I have a suggestion for improving math aptitude but it is not what you are looking for…
Work through All books of Art of Problem solving starting from Algebra. These are not drill books. Those are books for mathy kids by Mathematicians to deeply understand math, not to take AP exams… Do not forget to buy solution manuals they are golden.
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This may be true as you transition as a math major through logic to some aspects of linear algebra, some aspects of discrete math, real and complex analysis etc. For calculus AB and algebra, it’s really just computation where I would think few kids really hit their cognitive ceiling, and it’s a lot more about practice. Even geometric proofs seem more cognitively challenging than applying the chain rule.
AOPS also is about practice, really. The first 10 of 13 questions for each unit are basically practice / computation. The last few generally require some decoding or trick. Those tricks / techniques are what the AIME / IMO tests are about, but are rarely relevant for AP Calc AB which is strongly computational. This issue of AOPS vs. AP has been discussed on many forums on CC.
To me, making small computational errors on tests, if she didn’t have this problem before, sounds like math anxiety. Which would be made worse if the class is moving too quickly for her. Taking 2 hours a night to complete the homework makes me think she is having issues with the concepts. Either way I would also suggest she move down to the regular calculus class if she can.
I also have seen people hit that math wall. And Calc 1 was a common place to hit it.
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Let me respectively disagree.
Example. I was teaching my mathy kid long time ago something about prealgebra (it was AoPS.) I believe it was some multiple choice problem. Do not remember details. But my child solved problem in seconds before I got to the answer. I, with Math degree, was speachless for a second and then asked him how he did it. He said, “Oh, this is very easy. This and this is impossible because of this, this and that because of that, here is your answer, I do not need to make any calculations…”
That is math aptitude on different level and thinking outside of the box. That went all the way up for advanced math. That child was like sniffing dog for math. Never bothered to lift a pen in many problems. And that child lost interest to math too at some point. Perfect fit for Cybersecurity.
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Two hours of homework per night in AP Calculus is not necessarily excessive, especially so early in the school year. AP Calculus is a huge step up from precalculus. It is often the first class in which bright students falter. They falter not because the material is too difficult, but because they are not accustomed to having to work so hard in an academic course. The students need to overcome the mindset that this should be easy and that if it is not easy, they are not good at it.
The first thing YOUR DAUGHTER should do is meet with her teacher. She should express her concerns, including letting the teacher know how much time the homework is taking her, and ask for suggestions for improvement. The teacher is the best person to advise your daughter whether it would be in her best interest to drop down to an Algebra 3 or non-AP Calculus course or stay in AP Calculus but be prepared to work harder than she has ever had to work on the past. One of the teacher’s suggestions will likely be that your daughter meet with a peer tutor. If the teacher does not suggest this, you should do so. You should make it clear to your daughter that seeking help when needed is what smart people do.
If you wish, set up a separate parent-teacher conference to express your concerns. You may find that teacher expects students to be struggling at this point and that the workload becomes more manageable as students learn new study tactics.
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rurci3 may be helpful in identifying any gaps in precalculus knowledge that is necessary or helpful to succeed in calculus.
It does seem odd to me that a student three grade levels ahead in math is now suddenly struggling in math, after doing well in previous honors math courses.
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A few thoughts:
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Have her ask the teacher to retake one of the tests, particularly if there’s a variant of the test, untimed. This doesn’t need to be for a grade, but it’s going to help to see if it’s the timing/stress/anxiety that’s causing the problem or if there’s a problem with algebraic fundamentals or something else.
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Consider dropping AP calc this year and retaking it next year. Not necessarily because there’s some fundamental issue in your D’s math skills, but because your D’s brain will have another year to mature. So many skills (whether learning to read or executive functioning skills, etc) are often acquired without any additional effort by simply giving the brain time to mature. Your D is taking calculus 3 years younger than it would typically be taken. Don’t underestimate the impact of brain maturity.
