AP Calculus BC
Semester 1 Exam Study Guide

The exam will be on Thursday December 16, 2021. 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 7, 8, and 9.

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):
NO calculator Part A (Must be turned in before Calculators):

Calculator Part B:

The Actual AP test is on Monday May 9, 2021 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 without 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 folder.

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.


Here is a check list of the topics from the first semester:

  • Logistic and Exponential Modeling
  • Partial Fractions
  • Arc Length
  • Area of a Surface of Revolution
  • Basic Integration Rules (page 522)
  • Integration by Parts (Ultra-Violet Voodu)
  • Trigonometric Integrals (odd and even powers of sine and cosine)
  • Integration Using Partial Fractions
  • Indeterminate Forms and L’Hôpital’s Rule
  • Improper Integrals
  • Sequences
  • Properties of limits
  • Squeeze them for limits
  • Absolute value theorem
  • Bounded monotonic serum
  • Geometric series and convergence
  • Properties of infinite series
  • Limit and term of the convergent series there're him
  • And term test for divergence only
  • The integral test NP series test
  • Alternating series
  • Alternating series remainder zero
  • Direct comparison test
  • Limit comparison test
  • The ratio test
  • Taylor polynomials and approximations
  • Power series
  • Interval convergence
  • Radius of convergence
  • Representing functions by power series
  • Taylor and Maclaurin series
  • Helpful Links

    1. AP Calculus Free Response Questions Arranged by Topic
    2. Sample Questions 2014 from the College Board. The BC Questions start at p 25. You should be able to solve MC #2, 3. at this point.
    3. Past Exam Questions from the College Board.
    4. Past Exam Answers from Mr Calculus.
    5. Past Exam Answers from Skylit.com.
    6. Exam Information from the College Board
    7. AP Exam Info
    8. Additional practice problems and videos can be found on DeltaMath.com, and myAp.collegeboard.com.
    9. Example Multiple choice and Free response questions are in the AP Course Description (p 45 for AB Questions, page 75 for BC questions)
    10. MC questions from 1969-1998
    11. MC Questions from 2003
    12. 2008 Complete Exam
    13. Video Links from the homework page
    14. Worksheet links from the homework page
    15. Worksheets from the class Google Classroom page.
    16. Exercises from Khan AP Calculus BC

    It would be good to go over old quizzes, Webwork, 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!