AP Calculus BC

[devara27495]

TL;DR Summary: Just wanted some advice.

So basically, I have the AP Calculus BC exam in less than a month, and I have only covered until Unit 6 or 7 of the cirriculum. I am self studying this course (no teacher) and have not had much time to study bc of 6 other APs. I need to finish 8, 9, and 10 in around 2-3 weeks. What can I do ? I would appreciate any help or resources you could provide. Also, I have not taken AP Calculus AB before. Could I learn everything else from Barrons/Princeton and then do past exams/frqs?

Units 1-3: I am 80% confident in.
Units 4-6: I am 50% confident in.

 

[berkeman]

What's BC in this context? Boundary Conditions? Or like study units A-B-C-D-E, etc.?

If you could be more specific about what-all you will be tested on and what you still need to learn, that would help us to suggest study alternatives.

 

[devara27495]

What's BC in this context? Boundary Conditions? Or like study units A-B-C-D-E, etc.?

If you could be more specific about what-all you will be tested on and what you still need to learn, that would help us to suggest study alternatives.

Unit 1: Limits and Continuity​

• Finding Limits Graphically and Numerically
• Evaluating Limits Analytically
• One-sided Limits
• Continuity and Intermediate Value Theorem
• Infinite Limits
• Limits at Infinity

Unit 2: Differentiation Definition and Fundamental Properties​

• The Derivative and the Tangent Line Problem
• Basic Differentiation Rules
• Equations of a tangent Line
• The Natural Logarithmic Functions: Differentiation
• The Product and Quotient Rules

Unit 3: Differentiation: Composite, Implicit, and Inverse Functions​

• The Chain Rule
• Implicit Differentiation
• Inverse Functions
• Inverse Trigonometric Functions and Differentiation

Unit 4: Contextual Applications of Differentiation​

• Velocity and Acceleration
• Related Rates - Introduction
• Related Rates - Advanced Examples
• Indeterminate Forms and L'Hopital's Rule

Unit 5: Analytical Applications of Differentiation​

• Rolle's Theorem
• The Mean Value Theorem
• Extrema on an Interval
• Extrema on a Closed Interval
• Increasing and Decreasing Functions and the First Derivative Test
• Concavity and the Second Derivative Test
• A Summary of Curve Sketching
• Optimization Problems

Unit 6 Integration and Accumulation of Change​

• Left and Right Side Approximations
• Area - Midpoint and Trapezoidal Approximations
• Riemann Sums and Definite Integrals
• Antidifferentiation and Indefinite Integration
• The Fundamental Theorem of Calculus
• Integration by Substitution
• The Natural Logarithmic Functions: Integration
• Exponential Functions: Differentiation and Integration
• Bases Other Than e and Applications
• Inverse Trigonometric Functions and Integration
• Trigonometric Integrals
• Trigonometric Substitution
• Integration by Parts
• Partial Fractions
• Improper Integrals

Unit 7: Differential Equations​

• Slope Fields
• Separation of Variables
• Differential Equations: Growth and Decay

Unit 8: Applications of Integration​

• Area of a Region Between Two Curves
• Area of a Region Between Two Curves - Advanced Examples
• Volume: Solids with Known Cross Sections
• Volume: The Disk Method
• Volume: The Shell Method
• Arc Length

Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions​

• Parametric Equations
• Differentiation of Parametric Equations
• Vector-Valued Functions
• Differentiation and Integration of Vector-Valued Functions
• Velocity and Acceleration Using Parametric and Vector-Valued Functions
• Polar Coordinates and Polar Graphs
• Polar Form of a Derivative
• Areas in Polar Coordinates

Unit 10: Infinite Sequences and Series​

• Sequences
• Infinite and Geometric Series
• The Integral Test and p-Series
• Comparisons of Series and the Ratio Test
• Alternating Series
• Taylor Polynomials and Approximations
• Power Series
• Taylor and Maclaurin Series
• Representation of Functions by Power Series

this has a more accurate list of all the topics : https://apcentral.collegeboard.org/media/pdf/ap-calculus-ab-bc-course-at-a-glance_0.pdf

attached image has question percentages, omit the AB column, just look at the BC.

 

[devara27495]

@berkeman

 

[CrysPhys]

What's BC in this context? Boundary Conditions? Or like study units A-B-C-D-E, etc.?

If you could be more specific about what-all you will be tested on and what you still need to learn, that would help us to suggest study alternatives.

When I took the AP Calculus exam eons ago, there was only a single exam. Now there are two: AB and BC, with BC covering more advanced material than AB. See https://blog.collegeboard.org/difference-between-ap-calculus-ab-and-bc.

 

[berkeman]

@berkeman

I'm waiting for others more familiar with this curriculum to respond. I've done my job so far to get more background information out of you to aid in others' responses.

