Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:Examples of compacted integrated math:
https://elm.sweetwaterschools.org/compacted-integrated-math-integrated-math-course-i-placement/

https://rdmcounseling.weebly.com/7th-grade-course-selection.html

You don’t seem to be familiar with the US curriculum, and just posted the first Google hits you could find.

Integrated math I, II, III refers to a mix of three years of algebra and geometry taught instead of the Algebra 1, Geometry, Algebra 2 sequence.

Integrated compacted math 6/7/8 doesn’t really mean much it’s the same curriculum but compacted so kids can accelerate.

In California schools there’s a push for integrated math which originates with social justice champions like Jo Boaler, whose initiative received a lot of criticism.

A feature of CA math pathways is the compacted IM 3 with precalculus which is disastrous. Also they make AP Calculus AB a prerequisite for BC which is ill advised.

Ding dong - did you open the second link?

Integrated math can be compacted, just like any other sequence.

Really, so any math sequence can be compacted?

The regular math sequence is Algebra 1, Geometry, Algebra 2, Precalculus, Calculus, Linear Algebra and Differential Equations, and you might add along the line Statistics and Discrete Math.

You don’t see this sequence compacted especially for the higher level classes unless the class is useless like compacted Algebra 2 and Precalculus or if it’s a magnet high school like Blair Functions but even then the kids come with Algebra 2 done plus a ton of enrichment.

You seem to be more familiar with elementary and middle school compaction classes. It’s done because those classes move very slowly and there’s a lot of repetition, high school math is different.

Thanks for proving my point. Yes, some schools do in fact compact HS-level math. One of my kids is in a compacted path right now. I am plenty aware.

Any sequence can be accelerated. Look at AB vs. BC -- BC is compacted.

Maybe you are stuck on the language? Compacted just means accelerated. They cover more content in less time.

Capiche?

Not sure why you insist on this as you’re clearly out of your depth. Calculus BC is not compacted, it covers Calculus 1 and 2, typically taught over one semester each in college, or one year in high school. You can say Calculus AB is more fluffy or equivalent to a lower level calculus like college equivalent of Calculus for life sciences and business majors.

LOL. Again, thanks for proving my point.

https://blog.collegeboard.org/difference-between-ap-calculus-ab-and-bc
"In other words, AP Calculus BC covers more content than AP Calculus AB"

"All topics in the eight units of AP Calculus AB are also included in AP Calculus BC. However, AP Calculus BC contains two additional units (Units 9 and 10), plus some extra topics in Units 6─8."

"AP Calculus AB focuses on topics that are taught in the college-equivalent first-semester calculus class. AP Calculus BC focuses on topics covered in both first- and second-semester calculus classes."

AB = Calc 1
BC = Calc 1 + 2

More content covered in less time = accelerated = compacted.

It must be hard for you to struggle so much with math and language.

You can call whatever you want accelerated or compacted, that doesn’t mean the rest of the world agrees. I had a good laugh at “compacted” and “accelerated” calculus.

While class contents vary, AP Calculus AB is more than just Calculus 1. Applications of integration and differential equations are usually Calculus 2 along with series and parametric functions. Other topics from Calculus 2, ie techniques of integration, and some integration applications like moments are missing from AP Calculus BC. That doesn’t mean college calculus is doubly accelerated and compacted compared to already accelerated and compacted BC. It’s just that there are different classes, students, majors, and graduation requirements.

By this silly argument Honors Precalculus would also be compacted and accelerated compared to regular Precalculus because it includes additional topics of vector algebra and conics. It’s not, it’s a different class that go into more depth and more topics.

Semantics aside, your entire point is finding some snippets online that you think validate your word choices. Try to contribute with something more substantive.

I'm sorry you are struggling with the definitions of these words. Maybe pick up a dictionary?

As for the content covered by AB/BC, I trust the College Board on this:
"AP Calculus AB focuses on topics that are taught in the college-equivalent first-semester calculus class. AP Calculus BC focuses on topics covered in both first- and second-semester calculus classes."

"The two courses cover content and skills that are introduced in a first-semester calculus course at the college level. All topics in the eight units of AP Calculus AB are included in AP Calculus BC."
https://blog.collegeboard.org/difference-between-ap-calculus-ab-and-bc

Integrated math is just the sequencing of content. Integrated math courses can be designed to be accelerated/compacted or advanced, just like any other sequence.

I’d take the College Board description with a grain of salt because they also have to back up the AP exam course equivalence.

Differential equations and Applications of integration from the description the AP Calculus AB syllabus are usually found in Calculus 2. While contents vary, see if you can find a Calculus 1 college course that covers these topics.

An example from UC Berkeley:

Calculus 1, Math 51
This course is intended for STEM majors. An introduction to differential and integral calculus of functions of one variable, with applications and an introduction to transcendental functions.

Calculus 2, Math 52
Techniques of integration; applications of integration. Infinite sequences and series. First-order ordinary differential equations. Second-order ordinary differential equations; oscillation and damping; series solutions of ordinary differential equations.

Arguably AP Calculus BC is not as in depth as a college calculus class. Even at the community college where my dual enrollment student took calculus there were many topics not touched in the AP Calculus BC. A few examples: logarithmic differentiation, techniques of integration (ie trig substitution), applications of integration (surface area of revolution, cylindrical shell etc), first order linear differential equations (AP only does exponential and logistic, college classes include integration multiplication factors). As shown in the example from Berkeley on Calculus 2, some classes go in even more depth for differential equations.

Berkeley is not representative of college math classes in general - it's in the top 20 out of 6000, or top one third of a percent.

https://www.mvsu.edu/academics/academic-programs/arts-sciences/departments/mathematics-computer-information-sciences/undergraduate/bs-mathematics/courses

MA 300. CALCULUS II. Differentiation and integration of transcendental functions, techniques of integration

https://kranishapcalculus.weebly.com/uploads/7/0/7/1/70719881/ap_calculus_bc_syllabus.pdf - this BC syllabus covers logs

Anonymous wrote:

Anonymous wrote:This is why the US has a math problem. Pedantic arguing of how to place math topics in high school that kids in countries like Turkey master in late elementary and middle school.

