I'm not sure if it's the best decision.

Should I go straight to Calculus 2 my first semester instead?

Use the results of whatever your university's (or college's) Mathematics Placement Test says.

 

[symbolipoint]

I didn't take any math in my senior year of high school.

Because I passed the AP exam for Calc AB, I cannot get any credit from taking Calculus 1.

If that is your case, THEN ENROLL IN CALCULUS 1, unless your current competence is less.

 

[vela]

If I were to take Calculus 1 my first semester, I will have to take 2 math courses my next semester (Discrete Mathematics and Calculus 2).

I think that would be more difficult, so I'm not sure if it's the best decision.

Should I go straight to Calculus 2 my first semester instead?

Is there a reason you think you should take Calc 1? You self-studied the material and then saw it again in AP Calc BC. What's the point of seeing it a third time?

Why do you think taking two math courses is going to be difficult? What else are you taking? What are you majoring in?

 

[gwnorth]

Since you did well on the Calculus AB exam and you've already taken Calculus BC, I see no value in doing Calculus I again. If you want to be sure, see if you can get a hold of the final exam for Calculus I at your school and see how you do on it.

 

[mathwonk]

I am a retired college professor who had many students in your situation. Unfortunately none of them ever asked my advice on what to do. The short answer to your question is to interview with your college professors who will teach the classes you are considering and let them guide you.

The problem in my case was that my courses in college were a lot more demanding than the ones my students took in high school. So if I had a student who was advanced, as suggested by taking calculus in high school, then they made a mistake by taking ordinary calc 2 in college in two senses. i.e. it was a non honors class, hence the students in the class were not their peers in terms of ability, but also it was more demanding than what they were used to, so it was actually too hard for them.

Hence I would have advised them to sign up for the first year honors class, and retake calc 1 but from a higher point of view, e.g. possibly a spivak type class.

You say you cannot get credit for calc 1 since you scored too high on the AP test. At my school this was not technically the case, but it was true that you cannot get credit twice for the same course. So you can either choose to get exemption credit for calc 1 based on your AP test, or you can forego credit for that test score and then get credit for the course itself. Either way is more or less the same, but we did offer credit for the high level spivak type course of calc 1, I believe. In my opinion it is short sighted to seek college credit for high school courses, since those courses are often, but not always, less demanding and less useful as preparation for second year college classes.

However: the fact that so many high school students do take calc in high school and then ask for credit in college, has forced colleges to accommodate them, often by simply dumbing down the college level classes to a level that they can handle. Since there is no way for you to predict exactly what will be expected in your classes, you absolutely should meet with and discuss your background with your future teachers.

even then it may not turn out perfectly, and you may need to scramble to catch up, or drop back, or possibly advance further. good luck!

For your comparison, I attach one of my class notes from first semester and one from second semester honors calc, (but not "super honors" spivak calc) which my students found hard. The approach to convergence of sequences, via norms, is one I learned in a sophomore diff eq class in college. The approach to exponential functions is standard in many good traditional books like Edwards and Penney.

 

[symbolipoint]

it is short sighted to seek college credit for high school courses, since those courses are often, but not always, less demanding and less useful as preparation for second year college classes.

That is a very soft way of giving extremely important advice. Mathwonk, would you say instead something like, 'enroll into the courses for which you have the proficiency requirements'.?

 

[CrysPhys]

However: the fact that so many high school students do take calc in high school and then ask for credit in college, has forced colleges to accommodate them, often by simply dumbing down the college level classes to a level that they can handle. Since there is no way for you to predict exactly what will be expected in your classes, you absolutely should meet with and discuss your background with your future teachers.

It's been many decades since I graduated from high school, and I realize that AP programs have changed over time. Could you please clarify the above? Why are colleges "forced to accommodate" high school students seeking college credit for AP courses? Are you saying that they will go out of business if they don't?

If I recall correctly after these many, many moons, I took 3 AP courses in my high school senior year, and got a 5 in each AP exam. The college I went to offered zero credit for AP courses, but that was not a factor in my decision in choosing a college.