 

[PhDeezNutz]

https://tutorial.math.lamar.edu/classes/calcII/calcII.aspx

AB is basically calc 1 and BC is basically calc 2.

These reference sheets might also be helpful

https://bpb-us-e2.wpmucdn.com/sites.../10/Series-Reference-Guide-MATH-2414-2419.pdf


https://bpb-us-e2.wpmucdn.com/sites.../10/Series-Reference-Guide-MATH-2414-2419.pdf

 

[jedishrfu]

I think your best bet is Khan Academy and as a backup MathIsPower4u.com short videos. Methodically go thru each section and watch the related video topics and try to do the problems they do then check their solution against yours.

MathIsPower4U.com is good in this aspect as they will likely have their videos organized by a similar list of topics.

https://mathispower4u.com/calc-ii.php

It's tough to do this in 2-3 weeks though.

Also I'd take practice tests for the Calculus BC to see where you fall down and focus on thos topics to give you a fighting chance when you take the exam.

 

[Mark44]

What's BC in this context?

I'm waiting for others more familiar with this curriculum to respond.

As noted by the OP and @PhDeezNutz, the AB and BC suffixes are Calc 1 and Calc 2, roughly derivatives and integrals, respectively.

 

[Muu9]

Actually, BC is a one year course covering both calc 1 and 2 content

 

[PhDeezNutz]

Actually, BC is a one year course covering both calc 1 and 2 content

Good point I forgot. It’s been awhile.

 

[gleem]

Units 1-3: I am 80% confident in.
Units 4-6: I am 50% confident in.

You say confident: I will assume proficient. Based on the percentage each section will count, you can figure out your proficiency for the remaining sections. If the passing score is 70% based on your estimates for sections one through six, you must be 82% proficient for sections seven through 10.

If you can improve your proficiency in sections four to six to 80%, then you can pass with a proficiency of 59% on the last four sections. Aceing the first six sections would only require a 36% proficiency in the last four.

Considering your time constraint, it would be wise to spend some time reviewing the old material while learning the new and raise your proficiency in the first six sections.

 

[Muu9]

https://www.reddit.com/media?url=ht...bp&s=6e9c0be3655bbc0ed0cd5e8a1ad232ff893e1ea4
The grading for the BC exam is quite generous.

 

[devara27495]

So one person said Paul's online notes, another person said Khan academy and math4power....

Has anyone seen the mit ocw calculus course , is it good for ap?

https://ocw.mit.edu/courses/18-01sc-single-variable-calculus-fall-2010/

menu is on the left.

 

[devara27495]

or do i just stick to barrons + khan

 

[Muu9]

So one person said Paul's online notes, another person said Khan academy and math4power....

Has anyone seen the mit ocw calculus course , is it good for ap?

https://ocw.mit.edu/courses/18-01sc-single-variable-calculus-fall-2010/

menu is on the left.

It's more difficult than BC calc

 

[gleem]

grading for the BC exam is quite generous.

I'll say that since a qualifying grade of 3, you need to get only 38 to 47% of the question depending on the exam (year given).

That said, you should definitely try to do your best on units 1 - 6, as they constitute about 50% of the exam.

 

[devara27495]

I'll say that since a qualifying grade of 3

I want to aim for a 5.

 

[CrysPhys]

I'll say that since a qualifying grade of 3, you need to get only 38 to 47% of the question depending on the exam (year given).

That said, you should definitely try to do your best on units 1 - 6, as they constitute about 50% of the exam.

Some schools have a higher threshold to receive college credit. E.g., MIT requires a 5 on the BC. See https://firstyear.mit.edu/academics-exploration/ap-transfer-credit/advanced-placement/ :

"A score of 5 on the Calculus BC exam will grant you credit for 18.01.

A score of 5 on the Calculus AB exam allows you to enroll in the accelerated Calculus sequence of 18.01A/18.02A."

At MIT, 18.01 is first semester freshman calculus. Eons ago when I was a freshman at MIT, we got no credit whatsoever for AP exams, even with a 5.

 

[CrysPhys]

I want to aim for a 5.

It's great to aim high. But given the short time left, and the scenario you've placed yourself into, you might just need to accept the fact that you've overextended yourself:

I am self studying this course (no teacher) and have not had much time to study bc of 6 other APs.

 

[jedishrfu]

You need to focus on your weak spots, so you need to quickly identify them via a practice test or two. From there, MathIsPower4U.com can help you focus on these weak spots, as their videos are organized into small chunks of 5 to 10 minutes, each focused on a particular problem.

You must study for the test.