It sure seems likely to be part of the problem, but perhaps not the whole problem.

Anonymous wrote:This is why the US has a math problem. Pedantic arguing of how to place math topics in high school that kids in countries like Turkey master in late elementary and middle school.

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:Examples of compacted integrated math:
https://elm.sweetwaterschools.org/compacted-integrated-math-integrated-math-course-i-placement/

https://rdmcounseling.weebly.com/7th-grade-course-selection.html

You don’t seem to be familiar with the US curriculum, and just posted the first Google hits you could find.

Integrated math I, II, III refers to a mix of three years of algebra and geometry taught instead of the Algebra 1, Geometry, Algebra 2 sequence.

Integrated compacted math 6/7/8 doesn’t really mean much it’s the same curriculum but compacted so kids can accelerate.

In California schools there’s a push for integrated math which originates with social justice champions like Jo Boaler, whose initiative received a lot of criticism.

A feature of CA math pathways is the compacted IM 3 with precalculus which is disastrous. Also they make AP Calculus AB a prerequisite for BC which is ill advised.

Ding dong - did you open the second link?

Integrated math can be compacted, just like any other sequence.

Really, so any math sequence can be compacted?

The regular math sequence is Algebra 1, Geometry, Algebra 2, Precalculus, Calculus, Linear Algebra and Differential Equations, and you might add along the line Statistics and Discrete Math.

You don’t see this sequence compacted especially for the higher level classes unless the class is useless like compacted Algebra 2 and Precalculus or if it’s a magnet high school like Blair Functions but even then the kids come with Algebra 2 done plus a ton of enrichment.

You seem to be more familiar with elementary and middle school compaction classes. It’s done because those classes move very slowly and there’s a lot of repetition, high school math is different.

Thanks for proving my point. Yes, some schools do in fact compact HS-level math. One of my kids is in a compacted path right now. I am plenty aware.

Any sequence can be accelerated. Look at AB vs. BC -- BC is compacted.

Maybe you are stuck on the language? Compacted just means accelerated. They cover more content in less time.

Capiche?

Not sure why you insist on this as you’re clearly out of your depth. Calculus BC is not compacted, it covers Calculus 1 and 2, typically taught over one semester each in college, or one year in high school. You can say Calculus AB is more fluffy or equivalent to a lower level calculus like college equivalent of Calculus for life sciences and business majors.

LOL. Again, thanks for proving my point.

https://blog.collegeboard.org/difference-between-ap-calculus-ab-and-bc
"In other words, AP Calculus BC covers more content than AP Calculus AB"

"All topics in the eight units of AP Calculus AB are also included in AP Calculus BC. However, AP Calculus BC contains two additional units (Units 9 and 10), plus some extra topics in Units 6─8."

"AP Calculus AB focuses on topics that are taught in the college-equivalent first-semester calculus class. AP Calculus BC focuses on topics covered in both first- and second-semester calculus classes."

AB = Calc 1
BC = Calc 1 + 2

More content covered in less time = accelerated = compacted.

It must be hard for you to struggle so much with math and language.

You can call whatever you want accelerated or compacted, that doesn’t mean the rest of the world agrees. I had a good laugh at “compacted” and “accelerated” calculus.

While class contents vary, AP Calculus AB is more than just Calculus 1. Applications of integration and differential equations are usually Calculus 2 along with series and parametric functions. Other topics from Calculus 2, ie techniques of integration, and some integration applications like moments are missing from AP Calculus BC. That doesn’t mean college calculus is doubly accelerated and compacted compared to already accelerated and compacted BC. It’s just that there are different classes, students, majors, and graduation requirements.

By this silly argument Honors Precalculus would also be compacted and accelerated compared to regular Precalculus because it includes additional topics of vector algebra and conics. It’s not, it’s a different class that go into more depth and more topics.

Semantics aside, your entire point is finding some snippets online that you think validate your word choices. Try to contribute with something more substantive.

I'm sorry you are struggling with the definitions of these words. Maybe pick up a dictionary?

As for the content covered by AB/BC, I trust the College Board on this:
"AP Calculus AB focuses on topics that are taught in the college-equivalent first-semester calculus class. AP Calculus BC focuses on topics covered in both first- and second-semester calculus classes."

"The two courses cover content and skills that are introduced in a first-semester calculus course at the college level. All topics in the eight units of AP Calculus AB are included in AP Calculus BC."
https://blog.collegeboard.org/difference-between-ap-calculus-ab-and-bc

Integrated math is just the sequencing of content. Integrated math courses can be designed to be accelerated/compacted or advanced, just like any other sequence.

I’d take the College Board description with a grain of salt because they also have to back up the AP exam course equivalence.

Differential equations and Applications of integration from the description the AP Calculus AB syllabus are usually found in Calculus 2. While contents vary, see if you can find a Calculus 1 college course that covers these topics.

An example from UC Berkeley:

Calculus 1, Math 51
This course is intended for STEM majors. An introduction to differential and integral calculus of functions of one variable, with applications and an introduction to transcendental functions.

Calculus 2, Math 52
Techniques of integration; applications of integration. Infinite sequences and series. First-order ordinary differential equations. Second-order ordinary differential equations; oscillation and damping; series solutions of ordinary differential equations.

Arguably AP Calculus BC is not as in depth as a college calculus class. Even at the community college where my dual enrollment student took calculus there were many topics not touched in the AP Calculus BC. A few examples: logarithmic differentiation, techniques of integration (ie trig substitution), applications of integration (surface area of revolution, cylindrical shell etc), first order linear differential equations (AP only does exponential and logistic, college classes include integration multiplication factors). As shown in the example from Berkeley on Calculus 2, some classes go in even more depth for differential equations.

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:Examples of compacted integrated math:
https://elm.sweetwaterschools.org/compacted-integrated-math-integrated-math-course-i-placement/

https://rdmcounseling.weebly.com/7th-grade-course-selection.html

You don’t seem to be familiar with the US curriculum, and just posted the first Google hits you could find.

Integrated math I, II, III refers to a mix of three years of algebra and geometry taught instead of the Algebra 1, Geometry, Algebra 2 sequence.

