First place Common Core only goes up to Algebra II. Or Common Core Algebra II. So you are asking two questions here. Common Core has no affect on how College Board (a private company) designed it's Calculus classes. Common Core has no plan for after Algebra II and districts are doing very different things for their higher level math. It's goal is to get most student to finish Algebra II by the end of H.S. (In my state you are only required to take one class above algebra..)
Second since Common Core only goes up to Algebra II (or Math III) you will have to see how your school or district handles this. There is NO one standard way of how to handle upper level math courses.
I'll start with Calculus question since it's simpler. AB & BC Calc are supposed to be either/or courses. But it seems this varies school to school. AP Classes are supposed to be "College Course" not High School courses. Check out the AP web-site for more details of those classes. According to them (and DS17's school) Calc AB is 2/3 of the normal college course (2 quarters or 1+ semesters) in Calculus and BC is a full year. But I've heard of many schools (through this board) that do this as a 2 year sequence. In my son's school AB is taught either/or.. they use exactly the same book. Except AB goes slower & only covers 2/3 of the material before the AP Test. BC requires being in the honors track, and if you are not covering several chapters as homework over the summer. Universities vary as to how these two tests are mapped to their courses. But I've seen a 4-5 on the AB test cover 1 college semester, 2 calculus quarters. And BC vary even more wildly.
First.. C-Math 1, Math2, Math3 is the same material as CC-Agebra, CC-Gemoetry, CC-Algebra II sequence but taught is in a different 'coordinated' order.
Common Core is complicated since the courses DON'T ALIGN with the old sequence. This is why there is a lot of confusion. Common Core added a course call Common Core 8th grade. This class includes some pre-algebra, about 3-4 chapters from pre-CC algebra books and 3-4 chapters from pre-CC geometry books. (Before CC average 8th grades were taking either pre-algebra or algebra in 8th grade) Standard Trig was pushed down into this sequence. (It's spread out.) Basically if you finish the sequence you cover more material and don't have to take a Trig course.
Because of this my local district decided you could go straight from CC-Algebra II straight to AB Calculus without needed a pre-algebra class. But honestly my district hasn't really figured out how they are going to handle the courses more advanced that Algebra II yet. They have to figure it out by next year.
This gets even more complicated when you start adding "compacted" classes for gifted/advanced kids. Common Core recommends that no one skip any math class. Instead this 3-year sequence is often "compacted" into a 2-year accelerated class instead. Some 7-8th graders are taking compacted 7th,8th-Algebra in two years.
To add to this discussion. The new SAT is now aligned to the Common Core Algebra II. The math on the SAT is now easier in some ways & harder in others. If you haven't taken Algebra II you won't have seen enough material. BUT the questions used to be trickier questions & the new test the questions are a lot more straight forward. It's more a test of if you have learned the material than can you think like a mathematician.
Last edited by bluemagic; 11/14/16 12:18 AM.