Qtr 1 Study Guide - AP Calculus AB

All questions (16 MC worth 16 points and 6 FR worth 16 points) will be through TestPortal (You can see the Start Page here.) You will be e-mailed (to your @sfhighschool.net address) the link and code Friday. The exam begins at 10:15 Friday October 16, 2020. On TestPortal, you can upload your answers to the Free Response questions as you go along. Ten minutes are added to your test time for uploading. You can practice uploading with paper and your iPad here. I will be available on Zoom to answer your concerns.

(The Actual AP Exam is on Tuesday May 4, 2021 at 8:00 AM. BTW, that exam starts with a Multiple Choice Section (105 minutes) and ends with a Free Response Section (90 minutes--that is over 3 hours!. In the multiple choice section, a calculator is not permitted on the first 30 questions (60 minutes, 2 minutes each), but required on the last 15 questions (45 minutes, three minutes each). The Free response section starts with the 2 calculator required questions(30 minutes, 15 minutes each), and ends with 4 questions that are to be answered with a calculator (60 minutes, also 15 minutes each).)

  1. Unless otherwise specified, answers (numeric or algebraic) need not be simplified. (Usually 5/10 or √12 is ok, but transcendental functions are not algebraic. If it is a transcendental function don't leave it as cos π/2; instead write 0. Instead of ln 1, write 0. Instead of e0, write 1, etc. ).
  2. If you use decimal approximations in calculations, your work will be scored on accuracy. Unless otherwise specified, your final answers should be accurate to three places after the decimal point.
  3. Unless otherwise specified, the domain of a function f is assumed to be the set of all real numbers x for which f (x) is a real number.
  4. The inverse of a trigonometric function f may be indicated using the inverse function notation f -1 or with the prefix "arc" (e.g., sin-1 x = arcsin x ).
  5. Show all of your work. Clearly label any functions, graphs, tables, or other objects that you use. Your work will be scored on the correctness and completeness of your methods as well as your answers. Answers without supporting work will usually not receive credit. Justifications require that you give mathematical (noncalculator) reasons.
The College Board (that administers the AP exams) has this helpful passage about what should be included in a free response question:
Students are expected to show enough of their work for Readers to follow their line of reasoning. To obtain full credit for the solution to a free-response problem, students must communicate their methods and conclusions clearly. Answers should show enough work so that the reasoning process can be followed throughout the solution. This is particularly important for assessing partial credit. Students may also be asked to use complete sentences to explain their methods or the reasonableness of their answers, or to interpret their results.

For results obtained using the calculator capabilities of plotting, finding zeros, finding the numerical derivative or integral, students are required to write the setup (e.g., the equation being solved, or the derivative or definite integral being evaluated) that leads to the solution, along with the result produced by the calculator.

For example, if the student is asked to find the area of a region, the student is expected to show a definite integral (i.e., the setup) and the answer. The student need not compute the antiderivative; the calculator may be used to calculate the value of the definite integral without further explanation.

For solutions obtained using the calculator capabilities, students must also show the mathematical steps that lead to the answer; a calculator result is not sufficient. For example, if the student is asked to find a relative minimum value of a function, the student is expected to use calculus and show the mathematical steps that lead to the answer. It is not sufficient to graph the function or use a built-in minimum finder.

When a student is asked to justify an answer, the justification must include mathematical reasons, not merely calculator results. Functions, graphs, tables, or other objects that are used in a justification should be clearly identified.

 

The material on the exam will be mostly from chapters 1 and 2 (and indirectly chapter P, the prerequisites review) which include: You need to know the derivatives of polynomials and the six trig functions, ex and ln x (Some review materials from Khan Academy are helpful).

Math is always cumulative and knowledge of the material covered in chapters P and 1 could be incorporated in solutions of problems from chapter 2.

The homework and worksheets from chapter 2 are good study aids, but you really need to understand the concepts in order to solve some problems. I have placed Multiple choice questions and answers for chapters P, 1, and 2 in pusPortals. I have made optional online assignments on APClassroom and Khan Academy that related to these topics if you like to practice online.

Helpful Links

  1. DeltaMath Has Practice Problems with solutions and video links
  2. Fr. Chris's Podcast has 10 Chapter 1 videos and 22 Chapter 2 Videos
  3. Ch 2 worksheet (solutions in files section of Plus Portals)
  4. Test Practice ChP-1 (solutions in files section of Plus Portals)
  5. 77 Problems and Solutions ChP Practice.pdf in files section of Plus Portals
  6. 77 Problems and Solutions Ch1 Practice.pdf in files section of Plus Portals
  7. 77 Problems and Solutions Ch2 Practice.pdf in files section of Plus Portals
  8. The Packet that summarizes everything you need for this course
  9. Khan Academy's AP Calculus AB Web site Has a lot of great interactive assignments that provide hints, solutions, and links to videos that explain every topic on the AP Exam. You would want to go over the assignments for the topics listed above and consult our class at KhanAcademy (Add coach and type Class code JXPVXD). In particular, I placed 4 optional assignments there, but there are plenty of other exercises and videos there as well
  10. Khan Academy's AP Calculus AB (Join UCE8NZHF for Block A, and join TYSB6SVP for Block B)
  11. myAP.collegeboard.org AP Classroom (6XRDNG for Block A, AEEAEX for Block B)
  12. Past Exam Questions from the College Board.
  13. Past Exam Answers from Mr Calculus.
  14. Past Exam Answers from Skylit.com.
  15. Exam Information from the College Board
  16. AP Exam Info
  17. Example Multiple choice and Free response questions are in the AP Course Description (p 45 for AB Questions, page 75 for BC questions--for Qtr 1 you should be able to answer and AB question and MCQ 2,3,5 and FRQ 2)
  18. MC questions from 1969-1998
  19. MC Questions from 2003
  20. 2008 Complete Exam
  21. Video Links from the homework page
  22. Worksheet links from the homework page
  23. Worksheets from the class Google classroom page.

It would be good to go over old quizzes, homework and tests; review what you did well, and learn from any mistakes.

 

Bring a calculator, a number 2 pencil and good eraser as all scantron responses are graded according to what the machine interprets (this is to prepare you to the cruel reality of how it is with AP Exams and other standardized tests)

The exam is worth 20%, and will be curved.

Remember to a good night's rest, and eat a healthy breakfast!

Good Luck!