Integrated compacted math 6/7/8 doesn’t really mean much it’s the same curriculum but compacted so kids can accelerate.

In California schools there’s a push for integrated math which originates with social justice champions like Jo Boaler, whose initiative received a lot of criticism.

A feature of CA math pathways is the compacted IM 3 with precalculus which is disastrous. Also they make AP Calculus AB a prerequisite for BC which is ill advised.

Ding dong - did you open the second link?

Integrated math can be compacted, just like any other sequence.

Really, so any math sequence can be compacted?

The regular math sequence is Algebra 1, Geometry, Algebra 2, Precalculus, Calculus, Linear Algebra and Differential Equations, and you might add along the line Statistics and Discrete Math.

You don’t see this sequence compacted especially for the higher level classes unless the class is useless like compacted Algebra 2 and Precalculus or if it’s a magnet high school like Blair Functions but even then the kids come with Algebra 2 done plus a ton of enrichment.

You seem to be more familiar with elementary and middle school compaction classes. It’s done because those classes move very slowly and there’s a lot of repetition, high school math is different.

Thanks for proving my point. Yes, some schools do in fact compact HS-level math. One of my kids is in a compacted path right now. I am plenty aware.

Any sequence can be accelerated. Look at AB vs. BC -- BC is compacted.

Maybe you are stuck on the language? Compacted just means accelerated. They cover more content in less time.

Capiche?

Not sure why you insist on this as you’re clearly out of your depth. Calculus BC is not compacted, it covers Calculus 1 and 2, typically taught over one semester each in college, or one year in high school. You can say Calculus AB is more fluffy or equivalent to a lower level calculus like college equivalent of Calculus for life sciences and business majors.

LOL. Again, thanks for proving my point.

https://blog.collegeboard.org/difference-between-ap-calculus-ab-and-bc
"In other words, AP Calculus BC covers more content than AP Calculus AB"

"All topics in the eight units of AP Calculus AB are also included in AP Calculus BC. However, AP Calculus BC contains two additional units (Units 9 and 10), plus some extra topics in Units 6─8."

"AP Calculus AB focuses on topics that are taught in the college-equivalent first-semester calculus class. AP Calculus BC focuses on topics covered in both first- and second-semester calculus classes."

AB = Calc 1
BC = Calc 1 + 2

More content covered in less time = accelerated = compacted.

It must be hard for you to struggle so much with math and language.

You can call whatever you want accelerated or compacted, that doesn’t mean the rest of the world agrees. I had a good laugh at “compacted” and “accelerated” calculus.

While class contents vary, AP Calculus AB is more than just Calculus 1. Applications of integration and differential equations are usually Calculus 2 along with series and parametric functions. Other topics from Calculus 2, ie techniques of integration, and some integration applications like moments are missing from AP Calculus BC. That doesn’t mean college calculus is doubly accelerated and compacted compared to already accelerated and compacted BC. It’s just that there are different classes, students, majors, and graduation requirements.

By this silly argument Honors Precalculus would also be compacted and accelerated compared to regular Precalculus because it includes additional topics of vector algebra and conics. It’s not, it’s a different class that go into more depth and more topics.

Semantics aside, your entire point is finding some snippets online that you think validate your word choices. Try to contribute with something more substantive.

I'm sorry you are struggling with the definitions of these words. Maybe pick up a dictionary?

As for the content covered by AB/BC, I trust the College Board on this:
"AP Calculus AB focuses on topics that are taught in the college-equivalent first-semester calculus class. AP Calculus BC focuses on topics covered in both first- and second-semester calculus classes."

"The two courses cover content and skills that are introduced in a first-semester calculus course at the college level. All topics in the eight units of AP Calculus AB are included in AP Calculus BC."
https://blog.collegeboard.org/difference-between-ap-calculus-ab-and-bc

Integrated math is just the sequencing of content. Integrated math courses can be designed to be accelerated/compacted or advanced, just like any other sequence.

I’d take the College Board description with a grain of salt because they also have to back up the AP exam course equivalence.

Differential equations and Applications of integration from the description the AP Calculus AB syllabus are usually found in Calculus 2. While contents vary, see if you can find a Calculus 1 college course that covers these topics.

An example from UC Berkeley:

Calculus 1, Math 51
This course is intended for STEM majors. An introduction to differential and integral calculus of functions of one variable, with applications and an introduction to transcendental functions.

Calculus 2, Math 52
Techniques of integration; applications of integration. Infinite sequences and series. First-order ordinary differential equations. Second-order ordinary differential equations; oscillation and damping; series solutions of ordinary differential equations.

Arguably AP Calculus BC is not as in depth as a college calculus class. Even at the community college where my dual enrollment student took calculus there were many topics not touched in the AP Calculus BC. A few examples: logarithmic differentiation, techniques of integration (ie trig substitution), applications of integration (surface area of revolution, cylindrical shell etc), first order linear differential equations (AP only does exponential and logistic, college classes include integration multiplication factors). As shown in the example from Berkeley on Calculus 2, some classes go in even more depth for differential equations.

Let's see what Georgetown thinks about AB vs. BC.
https://mathstat.georgetown.edu/undergraduate/advanced-placement/

If you get a 5 on AB, you can place out of MATH-1350.

If you get a 5 on BC, you can place out of MATH-1350 and MATH-1360.

You’re quite dense to say the least, read what was said up thread, you get worked up from misunderstanding posts. Calculus AB contains some Calculus 2 material, read the description of Math 1360 and you’ll see some of those topics are in AB, namely techniques of integration and applications of integration.

AB gets credit for Calculus 1, while BC gets credit for Calculus 1&2. This statement is not mutually exclusive with the first paragraph. AB can cover a portion of the Calculus 2 material but not get credit for it.

Now you're just being oppositional. LOL.

BC covers more content in a shorter period of time. It's irrelevant if AB happens to cover some of the calc 2 content. It doesn't cover enough to push you along further in the pathway. We can call it "calc 1 advanced" if you'd like.

