Semester 1 Study Guide - AP Calculus AB

The Semester exam will have some multiple choice questions (2 min each), some response questions. The exam covers all the material we covered from Chapters P-4 (Yes, Qtr 1 stuff too). For Each chapter:

  1. Review Notes and Examples (See Topics in Portals for filled in Notes and Examples)
  2. Over 20 ∆Math Practice Assignments (good for practicing skills)
  3. Chapter Checklist and Practice Problems (good for problems where you need to decide what skills are needed):
    1. Ch 1 Practice (Solutions)
    2. Ch 2A Practice (Solutions)
    3. Ch 2B/3 Practice ( Solutions)
    4. Ch 4 Practice (Solutions)
  4. Multiple Choice Problems from the textbook (To gain confidence in choosing the answer from distractors):
    1. Qtr 1 MC (Ch P-2)
    2. Ch 3 MC
    3. Ch 4 MC
    4. Sem 1 MC Questions (from an old edition of our textbook)
Additional practice can be found on, and

The questions on the exam do not require difficult calculations, but an understanding of the concepts. There is more thought than brute force necessary to come up with the correct solutions.

The AP Calculus AB Semester 1 Exam is on Thursday, December 16 from 10:15-11:45.

It will have one part that does not allow calculators, and another part that does. Within each there will be "free response" questions, and "Multiple Choice" style questions in the style of AP Calculus Exam.

The pacing is the same as the AP exam, but in a different order and slightly less than half as long (the actual AP exam is 3 hours 15 minutes):

The Actual AP Exam is on Monday May 9, 2022 at 8:00 AM. That exam starts with a Multiple Choice Section (105 minutes) and ends with a Free Response Section (90 minutes). 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).

The following guidelines for this exam are the same as the AP exam:

  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: DO NOT ROUND UNTIL THE LAST STEP. Take advantage of storing your intermediate results. Store intermediate values ([STO] [Alpha] A) is a fast and accurate way to do this. Unless otherwise specified, your final answers should be accurate to three places after the decimal point. This means you should only round once, and as the last step.
  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 (Sometimes refered to as a "bald" answer). Justifications require that you give mathematical (noncalculator) reasons. You may need to mention how the conditions for a theorem have been met before using the theorem.
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 Semester exam will be mostly from chapters 1 through 4 (and indirectly chapter P, the prerequisites review). These topics include:
  1. limits
  2. The definition of continuity
  3. The Intermediate Value Theorem (IVT)
  4. The definition of differentiability
  5. The limit process for finding a derivative
  6. Differentiating using the power
  7. Product, quotient, and chain rules
  8. Implicit differentiation
  9. Related rates
  10. Extreme Value Thm (EVT)
  11. Candidates Test for extrema on a closed interval
  12. Rolle's Thm, Mean Value Theorem (MVT) for derivatives
  13. Mean Value Thm (MVT) for integrals
  14. 1st Derivative and 2nd Derivative Test for extrema
  15. Curve sketching, limits at infinity
  16. Optimization Problems
  17. Antiderivatives and Indefinite Integrals
  18. Riemann Sums and Definite Integrals
  19. The Fundamental Theorem of Calculus
  20. Integration by Substitution (u-sub)
You need to know the derivatives and antiderivatives of polynomials and the six trig functions, ex and ln x.

Math is always cumulative and knowledge of the material covered in earlier courses are presumed and may be needed to solve problems.

I have made optional online assignments on myAP Classroom and Delta Math that related to these topics if you like to practice online.

Helpful Links

  1. Preview of the Sem 1 Exam First Page
  2. DeltaMath Practice
  3. 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
  4. Khan Academy's AP Calculus AB
  5. AP Classroom now has short Daily Videos for Units 1-6
  6. Past Exam Questions from the College Board.
  7. Past Exam Answers from Mr Calculus.
  8. Past Exam Answers from
  9. Exam Information from the College Board
  10. AP Exam Info
  11. Example Multiple choice and Free response questions are in the AP Course Description (Exam questions begin around page 228)
  12. AP Calculus Free Response Questions Arranged by Topic
  13. MC questions from 1969-1998
  14. MC Questions from 2003
  15. 2008 Multiple choice Questions and answers
  16. Video Links from the homework page
  17. Videos from the Mathorama Podcast
  18. Worksheets from the class Google classroom page.
  19. Syllabus has a grade calculator.

It would be good to go over old worksheets, quizzes, 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 on the exam and have a great Christmas vacation!