Questions about Precalculus topics for Calculus

[Grantmom]

Can someone explain to me about the progression of topics through Precalculus and what is needed for Calculus?  As far as what topics are covered in which math "classes", does it vary?  I have been looking at some different curricula, and seen different things.  For example, the Thinkwell Precalculus says it combines Algebra 2 and Trig, so does that mean that if you do Precalculus, you don't need to do Alg 2 and Trig?  You could just go from Algebra to Precalculus?  And then what about Geometry?

 

Just trying to sort things out in my head from looking at different sequences.  Thanks for any insight!

[mumto2]

Mainly this is a bump!

 

I never used Thinkwell but was curious because we have been a math intensive family.

 

Looked at the website and I think you are supposed to do Algebra 1, Geometry, then chose either 1 year precalc ( to get both trig and algebra 2 http://www.thinkwellhomeschool.com/products/pre-calculus)or split into two courses. I think it is for acceleration to get Calculus in for twelfth grade if Algebra 1 is being done in ninth.

 

Fwiw, you are wise to study the sequence especially if you may not stay with one program for high school. Geometry can come before or after Algebra 2 depending on the program.

[kiana]

It is going to depend on the scope and sequence of the classes that you choose. 

 

For most sequences it will not work to go directly from algebra to precalculus. Algebra 2 deepens and extends the topics learned in algebra 1 and is a prerequisite for precalculus. It might be hypothetically possible for a talented student to make the leap, but in a homeschooling situation it would be far better for them to move rapidly through algebra 2 and then rapidly through precalculus, or to choose a more challenging program, than to skip the year. In a PS situation this might sometimes be appropriate. 

 

It looks like Thinkwell's trigonometry is actually more of a precalculus class and so the precalculus combo of algebra 2/trig would be designed precisely for the accelerated student who would want to move rapidly through both. 

[Mike in SA]

Acceleration to calculus is extraordinarily risky.  It can be done, but WHY?  If a student plans on doing higher math in college, then a strong background in trigonometry is essential.  Calculus can be taken in college without fear of falling behind.

 

We may be a little nuts (both mathematicians), but we had our kids process 2-3 books at each level before moving on.  It keeps their foundation strong, but doesn't really slow them at all over the long run.  One can always double down - for example, take precalculus and statistics simultaneously.

[MarkT]

I recently did a review of the Thinkwell Precalc text book. I believe that text book matches the video course quite well.

http://forums.welltrainedmind.com/topic/542418-homeschool-high-school-math/page-2?do=findComment&comment=7119710

 

JH CTY has a good list (choose List of Topics):

http://cty.jhu.edu/ctyonline/courses/mathematics/precalculus.html

 

The progression exists for a reason with each course building upon the next (IMO the Algebra part of the Thinkwell Precalc is a little weak).  

You need a Geometry course as well before you do many of the Precalculus topics.

 

 

Edited July 31, 2016 by MarkT

[Grantmom]

But the Thinkwell Precalculus states that it is the material from the Algebra 2 and Trig courses, so I just wanted to clarify that that indeed meant that it was just those two classes combined into one.  Because in other curricula, I have seen the progression of Alg 1, Geo, Alg 2, Precalc, then Calc.

 

And I agree that there is no harm in solidifying concepts and taking your time, just asking specifically about what is needed to know before getting to Calculus.

Edited July 31, 2016 by Grantmom

[Mike in SA]

But the Thinkwell Precalculus states that it is the material from the Algebra 2 and Trig courses, so I just wanted to clarify that that indeed meant that it was just those two classes combined into one.  Because in other curricula, I have seen the progression of Alg 1, Geo, Alg 2, Precalc, then Calc.

 

And I agree that there is no harm in solidifying concepts and taking your time, just asking specifically about what is needed to know before getting to Calculus.

 

Fair enough.  Thinkwell's structure is not typical - what they call college algebra is not really the same as what most do.

 

For calculus, you should cover the full content of a college algebra course, including analytic geometry, and the full course of a trigonometry course, including a heavy dose of trigonometric identities.

 

Normally, precalculus takes the topics NOT covered by a typical geometry/algebra 2 sequence, in order to bring the student up to par with the above.  It will have quite a few applied problems from the sciences, and also introduce analytical proof methods like induction.

 

The best way of describing the content would be to refer you to look at a typical precalculus book, like Larson, Swokowski, or Sullivan.  I wouldn't recommend comparing to AoPS, as it is far more accelerated - it won't cover some common topics because they are covered in intermediate algebra, but adds a heavy dose of complex and vector analysis (helpful, but not needed for calculus).

 

[catz]

Acceleration to calculus is extraordinarily risky.  It can be done, but WHY?  If a student plans on doing higher math in college, then a strong background in trigonometry is essential.  Calculus can be taken in college without fear of falling behind.

 

We may be a little nuts (both mathematicians), but we had our kids process 2-3 books at each level before moving on.  It keeps their foundation strong, but doesn't really slow them at all over the long run.  One can always double down - for example, take precalculus and statistics simultaneously.