Let's look at three students who are starting at Georgetown this fall:
11 - precalculus
12 - ap calc ab (low score)
13.1 - math 1350
13.2 - math 1360

11 - precalculus
12 - ap calc ab (score 5)
13.1 - math 1360
13.2 - math 2140+

11 - precalculus
12 - ap calc bc (score 5)
13.1 - math 2140+
13.2 - math 2250+

By covering the additional content at a faster pace than AB, kids who take BC and score a 5 may be able to place out of an extra calculus class in college and take higher-level math courses sooner. It's "accelerated" over Calc AB.

My original point stands:
Integrated math can be compacted, just like any other sequence.

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:Examples of compacted integrated math:
https://elm.sweetwaterschools.org/compacted-integrated-math-integrated-math-course-i-placement/

https://rdmcounseling.weebly.com/7th-grade-course-selection.html

You don’t seem to be familiar with the US curriculum, and just posted the first Google hits you could find.

Integrated math I, II, III refers to a mix of three years of algebra and geometry taught instead of the Algebra 1, Geometry, Algebra 2 sequence.

Integrated compacted math 6/7/8 doesn’t really mean much it’s the same curriculum but compacted so kids can accelerate.

In California schools there’s a push for integrated math which originates with social justice champions like Jo Boaler, whose initiative received a lot of criticism.

A feature of CA math pathways is the compacted IM 3 with precalculus which is disastrous. Also they make AP Calculus AB a prerequisite for BC which is ill advised.

Ding dong - did you open the second link?

Integrated math can be compacted, just like any other sequence.

Really, so any math sequence can be compacted?

The regular math sequence is Algebra 1, Geometry, Algebra 2, Precalculus, Calculus, Linear Algebra and Differential Equations, and you might add along the line Statistics and Discrete Math.

You don’t see this sequence compacted especially for the higher level classes unless the class is useless like compacted Algebra 2 and Precalculus or if it’s a magnet high school like Blair Functions but even then the kids come with Algebra 2 done plus a ton of enrichment.

You seem to be more familiar with elementary and middle school compaction classes. It’s done because those classes move very slowly and there’s a lot of repetition, high school math is different.

Thanks for proving my point. Yes, some schools do in fact compact HS-level math. One of my kids is in a compacted path right now. I am plenty aware.

Any sequence can be accelerated. Look at AB vs. BC -- BC is compacted.

Maybe you are stuck on the language? Compacted just means accelerated. They cover more content in less time.

Capiche?

Not sure why you insist on this as you’re clearly out of your depth. Calculus BC is not compacted, it covers Calculus 1 and 2, typically taught over one semester each in college, or one year in high school. You can say Calculus AB is more fluffy or equivalent to a lower level calculus like college equivalent of Calculus for life sciences and business majors.

LOL. Again, thanks for proving my point.

https://blog.collegeboard.org/difference-between-ap-calculus-ab-and-bc
"In other words, AP Calculus BC covers more content than AP Calculus AB"

"All topics in the eight units of AP Calculus AB are also included in AP Calculus BC. However, AP Calculus BC contains two additional units (Units 9 and 10), plus some extra topics in Units 6─8."

"AP Calculus AB focuses on topics that are taught in the college-equivalent first-semester calculus class. AP Calculus BC focuses on topics covered in both first- and second-semester calculus classes."

AB = Calc 1
BC = Calc 1 + 2

More content covered in less time = accelerated = compacted.

It must be hard for you to struggle so much with math and language.

You can call whatever you want accelerated or compacted, that doesn’t mean the rest of the world agrees. I had a good laugh at “compacted” and “accelerated” calculus.

While class contents vary, AP Calculus AB is more than just Calculus 1. Applications of integration and differential equations are usually Calculus 2 along with series and parametric functions. Other topics from Calculus 2, ie techniques of integration, and some integration applications like moments are missing from AP Calculus BC. That doesn’t mean college calculus is doubly accelerated and compacted compared to already accelerated and compacted BC. It’s just that there are different classes, students, majors, and graduation requirements.

By this silly argument Honors Precalculus would also be compacted and accelerated compared to regular Precalculus because it includes additional topics of vector algebra and conics. It’s not, it’s a different class that go into more depth and more topics.

Semantics aside, your entire point is finding some snippets online that you think validate your word choices. Try to contribute with something more substantive.

I'm sorry you are struggling with the definitions of these words. Maybe pick up a dictionary?

As for the content covered by AB/BC, I trust the College Board on this:
"AP Calculus AB focuses on topics that are taught in the college-equivalent first-semester calculus class. AP Calculus BC focuses on topics covered in both first- and second-semester calculus classes."

"The two courses cover content and skills that are introduced in a first-semester calculus course at the college level. All topics in the eight units of AP Calculus AB are included in AP Calculus BC."
https://blog.collegeboard.org/difference-between-ap-calculus-ab-and-bc

Integrated math is just the sequencing of content. Integrated math courses can be designed to be accelerated/compacted or advanced, just like any other sequence.

I’d take the College Board description with a grain of salt because they also have to back up the AP exam course equivalence.

Differential equations and Applications of integration from the description the AP Calculus AB syllabus are usually found in Calculus 2. While contents vary, see if you can find a Calculus 1 college course that covers these topics.

An example from UC Berkeley:

Calculus 1, Math 51
This course is intended for STEM majors. An introduction to differential and integral calculus of functions of one variable, with applications and an introduction to transcendental functions.

Calculus 2, Math 52
Techniques of integration; applications of integration. Infinite sequences and series. First-order ordinary differential equations. Second-order ordinary differential equations; oscillation and damping; series solutions of ordinary differential equations.

Arguably AP Calculus BC is not as in depth as a college calculus class. Even at the community college where my dual enrollment student took calculus there were many topics not touched in the AP Calculus BC. A few examples: logarithmic differentiation, techniques of integration (ie trig substitution), applications of integration (surface area of revolution, cylindrical shell etc), first order linear differential equations (AP only does exponential and logistic, college classes include integration multiplication factors). As shown in the example from Berkeley on Calculus 2, some classes go in even more depth for differential equations.

Let's see what Georgetown thinks about AB vs. BC.
https://mathstat.georgetown.edu/undergraduate/advanced-placement/

If you get a 5 on AB, you can place out of MATH-1350.

If you get a 5 on BC, you can place out of MATH-1350 and MATH-1360.