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I too would recommend dropping the class and switching either to Calculus Honors or AP stats or some Algebra/precalc-based math class - especially since she’s spending so much time on it.
It could really just be a matter of the brain maturing, such that in a year the class will be fine without much intervention on your part.
She can take Calc AB in 11th grade and Calc BC in 12th and still be quite advanced.
As an aside, if she’s thinking premed, she has time to explore health professions (nursing, NP, PA, Occupational Therapy…) through volunteering, especially among people in a different environment than her own. In addition, Biology is not the best major for premeds - except with coupled with something like statistics or bioinformatics.
There are also allied health professions like Radiology Therapy (as one of several), which I recently discovered. These folks counsel, guide, comfort and do more in addition to the actual formal work. Very impactful careers but degrees not at all colleges but some.
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I wouldn’t panic over 4 weeks of data. Especially if she is doing well with the concepts and with problem sets at home.
Also, I don’t know how the grading is structured but I’m guessing that the bulk of the semester grade will come from future exams.
This seems like a very simple matter of learning to pay attention to details (yes this is a skill), and under some time pressure.
I’d have her chat with the teacher with the goal of identifying strategies for improving on future (more important) tests. She’s absolutely not the first to go through this. For all you know many could be going through the same thing, and the teacher uses a strategy of tough grading early to hammer the importance of being detail oriented.
If she’s not having the same issues on take-home work, have her pick a portion of that work and subject it to time constraints. This is good practice.
Also: if she ends up with a B in calc AB in 10th grade it is very unlikely to have a negative effect on college admissions at 99.9% of colleges.
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I agree with this recommendation. Math is one area where a strong foundation is critical. Smart students can sometimes make it through precalc, but will hit a wall when doing the calculus course this student is taking.
Since the kid is only a sophomore, there is no rush to complete calculus this year.
And honestly, it does not matter what this maybe 15 year old thinks they want to do in college. That math foundation needs to be there.
And yes, I understand this student seems to be understanding the material and is faltering on the tests. That means, to me, that this understanding is not at the automatic level.
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Agree…
What does she plan to take in grades 11 and 12 for math?
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Thank so much for taking time to response. Some are really valuable suggestions, Dropping a course is not an option for my D due to school policies. Even if I fight the policies, it will ruin her schedule with other course with negative psychological impact. Too soon to give up. I am surprised how some members even confidently suggest this an option without adequate knowledge . It is not possible to describe exact situation in words, every child and situation is unique imho. Anyways plan to continue to learn everyday from mistakes, keep chugging along, impose discipline around neatness and follow defined patterns when solving questions. Thanks for your suggestions on additional resources, at this point it seems like doing only the homework properly will give the right kind of practice, adding any other resources would consume precious time. She said she will do extra curricular when she is 16, she has been turned down so far because of age. She is in good spirit… To be Continued … 
Btw I did meet with teach and there is math tutor available from school that will help as well. Thanks for the valuable suggestion
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Calc BC if love for math remain (she is at least B or B+ I guess 
Sounds like she’s doing ok if she has a B or B+. If the tutor can help her with her most common mistakes first it should turn things around in terms of speed then she can tackle the rest. 2 hours is still too much hw dfor just one HS subject imho (it’s more similar to what you can expect from college where students only have 5 classes) but it is what it is I suppose. Hopefully the tutor will help her with creating automatic recognition thus increase speed and decrease the time needed to complete the math hw.
BTW Make sure to map out her math classes for Jr and Sr year so she doesn’t run out of classes and check that she is getting 9 hours of sleep.
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Please don’t have your daughter ignore extra curricular activities. Selective colleges look for students who have robust extra curricular activities in addition to a rigorous course load (and good grades).
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And now you say she has a B to B+. She is doing fine, in my opinion.
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Maybe OP can clarify - I thought she was saying - to take Calc BC if the love for math remains - which she might measure as having a B or B+ - not that it’s there now.
Anyway, OP (and student) have made a choice how to attack - so I wish them luck.
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