 

[CrysPhys]

That is a very soft way of giving extremely important advice. Mathwonk, would you say instead something like, 'enroll into the courses for which you have the proficiency requirements'.?

But doesn't this really mean that the AP exam system is flawed? That is, the score on an AP exam is supposed to indicate the proficiency of the student.

 

[Vanadium 50]

But doesn't this really mean that the AP exam system is flawed?

Flawed? I'm shocked. Shocked!

Let's consider it as if it were working as designed. Little Joey or Susie gets a passing score in Calc AB. They would get probably 3 hours of credit at Pig's Knuckle Community College (not a real place) for that. So would someone who took the class there and got a C-. Is that setting the bar very high?

Now Joey and Susie go to Top Notch College. Is it any surprise than TNC expects their students who pass Calc 1 to be more proficient than that?

Furthermore, the chair of TNC has been told by Admissions that she needs to accept AP credit, because it's a recruiting tool for excellent students, and if TNC doesn't accept them, the students will go somewhere else. So she needs to rig up some sort of fix, such as "OK, you get 3 hours of general university credit, but we'd really like to see you enroll in Honors Calc 1."

 

[symbolipoint]

But doesn't this really mean that the AP exam system is flawed? That is, the score on an AP exam is supposed to indicate the proficiency of the student.

No, no no; not at all. Student may well score adequately for some grade, but KEEPING the proficiency is something else. Three months of time change is fine for some students, but may be too much for other students. Even when I was regular college student, the only way I could manage successful passage of Mathematics courses was to review and repeat.

 

[gwnorth]

There is great variability in the rigour of first year college courses running the gamut from gen eds for non-majors to the required entry level sequence for majors. Add to that the difference in school rigour from open admission community college to highly selective 4 year university and there is no way that AP courses can match the most intensive of these courses regardless if a school offers equivalent credit for them. Unless a student had a high school teacher who taught to an actual college syllabus it is likely that the material learned in many AP courses is only sufficient to meet the lower bar of a gen ed course. Many students take AP courses in grade 9 or 10 with no prior preparation beyond the regular high school curriculum which would lead one to believe that many AP courses are not in fact equivalent to more rigorous first year college courses. Also it is important to realize that AP exam scores are a scaled score converted from a composite score and are not a direct conversion from a percentage grade though a 5 is said to be roughly equivalent to a 75% (and it is actually lower than that for some subjects). The College Board claims that a 5 is equivalent to an A+. I don't know of any college that awards an A+ for a 75% unless the marks are curved and a 75% represents the top end of exam scores (which it does not for AP exams).

My son did Calculus AB in high school here in Canada. He said that the AP course was not that much more advanced than the regular high school grade 12 Calculus course which is part of our standard curriculum and is a required prerequisite for university Calculus I. While he felt that AP Calc AB was excellent preparation for Calc I, it was not fully equivalent. He said that it covered maybe 3/4's of the curriculum of his university's Calculus I course for Math/Engineering/Physics majors which is in itself about 1/2 a review of the grade 12 material. So at most he was a 1/4 semester more advanced than those students who just had grade 12 Calculus as preparation. His university does not offer transfer credit for AP courses if the course is required for the major. They will only grant credit for electives.

With regards to the OP however, they have completed AP Calc BC which is supposed to be equivalent to 2 semesters of first year Calculus so it is much more likely that they have actually mastered the content of Calculus I and would be ok moving straight to Calculus II. Given that they have had a gap of a year with no math courses it would probably be a good idea for them to review the material during the summer before classes begin.

 

[CrysPhys]

No, no no; not at all. Student may well score adequately for some grade, but KEEPING the proficiency is something else. Three months of time change is fine for some students, but may be too much for other students. Even when I was regular college student, the only way I could manage successful passage of Mathematics courses was to review and repeat.

But this particular argument would also apply to students who take Calc X their first year of university, take the summer off, and then take Calc (X+1) their second year. Yet I don't think second-year students would routinely ask whether they should repeat Calc X (unless they did really bad), or continue with Calc (X+1).