You’re quite dense to say the least, read what was said up thread, you get worked up from misunderstanding posts. Calculus AB contains some Calculus 2 material, read the description of Math 1360 and you’ll see some of those topics are in AB, namely techniques of integration and applications of integration.

AB gets credit for Calculus 1, while BC gets credit for Calculus 1&2. This statement is not mutually exclusive with the first paragraph. AB can cover a portion of the Calculus 2 material but not get credit for it.

Anonymous wrote:This isn’t a “why is math so bad in the Us ?” question that I have seen a few times here recently. It’s why is math taught the the way it is here? I mean: why is it taught in separate topics in middle/high school, ending in some form of calculus? I went to school in another country where math each year is a mix of many different topics and the final/hardest math class will have a mix of advanced topics including calculus, statistics, etc. I think it is taught this way in many other places too. I am certainly not assuming that the way I was taught was better (and I never even took the highest level offered in my curriculum), but I am wondering what is the reason for the way it is taught in the US?

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:The way you were taught is taught in some American schools. If you look for classes labeled Math I, Math II, or Integrated Math I, II they use this model.

Unfortunately, there are two problems with integrated math in the US:

1. It's not the standard track, so if you are halfway through a combo of algebra and geometry, and then, like many Americans, move, you're either going to be slotted ahead or behind where you should be.

2. The subtler problem is that, in the US, it is basically never something like Singapore's hardcore New Syllabus, but rather districts that adopt integrated math like to go with fluffy, inadequate discovery-oriented curricula.

Yes, exactly. Here is why:

Hidden within these progressive approaches to math is always the DEI agenda. Specifically “equity of outcome.” That means: everyone has to arrive at the same place and no one should be ahead of anyone else.

The easiest way to accomplish the “equity of outcome” goal is: lower the bar.

So that is what DEI departments in school districts across the country have been doing.

OMGERD DEI!!! SO SCARY!! AND REAL!!!!

Sounds like your issue is really the DEI boogeyman, not actually the progression of math content.

When you have kids in school, you'll understand.

+1

Unfortunately a lot of bizarre ideas in math teaching come from the left. Like ethno-mathematics, de-tracking, representation etc, While they may have some place in math history they are completely counterproductive when it comes to teaching math.

Integrated math falls into this category because it’s associated with removal of honors classes, so it’s a way to implement de-tracking.

Only because Republicans whipped up some hysteria around these topics and irrational people get confused easily.

If people actually took a moment to understand what integrated math is then they'd realize that it really doesn't have anything to do with detracking.

Trust me that I know what’s in the integrated math and what’s best for my child.

Integrated math is used as a detracking tool in several ways. First, when the switch is made from AGA to IM they eliminate honors classes and offer only one level of IM. Second, it’s not possible to take concurrent algebra and geometry which was one way to move to the upper track. Third, integrated math is a little bit of everything without going into depth because there not enough time, which hurts the top students the most.

Integrated math can be taught accelerated and/or advanced. It's just the sequencing of the topics. It's how they do math in many other countries.

You are conflating the topics and make baseless assumptions.

IM Math can be taught accelerated and compacted but in practice it isn’t common and it’s also not advisable.

Compaction is more common for Math 3-8 grades, although different districts have various approaches. Usually when it comes to Algebra 1 or IM1 it’s a full year and it’s rarely compacted although there may be exceptions to that. There are some compacted classes like IM3-Precalculus or the equivalent Algebra2-Precalculus, but there’s no good reason to cram two years of high school into one.

The point of the OP was to inquire about AGA vs IM. While schools have different classes and programs, and there’s no uniform answer across all, Algebra1-Geometry-Algebra2 is generally more rigorous than integrated math in US schools.

Your hole beef seems to be finding some exceptions, which nobody denies exist, but they are also are not as representative.

False.
Some ding dong keeps insisting that schools can't offer accelerated or advanced versions of integrated math:
"For integrated math there’s no opportunity to accelerate"
"IM classes are not compacted"
"Schools don't offer compacted IM classes"
"Integrated math falls into this category because it’s associated with removal of honors classes, so it’s a way to implement de-tracking"
"Integrated math is used as a detracking tool"

Which is clearly not true. Integrated math is simply the sequence of math content.

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:Examples of compacted integrated math:
https://elm.sweetwaterschools.org/compacted-integrated-math-integrated-math-course-i-placement/

https://rdmcounseling.weebly.com/7th-grade-course-selection.html

You don’t seem to be familiar with the US curriculum, and just posted the first Google hits you could find.

Integrated math I, II, III refers to a mix of three years of algebra and geometry taught instead of the Algebra 1, Geometry, Algebra 2 sequence.

Integrated compacted math 6/7/8 doesn’t really mean much it’s the same curriculum but compacted so kids can accelerate.

In California schools there’s a push for integrated math which originates with social justice champions like Jo Boaler, whose initiative received a lot of criticism.

A feature of CA math pathways is the compacted IM 3 with precalculus which is disastrous. Also they make AP Calculus AB a prerequisite for BC which is ill advised.

Ding dong - did you open the second link?

Integrated math can be compacted, just like any other sequence.

Really, so any math sequence can be compacted?

The regular math sequence is Algebra 1, Geometry, Algebra 2, Precalculus, Calculus, Linear Algebra and Differential Equations, and you might add along the line Statistics and Discrete Math.

You don’t see this sequence compacted especially for the higher level classes unless the class is useless like compacted Algebra 2 and Precalculus or if it’s a magnet high school like Blair Functions but even then the kids come with Algebra 2 done plus a ton of enrichment.

You seem to be more familiar with elementary and middle school compaction classes. It’s done because those classes move very slowly and there’s a lot of repetition, high school math is different.

Thanks for proving my point. Yes, some schools do in fact compact HS-level math. One of my kids is in a compacted path right now. I am plenty aware.

Any sequence can be accelerated. Look at AB vs. BC -- BC is compacted.

Maybe you are stuck on the language? Compacted just means accelerated. They cover more content in less time.

Capiche?