 

I'm a nutso math major too. My oldest hit higher math young so we took 2 years in alg 1, and 2 years in alg 2 (with multiple curriculum).  He has done Geometry, but honestly that's his weakest area and he could use some ongoing review.  He took the ACT last year and this and his math score came up 8 points repeating alg 2 and working through some more in depth problem solving on the side.  He's also not really mature enough to go to college super early nor does he have any interest in doing so (we have free DE here too so that helps).  I can see some real disadvantages to getting through too fast.

 

Anyway - I'm looking for a pre-calc/trig curriculum for this year so following ... :)  I especially want something heavy on the geometry review, trig focus. 

 

[JanetC]

Precalc is generally a review and reinforcement of Algebra 2/Trig with supplemental topics related to getting ready for calc or doing applied problems. An Algebra 2 curriculum will assume the student is seeing the material for the first time.

 

A motivated, mathy kid could theoretically skip algebra 2 (especially with the internet and the ability to google stuff when they got stuck). However, most kids should do Algebra 2 and Trig, and then possibly skip precalc if they finish strong and don't need review and reinforcement to be ready for calc.

 

[Grantmom]

I think in another thread someone mentioned that the math in precalculus isn't all needed for Calculus.  Not that you don't need it at all, but that you could theoretically start Calculus without having everything that is typically covered in Precalculus completed yet.  So, just trying to see what is linear and what isn't.  

[quark]

The plan for our DS was to do a very solid Algebra, Geometry, Algebra 2 with Trig. His tutor used the Dolciani/ Jurgensen books with some additional materials. He supplemented with AoPS and miscellaneous other math at the same time where possible. He skipped Precalculus, went directly into Calculus and finished his Calculus series without any issues whatsoever. He did need a very quick review of some Precalculus concepts (very short review of some concepts his Calculus classes didn't touch on maybe?) when taking the SAT Math2 which he aced. With a very strong math student it can be done. I had also read some years back on the boards, a respected boardie mentioning how the Dolciani Algebra 2 with Trig was solid and her DC (IIRC) skipping Precalculus after that.

 

We have a friend using Thinkwell. I think Thinkwell is unique in this area of Alg 2+ Trig and Precalculus overlapping so much. He found taking both highly repetitive (this is a kid who loves Thinkwell and will even repeat a course for fun despite his parents not assigning it) so IIRC he only continued with one. I can't remember if it was Precalc only or Alg2+ Trig only. He is on Thinkwell Calculus (finishing it I think).

 

ETA: DS's tutor introduced Analytic Geometry in the Alg2+ Trig course and then DS encountered even more Analytic Geometry when DEing Calculus (His Calculus 1,2 and 3 were called Analytic Geometry + Calculus I, II, III).

Edited July 31, 2016 by quark

[Mike in SA]

The plan for our DS was to do a very solid Algebra, Geometry, Algebra 2 with Trig. His tutor used the Dolciani/ Jurgensen books with some additional materials. He supplemented with AoPS and miscellaneous other math at the same time where possible. He skipped Precalculus, went directly into Calculus and finished his Calculus series without any issues whatsoever. He did need a very quick review of some Precalculus concepts (very short review of some concepts his Calculus classes didn't touch on maybe?) when taking the SAT Math2 which he aced. With a very strong math student it can be done. I had also read some years back on the boards, a respected boardie mentioning how the Dolciani Algebra 2 with Trig was solid and her DC (IIRC) skipping Precalculus after that.

 

We have a friend using Thinkwell. I think Thinkwell is unique in this area of Alg 2+ Trig and Precalculus overlapping so much. He found taking both highly repetitive (this is a kid who loves Thinkwell and will even repeat a course for fun despite his parents not assigning it) so IIRC he only continued with one. I can't remember if it was Precalc only or Alg2+ Trig only. He is on Thinkwell Calculus (finishing it I think).

 

ETA: DS's tutor introduced Analytic Geometry in the Alg2+ Trig course and then DS encountered even more Analytic Geometry when DEing Calculus (His Calculus 1,2 and 3 were called Analytic Geometry + Calculus I, II, III).

 

In other words, don't try this at home without a mathematician on the side.  :cool:

 

[kiana]

I think in another thread someone mentioned that the math in precalculus isn't all needed for Calculus.  Not that you don't need it at all, but that you could theoretically start Calculus without having everything that is typically covered in Precalculus completed yet.  So, just trying to see what is linear and what isn't.  

 

I wonder if you were reading a thread on AOPS precalculus? There is definitely a lot of linear algebra in there that isn't necessary for standard calculus classes.

 

Most precalculus texts don't have as much extra material. There are a few specific sections that could be easily skipped but which ones are going to depend on the text, and there isn't going to be like half a course's worth of material. 

[quark]

In other words, don't try this at home without a mathematician on the side.  :cool:

 

Perhaps. :001_smile: We have another friend who completely self studied all of her post precalculus math with the MIT OCW materials. She used some online forums for help (no doubt professional mathematicians were there helping out). DS stopped using the tutor after Alg2+Trig but he always had some form of mentorship or a source for help in place, either AoPS forums/ instructors, DE profs or online math forums like Math Stack Exchange.

 

For the OP, if it is helpful, our own experience with Thinkwell wasn't positive for math. It felt too rote and lectures didn't go deep enough.