Judging from other responses here, there is an issue with the level of proficiency developed by an AP course and indicated by the score on an AP exam.

 

[CrysPhys]

Many students take AP courses in grade 9 or 10 with no prior preparation beyond the regular high school curriculum which would lead one to believe that many AP courses are not in fact equivalent to more rigorous first year college courses.

Yes, I've found this bizarre. When I was in high school, only seniors could take AP courses. When my daughter was in high school, juniors could take some AP courses. Now I'm puzzled when I come across high-school freshmen and sophomores who are taking AP courses. Doesn't make sense if college-level courses are supposed to build on a foundation of high-school-level courses.

 

[Vanadium 50]

Now I'm puzzled when I come across high-school freshmen and sophomores who are taking AP courses.

The College Board is happy to sell tests to Freshmen. If they get a 1, it's not the College Board's problem, is it? And parents are happy to brag that their little Joey or Susie is taking AP classes. So who does it hurt exactly? Er...whom. Need to get my 5 in English.

Also, given that college standards are falling, this may not even be crazy. In a previous thread, we found a college that gives 3 hours of college credit for "Basic Mathematics", which is a prerequisite for something called "Pre-Algebra": Fundamental concepts in arithmetic, including fractions, decimals, ratios,proportions, percents; order of operations, measurement, and geometric formulas. 3 hours lecture, 1 hour laboratory.

If collleges give credit for middle-school work, why shouldn't high schoolers get credit?

 

[vela]

But doesn't this really mean that the AP exam system is flawed? That is, the score on an AP exam is supposed to indicate the proficiency of the student.

In my experience, the primary focus of many students, and often the teachers, is to do well on the AP exam, not to actually learn and understand the material at a college level. When I discovered one student didn't know what I thought was a basic concept, he mentioned how his teacher skipped it because it wasn't necessary for passing the AP exam. The bigger problem I observed was that many students had a high-schooler's approach to learning the material. They just wanted to memorize how to do different types of problems rather than understanding the material at a higher level. I imagine skipping Calc 1 and jumping straight into Calc 2 at a university might be a rude awakening for many students who discover that what's expected of them is now much higher.

For a good student/learner, the AP system may work as intended, but for most students, I think they and their parents are looking for AP credit to make their college applications look better. I don't know how well the system works for them.

My high school didn't offer any AP courses, but we had advanced physics and advanced chemistry courses. The teachers emphasized these were not AP courses. When asked about taking the AP exam, the teachers said students were free to take the AP exam if they wanted and could probably do well, but even if a student earned a high score, they recommended students still start at the beginning at whatever school they ended up at because (1) it didn't hurt to see the material again and (2) it's just easier for students to ensure they covered the same material their peers did.

 

[symbolipoint]

But this particular argument would also apply to students who take Calc X their first year of university, take the summer off, and then take Calc (X+1) their second year. Yet I don't think second-year students would routinely ask whether they should repeat Calc X (unless they did really bad), or continue with Calc (X+1).

EXACTLY! Yes! Exactly! That can and does happen. Three months of the summer is too long for some people (at least for a few people) if they do not maintain what they "knew" from their most recent course.

 

[CrysPhys]

EXACTLY! Yes! Exactly! That can and does happen. Three months of the summer is too long for some people (at least for a few people) if they do not maintain what they "knew" from their most recent course.

I still don't understand the point you're trying to make. Assume a college freshman:

(1) Takes a freshman college level course and at least passes; and

(2) Loses a good chunk of proficiency over the summer.

Then at the start of his sophomore year, he needs a catch-up review on his own once he starts his sophomore college level course on the same subject. That is, he does not have the option of: "Oops! I've forgotten too much over the summer. I guess I'll just have to repeat my freshman course, instead of signing up for the sophomore course."

But that's not the case with a high-school AP course. The freshman does have the option of: "Oops! My high-school AP course really was not the equivalent of a freshman college course after all. [Alternatively (according to your scenario), the high-school AP teacher did do a bang-up job, but the student forgot a good chunk over the summer.] I'll defer taking college credits for my high-school AP course; I won't place out of the freshman college course; I will sign up for the freshman college course."