Here's a Princeton Review summary of the test:

https://www.princetonreview.com/college-advice/ap-calculus-bc-exam

Notice that the test structure consists of multiple-choice questions in the first half, where there is no penalty for wrong answers. This means that you should make an educated guess if you don't know the answer. (Also, mark the questions you guessed in case you have time to revisit them to make a more informed guess.)

Here's another resource of practice tests. The 2023 test Multiple Choice and Free Response sections as PDF files.

https://www.mymathscloud.com/modules/ap-calculus/past-papers/bc


The second half consists of six problems that require you to outline your steps and reasoning to earn additional points.

 

[gleem]

I want to aim for a 5.

If you keep the proficiencies you have in parts 1 to 6 the same, you will need to answer 80% of the questions in parts 7 to 10. Your weakest area is 4,5,6, which constitutes about 35% of the test.

If you bring 4,5,6 up to 80%, you only need to get 55% in sections 7 to 10.

Also, remember that the subjects in sections 1 to 6 are important for the rest of the test, so if you are weak in those sections, you will be handicapping yourself in 7 to 10 right off the bat.

Since the grading and weighting in each section can vary from year to year, my estimates are very approximate.

You can aim, but make sure your bullets have enough powder to reach the target.

 

[gmax137]

Who here thinks cramming for two weeks is a better idea than taking the "usual" calculus sequence as a freshman? Suppose by some good luck the OP is able to place out of those classes - is he/she helping or hurting themselves?

Eons ago when I was a freshman at MIT, we got no credit whatsoever for AP exams, even with a 5.

Sounds like MIT has (had) similar thoughts.

 

[jedishrfu]

Yes, you miss so much when you test out of a course that is assumed by professors and needed by students in later courses.

In my freshman year, I was excited to have learned Differential Calculus over the summer and decided to test out. I did well except for limits, but after several meetings with my professor, he allowed me to advance to Integral Calculus. At the time, I felt elated that I had moved on so quickly, but later I realized I was taking much tougher courses earlier, which caused my GPA to drop.

Employers and grad schools often look at GPAs; they don't care what courses you took, as they assume you followed the standard path.

 

[Muu9]

they don't care what courses you took, as they assume you followed the standard path

Don't grad schools look at your coursework?

 

[devara27495]

Who here thinks cramming for two weeks is a better idea than taking the "usual" calculus sequence as a freshman? Suppose by some good luck the OP is able to place out of those classes - is he/she helping or hurting themselves?

Tbh I only care about getting the 5 on the ap exam. I think most med schools are looking for Calc 1 anyway.

 

[CrysPhys]

Tbh I only care about getting the 5 on the ap exam. I think most med schools are looking for Calc 1 anyway.

Am I parsing this correctly? You're not really interested in learning the material. You just want a zillion 5's on AP exams to impress the admissions committee. Why didn't you just sign up for the AB exam? Easier to get a 5 with that.

 

[jedishrfu]

Its never clear how they review things but consider their goal is to find good candidates as quickly as they can since they may receive hundreds of applicants.

They look at the GRE score (or used to) and then the GPA. Review of courses having only the title is harder and so tend to use college standing. If your GPA is poor its likely youll be rejected but if you protest citing the tougher courses taken then you might get the decision reversed.

 

[devara27495]

Why didn't you just sign up for the AB exam? Easier to get a 5 with that.

Did not want to do AB one year and then do the same thing a year later but just with 2 extra units.

 

[gleem]

@devara27495 would you please let us know how you did on the exam?

 

[mathwonk]

To amplify others' advice, as far as learning calculus goes, AP courses are better as preparation for superior quality college courses, not as a reason to skip those.

Since you seem currently more interested in efficiently gaming the admissions process for med school than in learning calculus, we may not be the best people to offer advice. Based on my wife's experience as a successful med school applicant however, I will suggest that your performance on the MCAT's may be more important than your score on an AP calc exam.

The interview is also crucial, and a grade - oriented approach to study and learning may not be helpful there. I know the admission pressures make it difficult to do otherwise at this early stage.

Since time is short, you might focus first on practice exams to identify weaknesses, and you may post questions here on topics and even individual problems that puzzle you.

good luck and best wishes.

 

[Muu9]

For MCAT and memorization-heavy premed courses like biology, check out Anki

 

[devara27495]

@devara27495 would you please let us know how you did on the exam?

Sure, the exam will be taken on May 12. Scores will come out in early July.

 

[devara27495]

Since you seem currently more interested in efficiently gaming the admissions process for med school than in learning calculus, we may not be the best people to offer advice. Based on my wife's experience as a successful med school applicant however, I will suggest that your performance on the MCAT's may be more important than your score on an AP calc exam.

Like I said, I am unsure of what I will be doing in the future. Maybe i might do calc 3? Who knows. I'll learn calc 2 again before i take that (if i do)
But for now, this is my main focus : getting a 4/5 on the AP calc exam.