Not sure why you insist on this as you’re clearly out of your depth. Calculus BC is not compacted, it covers Calculus 1 and 2, typically taught over one semester each in college, or one year in high school. You can say Calculus AB is more fluffy or equivalent to a lower level calculus like college equivalent of Calculus for life sciences and business majors.

LOL. Again, thanks for proving my point.

https://blog.collegeboard.org/difference-between-ap-calculus-ab-and-bc
"In other words, AP Calculus BC covers more content than AP Calculus AB"

"All topics in the eight units of AP Calculus AB are also included in AP Calculus BC. However, AP Calculus BC contains two additional units (Units 9 and 10), plus some extra topics in Units 6─8."

"AP Calculus AB focuses on topics that are taught in the college-equivalent first-semester calculus class. AP Calculus BC focuses on topics covered in both first- and second-semester calculus classes."

AB = Calc 1
BC = Calc 1 + 2

More content covered in less time = accelerated = compacted.

It must be hard for you to struggle so much with math and language.

You can call whatever you want accelerated or compacted, that doesn’t mean the rest of the world agrees. I had a good laugh at “compacted” and “accelerated” calculus.

While class contents vary, AP Calculus AB is more than just Calculus 1. Applications of integration and differential equations are usually Calculus 2 along with series and parametric functions. Other topics from Calculus 2, ie techniques of integration, and some integration applications like moments are missing from AP Calculus BC. That doesn’t mean college calculus is doubly accelerated and compacted compared to already accelerated and compacted BC. It’s just that there are different classes, students, majors, and graduation requirements.

By this silly argument Honors Precalculus would also be compacted and accelerated compared to regular Precalculus because it includes additional topics of vector algebra and conics. It’s not, it’s a different class that go into more depth and more topics.

Semantics aside, your entire point is finding some snippets online that you think validate your word choices. Try to contribute with something more substantive.

I'm sorry you are struggling with the definitions of these words. Maybe pick up a dictionary?

As for the content covered by AB/BC, I trust the College Board on this:
"AP Calculus AB focuses on topics that are taught in the college-equivalent first-semester calculus class. AP Calculus BC focuses on topics covered in both first- and second-semester calculus classes."

"The two courses cover content and skills that are introduced in a first-semester calculus course at the college level. All topics in the eight units of AP Calculus AB are included in AP Calculus BC."
https://blog.collegeboard.org/difference-between-ap-calculus-ab-and-bc

Integrated math is just the sequencing of content. Integrated math courses can be designed to be accelerated/compacted or advanced, just like any other sequence.

I’d take the College Board description with a grain of salt because they also have to back up the AP exam course equivalence.

Differential equations and Applications of integration from the description the AP Calculus AB syllabus are usually found in Calculus 2. While contents vary, see if you can find a Calculus 1 college course that covers these topics.

An example from UC Berkeley:

Calculus 1, Math 51
This course is intended for STEM majors. An introduction to differential and integral calculus of functions of one variable, with applications and an introduction to transcendental functions.

Calculus 2, Math 52
Techniques of integration; applications of integration. Infinite sequences and series. First-order ordinary differential equations. Second-order ordinary differential equations; oscillation and damping; series solutions of ordinary differential equations.

Arguably AP Calculus BC is not as in depth as a college calculus class. Even at the community college where my dual enrollment student took calculus there were many topics not touched in the AP Calculus BC. A few examples: logarithmic differentiation, techniques of integration (ie trig substitution), applications of integration (surface area of revolution, cylindrical shell etc), first order linear differential equations (AP only does exponential and logistic, college classes include integration multiplication factors). As shown in the example from Berkeley on Calculus 2, some classes go in even more depth for differential equations.

Let's see what Georgetown thinks about AB vs. BC.
https://mathstat.georgetown.edu/undergraduate/advanced-placement/

If you get a 5 on AB, you can place out of MATH-1350.

If you get a 5 on BC, you can place out of MATH-1350 and MATH-1360.

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:Examples of compacted integrated math:
https://elm.sweetwaterschools.org/compacted-integrated-math-integrated-math-course-i-placement/

https://rdmcounseling.weebly.com/7th-grade-course-selection.html

You don’t seem to be familiar with the US curriculum, and just posted the first Google hits you could find.

Integrated math I, II, III refers to a mix of three years of algebra and geometry taught instead of the Algebra 1, Geometry, Algebra 2 sequence.

Integrated compacted math 6/7/8 doesn’t really mean much it’s the same curriculum but compacted so kids can accelerate.

In California schools there’s a push for integrated math which originates with social justice champions like Jo Boaler, whose initiative received a lot of criticism.

A feature of CA math pathways is the compacted IM 3 with precalculus which is disastrous. Also they make AP Calculus AB a prerequisite for BC which is ill advised.

Ding dong - did you open the second link?

Integrated math can be compacted, just like any other sequence.

Really, so any math sequence can be compacted?

The regular math sequence is Algebra 1, Geometry, Algebra 2, Precalculus, Calculus, Linear Algebra and Differential Equations, and you might add along the line Statistics and Discrete Math.

You don’t see this sequence compacted especially for the higher level classes unless the class is useless like compacted Algebra 2 and Precalculus or if it’s a magnet high school like Blair Functions but even then the kids come with Algebra 2 done plus a ton of enrichment.

You seem to be more familiar with elementary and middle school compaction classes. It’s done because those classes move very slowly and there’s a lot of repetition, high school math is different.

Thanks for proving my point. Yes, some schools do in fact compact HS-level math. One of my kids is in a compacted path right now. I am plenty aware.

Any sequence can be accelerated. Look at AB vs. BC -- BC is compacted.

Maybe you are stuck on the language? Compacted just means accelerated. They cover more content in less time.

Capiche?

Not sure why you insist on this as you’re clearly out of your depth. Calculus BC is not compacted, it covers Calculus 1 and 2, typically taught over one semester each in college, or one year in high school. You can say Calculus AB is more fluffy or equivalent to a lower level calculus like college equivalent of Calculus for life sciences and business majors.

LOL. Again, thanks for proving my point.

https://blog.collegeboard.org/difference-between-ap-calculus-ab-and-bc
"In other words, AP Calculus BC covers more content than AP Calculus AB"

"All topics in the eight units of AP Calculus AB are also included in AP Calculus BC. However, AP Calculus BC contains two additional units (Units 9 and 10), plus some extra topics in Units 6─8."

"AP Calculus AB focuses on topics that are taught in the college-equivalent first-semester calculus class. AP Calculus BC focuses on topics covered in both first- and second-semester calculus classes."

AB = Calc 1
BC = Calc 1 + 2

More content covered in less time = accelerated = compacted.

It must be hard for you to struggle so much with math and language.

You can call whatever you want accelerated or compacted, that doesn’t mean the rest of the world agrees. I had a good laugh at “compacted” and “accelerated” calculus.

While class contents vary, AP Calculus AB is more than just Calculus 1. Applications of integration and differential equations are usually Calculus 2 along with series and parametric functions. Other topics from Calculus 2, ie techniques of integration, and some integration applications like moments are missing from AP Calculus BC. That doesn’t mean college calculus is doubly accelerated and compacted compared to already accelerated and compacted BC. It’s just that there are different classes, students, majors, and graduation requirements.

By this silly argument Honors Precalculus would also be compacted and accelerated compared to regular Precalculus because it includes additional topics of vector algebra and conics. It’s not, it’s a different class that go into more depth and more topics.

Semantics aside, your entire point is finding some snippets online that you think validate your word choices. Try to contribute with something more substantive.

I'm sorry you are struggling with the definitions of these words. Maybe pick up a dictionary?

As for the content covered by AB/BC, I trust the College Board on this:
"AP Calculus AB focuses on topics that are taught in the college-equivalent first-semester calculus class. AP Calculus BC focuses on topics covered in both first- and second-semester calculus classes."

"The two courses cover content and skills that are introduced in a first-semester calculus course at the college level. All topics in the eight units of AP Calculus AB are included in AP Calculus BC."
https://blog.collegeboard.org/difference-between-ap-calculus-ab-and-bc

Integrated math is just the sequencing of content. Integrated math courses can be designed to be accelerated/compacted or advanced, just like any other sequence.

I’d take the College Board description with a grain of salt because they also have to back up the AP exam course equivalence.

Differential equations and Applications of integration from the description the AP Calculus AB syllabus are usually found in Calculus 2. While contents vary, see if you can find a Calculus 1 college course that covers these topics.

An example from UC Berkeley:

Calculus 1, Math 51
This course is intended for STEM majors. An introduction to differential and integral calculus of functions of one variable, with applications and an introduction to transcendental functions.

Calculus 2, Math 52
Techniques of integration; applications of integration. Infinite sequences and series. First-order ordinary differential equations. Second-order ordinary differential equations; oscillation and damping; series solutions of ordinary differential equations.

Arguably AP Calculus BC is not as in depth as a college calculus class. Even at the community college where my dual enrollment student took calculus there were many topics not touched in the AP Calculus BC. A few examples: logarithmic differentiation, techniques of integration (ie trig substitution), applications of integration (surface area of revolution, cylindrical shell etc), first order linear differential equations (AP only does exponential and logistic, college classes include integration multiplication factors). As shown in the example from Berkeley on Calculus 2, some classes go in even more depth for differential equations.

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:The way you were taught is taught in some American schools. If you look for classes labeled Math I, Math II, or Integrated Math I, II they use this model.

Unfortunately, there are two problems with integrated math in the US:

1. It's not the standard track, so if you are halfway through a combo of algebra and geometry, and then, like many Americans, move, you're either going to be slotted ahead or behind where you should be.

2. The subtler problem is that, in the US, it is basically never something like Singapore's hardcore New Syllabus, but rather districts that adopt integrated math like to go with fluffy, inadequate discovery-oriented curricula.

Yes, exactly. Here is why:

Hidden within these progressive approaches to math is always the DEI agenda. Specifically “equity of outcome.” That means: everyone has to arrive at the same place and no one should be ahead of anyone else.

The easiest way to accomplish the “equity of outcome” goal is: lower the bar.

So that is what DEI departments in school districts across the country have been doing.

OMGERD DEI!!! SO SCARY!! AND REAL!!!!

Sounds like your issue is really the DEI boogeyman, not actually the progression of math content.

When you have kids in school, you'll understand.

+1

Unfortunately a lot of bizarre ideas in math teaching come from the left. Like ethno-mathematics, de-tracking, representation etc, While they may have some place in math history they are completely counterproductive when it comes to teaching math.

Integrated math falls into this category because it’s associated with removal of honors classes, so it’s a way to implement de-tracking.

Only because Republicans whipped up some hysteria around these topics and irrational people get confused easily.

If people actually took a moment to understand what integrated math is then they'd realize that it really doesn't have anything to do with detracking.

Trust me that I know what’s in the integrated math and what’s best for my child.

Integrated math is used as a detracking tool in several ways. First, when the switch is made from AGA to IM they eliminate honors classes and offer only one level of IM. Second, it’s not possible to take concurrent algebra and geometry which was one way to move to the upper track. Third, integrated math is a little bit of everything without going into depth because there not enough time, which hurts the top students the most.

Integrated math can be taught accelerated and/or advanced. It's just the sequencing of the topics. It's how they do math in many other countries.

You are conflating the topics and make baseless assumptions.

IM Math can be taught accelerated and compacted but in practice it isn’t common and it’s also not advisable.

Compaction is more common for Math 3-8 grades, although different districts have various approaches. Usually when it comes to Algebra 1 or IM1 it’s a full year and it’s rarely compacted although there may be exceptions to that. There are some compacted classes like IM3-Precalculus or the equivalent Algebra2-Precalculus, but there’s no good reason to cram two years of high school into one.

The point of the OP was to inquire about AGA vs IM. While schools have different classes and programs, and there’s no uniform answer across all, Algebra1-Geometry-Algebra2 is generally more rigorous than integrated math in US schools.

Your hole beef seems to be finding some exceptions, which nobody denies exist, but they are also are not as representative.

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:The way you were taught is taught in some American schools. If you look for classes labeled Math I, Math II, or Integrated Math I, II they use this model.

Unfortunately, there are two problems with integrated math in the US:

1. It's not the standard track, so if you are halfway through a combo of algebra and geometry, and then, like many Americans, move, you're either going to be slotted ahead or behind where you should be.

