Emergency Testing for the AB/BC Calculus Exam

 

(Scroll down to see the free emergency tests and free solutions.)

 

The scope of the the COVID-19 outbreak has shocked us and we are scrambling to understand and live in the new world, at least (hopefully) temporarily. Trying for some type of normalcy, the College Board is instituting some testing plans that they hope to implement. I am not sure when or how it will be put into place. But their idea is to test online.  They have done testing online in other subjects before but there are many kinks to work out (especially for math) and there isn't that much time. However, considering that we are all stuck indoors, they will devote as much time as needed.

 

This is what I believe is true so far: (March 23, 2020)

 

  • The plan is to use only free response questions. The exam will possibly have as few as 2 questions, each having about 5 subparts.
  • Students will probably have 22.5 minutes for each problem. That includes inputting the answer to the user interface.
  • No problems will be created where calculator use will be needed or even helpful.
  • Students will input answers into fields via a keyboard.  How that will work is beyond me.
  • BC students and AB students will not share a common question.
  • The College Board will release more detailed information about the structure of the exam on April 3. When this is released, I will include it here.

 

How I Can Help You: Based on that scant information, I have created a "test" that teachers can use that will be similar to how I believe the actual online exam will appear. These are good challenging sample problems that you can use right away and tailor them to your needs. In the spirit of everyone pitching in this crisis, the problems and solutions are free.

 

In constructing the AB exam, I found that to include just about all of the concepts that could be tested, some in a very small way, I needed 5 problems.  You may choose to give your students all of them or some of them. But considering that they have nothing but time on their hands, I would give them all 5. I doubt you are using them for grading purposes so why not?

 

Below are 1-page PDF's containing the problems and the solutions as well as the topics that the problems cover. If you choose to give fewer than 5 of them, you need to decide which ones cover the maximum amount of material. With the actual exam giving as few as 2 problems, it is clear to me that some AP topics will not be covered, even if the testers are very clever and combine concepts. But as a review, you should try to ensure that students see as wide a range of topics as possible.  They will have no idea what topics the actual exam will test and will not.

 

Grading: Students can self-grade as I am providing the solutions for free. But if you choose to grade them yourself (I probably would), you can ask students to use their phone to take pictures of their answers and email them to you. They would need to have a system of naming the images (I would use last name and problem number like Jones1a-1c). It is up to you to figure out what system works best for you.

 

In terms of grading, each problem has 10 points available (up from the usual 9 points). If you choose to grade them, I would give half-points. For instance, if a problem asked for a Riemann sum and the student showed the correct steps but calculated the answer incorrectly, I would not make it an all-or-nothing point value. With only a limited number of points, I suspect that the College Board will do the same.

 

Cheating: Now, more than ever, you need to stress to students that it does them absolutely no good to cheat. You are providing these exams to help them prepare without your everyday guidance. If they want to work with others online in solving these problems, that is up to them but the best way that they will get sense of where they are and what they need to work on is to do the problems themselves.

 

The AB Review Exams:  I have 2 versions of each of the 5 problems A and B. Test B contains the same basic problems as A but tweaked a bit with changed numbers or slightly different questions. If you are concerned about cheating, you could mix exams and give different sets of problems to different students. It is up to you how much effort you wish to put into it.

 

Feel free to download any or all of them.  Due to the fact that some

errors might be spotted, I will note when the last corrections were made

so you can always be sure you are downloading the most current version.

 

AB Test A AB Test B AB Topics Tested

Problem 1 Student

Problem 1 Solution

Both 3/24: 7:40 AM

Alt Problem 1 Student

3/24: 7:40 AM

Alt Problem 1 Solution

3/24: 9:00 PM

Trig, Rate of change,

Chain rule, Trapezoid,

IVT, MVT,

Related rates

Problem 2 Student

Problem 2 Solution

3/26 12:00 PM

Alt Problem 2 Student

Alt Problem 2 Solution

3/26 12:00 PM

Definite Integral,

Accumulation function,

Rate of change,

Function analysis,

Absolute extrema

Problem 3 Student

Problem 3 Solution

Alt Problem 3 Student

Alt Problem 3 Solution

Implicit differentiation

Function analysis

Linear approximation

Problem 4 Student

Problem 4 Solution

Alt Problem 4 Student

3/24 9:00 PM

Alt Problem 4 Solution

Differential equations

Slope fields,

2nd derivative test,

L'Hospital's rule,

ln and exponentials,

Trig

Problem 5 Student

3/23 10:00 PM

Problem 5 Solution

 3/24: 7:40 AM

Alt Problem 5 Student

Alt Problem 5 Solution

3/24 9:00 PM

Straight-line motion,

Trig, Chain rule, ln,

Continuity/differentiability

 