 

[symbolipoint]

I still don't understand the point you're trying to make. Assume a college freshman:

(1) Takes a freshman college level course and at least passes; and

(2) Loses a good chunk of proficiency over the summer.

I made no assumption that way. My comments were more general.

 

[symbolipoint]

But that's not the case with a high-school AP course. The freshman does have the option of: "Oops! My high-school AP course really was not the equivalent of a freshman college course after all. [Alternatively (according to your scenario), the high-school AP teacher did do a bang-up job, but the student forgot a good chunk over the summer.] I'll defer taking college credits for my high-school AP course; I won't place out of the freshman college course; I will sign up for the freshman college course."

Then you do understand.

 

[mathwonk]

I just looked up a sample AP test, part AB and part BC online and scanned it. It strikes me as both trickier and more elementary, (in the sense of being less abstract and less rigorous), than a course I would usually teach in college. It consists almost entirely of computations, but perhaps trickier than most I would ask. But there is almost no theory at all, which I always include. There are a few questions that require the student to know the statement of a standard theorem or two, like the Rolle theorem or Fundamental theorem of calculus, but there are no definitions required and no theorem statements, and no proofs. Even at the second tier public state university I taught at, many non honors classes did require a student at least to know the definition of a limit and of a derivative, and often to prove something easy like the product rule for derivatives. In my honors classes we would often prove the existence of a global maximum for a continuous function on a closed bounded interval. The language is also not entirely universal. The term "Maclaurin" series to denote the Taylor series set at x=0 has no historical justification, at least according to my Harvard calculus professor, and hence is often not used. The term "relative maximum" is also not universal, since it is not specific (relative to what?), and the term "local maximum" is preferred, by me at least. I would often prove something like the fact that all monotone functions on a bounded interval are integrable, whether continuous or not, (due to Isaac Newton), and give discontinuous examples to check understanding of this. So students who jump from this level of high school preparation into my second college course are seldom prepared for the level of abstraction they will encounter. In later years I found myself reteaching the material from the first course quickly in the beginning of calc 2, from a higher point of view, but it was hard for the students anyway.

Simple but abstract things are hard to grasp, like the idea that the product rule has two parts: a theoretical part: 1) the product fg is differentiable if both f and g are; and a computational part: 2) in that case, the derivative of fg is f'g+fg'. Some of my students thought the second part was all there is, so potentially they would try to apply the second formula even if one of f or g was not differentiable. They could learn to parrot that the integral of any continuous function exists and is differentiable with respect to its upper limit, and they knew that e^(x^2) is continuous, but some would still say that the integral of e^(x^2) does not exist, confusing existence of a function with its expressibility in "elementary terms". This misses the whole point that one can use integrals of known continuous functions to define new differentiable functions. Such theoretical subtleties were apparently not sufficiently addressed in AP courses, and take some getting used to. This idea of course is used to give a rigorous definition to the natural logarithm function as the integral of 1/x, and may be used to give a rigorous definition of the inverse trig functions, as integrals of functions like 1/(Sqrt(1-x^2)), and later on may be used to define so called "elliptic functions" by using cubic polynomials in place of quadratic ones. This is part of the struggle to have students appreciate that a "function" f is any way at all of specifying a value f(p) at each point p of a domain, and f need not be expressible as a familiar formula. Failing to grasp this blocks the way to much of mathematics.

https://secure-media.collegeboard.o...ple-questions-ap-calculus-ab-and-bc-exams.pdf

 

[jtbell]

even if a student earned a high score [on the AP exam], they recommended students still start at the beginning at whatever school they ended up at because (1) it didn't hurt to see the material again and (2) it's just easier for students to ensure they covered the same material their peers did.

These points matter in a subject that a student is going to major in, or at least take higher-level courses for some other reason.

Using AP credit to knock out a general-education requirement in a subject that a student will not pursue further, is fine with me.