2. The subtler problem is that, in the US, it is basically never something like Singapore's hardcore New Syllabus, but rather districts that adopt integrated math like to go with fluffy, inadequate discovery-oriented curricula.

Yes, exactly. Here is why:

Hidden within these progressive approaches to math is always the DEI agenda. Specifically “equity of outcome.” That means: everyone has to arrive at the same place and no one should be ahead of anyone else.

The easiest way to accomplish the “equity of outcome” goal is: lower the bar.

So that is what DEI departments in school districts across the country have been doing.

OMGERD DEI!!! SO SCARY!! AND REAL!!!!

Sounds like your issue is really the DEI boogeyman, not actually the progression of math content.

When you have kids in school, you'll understand.

+1

Unfortunately a lot of bizarre ideas in math teaching come from the left. Like ethno-mathematics, de-tracking, representation etc, While they may have some place in math history they are completely counterproductive when it comes to teaching math.

Integrated math falls into this category because it’s associated with removal of honors classes, so it’s a way to implement de-tracking.

Only because Republicans whipped up some hysteria around these topics and irrational people get confused easily.

If people actually took a moment to understand what integrated math is then they'd realize that it really doesn't have anything to do with detracking.

Trust me that I know what’s in the integrated math and what’s best for my child.

Integrated math is used as a detracking tool in several ways. First, when the switch is made from AGA to IM they eliminate honors classes and offer only one level of IM. Second, it’s not possible to take concurrent algebra and geometry which was one way to move to the upper track. Third, integrated math is a little bit of everything without going into depth because there not enough time, which hurts the top students the most.

Integrated math can be taught accelerated and/or advanced. It's just the sequencing of the topics. It's how they do math in many other countries.

You are conflating the topics and make baseless assumptions.

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:Examples of compacted integrated math:
https://elm.sweetwaterschools.org/compacted-integrated-math-integrated-math-course-i-placement/

https://rdmcounseling.weebly.com/7th-grade-course-selection.html

You don’t seem to be familiar with the US curriculum, and just posted the first Google hits you could find.

Integrated math I, II, III refers to a mix of three years of algebra and geometry taught instead of the Algebra 1, Geometry, Algebra 2 sequence.

Integrated compacted math 6/7/8 doesn’t really mean much it’s the same curriculum but compacted so kids can accelerate.

In California schools there’s a push for integrated math which originates with social justice champions like Jo Boaler, whose initiative received a lot of criticism.

A feature of CA math pathways is the compacted IM 3 with precalculus which is disastrous. Also they make AP Calculus AB a prerequisite for BC which is ill advised.

Ding dong - did you open the second link?

Integrated math can be compacted, just like any other sequence.

Really, so any math sequence can be compacted?

The regular math sequence is Algebra 1, Geometry, Algebra 2, Precalculus, Calculus, Linear Algebra and Differential Equations, and you might add along the line Statistics and Discrete Math.

You don’t see this sequence compacted especially for the higher level classes unless the class is useless like compacted Algebra 2 and Precalculus or if it’s a magnet high school like Blair Functions but even then the kids come with Algebra 2 done plus a ton of enrichment.

You seem to be more familiar with elementary and middle school compaction classes. It’s done because those classes move very slowly and there’s a lot of repetition, high school math is different.

Thanks for proving my point. Yes, some schools do in fact compact HS-level math. One of my kids is in a compacted path right now. I am plenty aware.

Any sequence can be accelerated. Look at AB vs. BC -- BC is compacted.

Maybe you are stuck on the language? Compacted just means accelerated. They cover more content in less time.

Capiche?

Not sure why you insist on this as you’re clearly out of your depth. Calculus BC is not compacted, it covers Calculus 1 and 2, typically taught over one semester each in college, or one year in high school. You can say Calculus AB is more fluffy or equivalent to a lower level calculus like college equivalent of Calculus for life sciences and business majors.

LOL. Again, thanks for proving my point.

https://blog.collegeboard.org/difference-between-ap-calculus-ab-and-bc
"In other words, AP Calculus BC covers more content than AP Calculus AB"

"All topics in the eight units of AP Calculus AB are also included in AP Calculus BC. However, AP Calculus BC contains two additional units (Units 9 and 10), plus some extra topics in Units 6─8."

"AP Calculus AB focuses on topics that are taught in the college-equivalent first-semester calculus class. AP Calculus BC focuses on topics covered in both first- and second-semester calculus classes."

AB = Calc 1
BC = Calc 1 + 2

More content covered in less time = accelerated = compacted.

It must be hard for you to struggle so much with math and language.

You can call whatever you want accelerated or compacted, that doesn’t mean the rest of the world agrees. I had a good laugh at “compacted” and “accelerated” calculus.

While class contents vary, AP Calculus AB is more than just Calculus 1. Applications of integration and differential equations are usually Calculus 2 along with series and parametric functions. Other topics from Calculus 2, ie techniques of integration, and some integration applications like moments are missing from AP Calculus BC. That doesn’t mean college calculus is doubly accelerated and compacted compared to already accelerated and compacted BC. It’s just that there are different classes, students, majors, and graduation requirements.

By this silly argument Honors Precalculus would also be compacted and accelerated compared to regular Precalculus because it includes additional topics of vector algebra and conics. It’s not, it’s a different class that go into more depth and more topics.

Semantics aside, your entire point is finding some snippets online that you think validate your word choices. Try to contribute with something more substantive.

I'm sorry you are struggling with the definitions of these words. Maybe pick up a dictionary?

As for the content covered by AB/BC, I trust the College Board on this:
"AP Calculus AB focuses on topics that are taught in the college-equivalent first-semester calculus class. AP Calculus BC focuses on topics covered in both first- and second-semester calculus classes."

"The two courses cover content and skills that are introduced in a first-semester calculus course at the college level. All topics in the eight units of AP Calculus AB are included in AP Calculus BC."
https://blog.collegeboard.org/difference-between-ap-calculus-ab-and-bc

Integrated math is just the sequencing of content. Integrated math courses can be designed to be accelerated/compacted or advanced, just like any other sequence.