What is not tested:

 

Straight line motion using integration

Areas between curves using integration

Applications of the accumulation function

Average value of a function

Volume of a solid with cross sections and disks/washers

 

AB Grading Template:  If you have Microsoft Excel, I have made available a grading template for teachers who give from 1 to all 5 problems to their students. You grade their work, enter the points for each subpart, and Excel will total their points and give a projected grade best on my best guess as what would constitute a 5, 4, 3, 2, 1.  If you grade an entire class, you can see which of the problems the class is weakest and concentrate your efforts in online learning for the content of these problems. You even have the ability to change the percentage that constitutes a 5, 4, 3, 2, if you want.

 

When you download this Excel template, it will most likely go to your download folder on your computer. Once you open it, I would suggest renaming it and putting it a place in which you have easy access.

 

Download Excel Grading template:

 

 

The BC Review Exams:  I have 2 versions of each of the 5 problems C and D. Test D contains the same basic problems as C but tweaked a bit with changed numbers or slightly different questions. If you are concerned about cheating, you could mix exams and give different sets of problems to different students. It is up to you how much effort you wish to put into it.

 

The first two problems are those that would normally be in the AB exam but are excluded for this revised exam. However they are fair game for BC students.  Problem 3 is also mostly an AB problem with subpart d) as a BC question. Problems 4 and 5 are BC problems. If the revised AP BC exam contains 3 problems, I would believe that 2 of the problems would be strictly BC problems and one of them would be an AB problem.

 

BC Test C BC Test D BC Topics Tested

Problem 1 Student

Problem 1 Solution

3/31 2:45 PM

 

Alt Problem 1 Student

Alt Problem 1 Solution

3/31 2:45 PM

 

Motion (Integration),

Average value of a function,

Displacement/distance,

Definite integral as area,

Accumulation funct.

Problem 2 Student

Problem 2 Solution

Alt Problem 2 Student

Alt Problem 2 Solution

 

Application of

Accumuation funct.,

FTC, 2nd FTC

u-substitution

Problem 3 Student

Problem 3 Solution

Alt Problem 3 Student

Alt Problem 3 Solution

Area, Volume of rotation,

Integration by parts,

Volume by cross-section

L'Hospital's Rule,

Improper Integrals,

Arc length

Problem 4 Student

3/31 9:45 AM

Problem 4 Solution

Alt Problem 4 Student

Alt Problem 4 Solution

Euler's Method,

L'Hospital's Rule, Trig,

Partial Fractions,

Differential equations,

Logistic growth

Problem 5 Student

Problem 5 Solution

 

Alt Problem 5 Student

Alt Problem 5 Solution

 

Taylor Polynomials,

Geometric series sum,

Convergence of geometric

and p-series, Ratio test,

Alternating series

 

 

What is not tested:

 

Parametric and polar curves

nth term, integral and comparison tests

Absolute/condition convergence

Radius and interval of convergence

Taylor and power series

 

BC Grading Template:  If you have Microsoft Excel, I have made available a grading template for teachers who give from 1 to all 5 AB problems and 1 to 5 BC problems to their students. You grade their work, enter the points for each subpart, and Excel will total their points and give a projected grade best on my best guess as what would constitute a 5, 4, 3, 2, 1.  If you grade an entire class, you can see which of the problems the class is weakest and concentrate your efforts in online learning for the content of these problems. You even have the ability to change the percentage that constitutes a 5, 4, 3, 2, if you want.

 

When you download this Excel template, it will most likely go to your download folder on your computer. Once you open it, I would suggest renaming it and putting it a place in which you have easy access.

 

Download Excel Grading template: