Qtr 1 Study Guide - AP Calculus AB

The exam begins at 10:15 Wednesday October 13, 2021.

As we progress this year I will make our assessments more and more like the AP Exam in May. The AP Exam in May 9, 2022 has both "Multiple Choice" and "Free Fesponse" sections. 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).

Similarly, the quarter exam will have one section that forbids a calculator, and another that requires a calculator. This exam will mostly have Free response questions, but I will add a few multiple choice questions worth 2 points each: 1 for your correct work, and 1 for the correct answer choice (So there won't be any scantrons this time).

  1. Unless otherwise specified, answers (numeric or algebraic) need not be simplified in Free Response questions. (For example, 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 for AP" even rhymes!). For example, if the value computed is 2.119548373, AP readers will accept 2.120 (rounded) or 2.119 (truncated), but not 2.12.
  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. Just like poor grammer or spelling will not receive full credit on an English exam, poor mathematical exposition may not receive full credit either (i.e., your work should look like you are communicating your progress to answering the question, not your scratch paper).
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 cover material discussed in chapters P (and indirectly all Hon. Alg 2), Chapter 1, sections 2.1 through 2.5, d/dx(ex) = ex, and d/dx(ln x) =1/x. Make sure you know:
  1. limits,
  2. the definition of continuity,
  3. the IVT,
  4. the definition of differentiability,
  5. the limit process for finding a derivative,
  6. d/dx(ex) = ex, and d/dx(ln x) =1/x,
  7. differentiating using the power, product, quotient, and chain rules,
  8. implicit differentiation
(See the Quick Reference for Qtr 1 below for good summary) 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. Quick Reference for Qtr 1
  2. Ch 2A Test Practice Questions ( solutions here)
  3. Chapter P and 1 Test Practice Questions ( Solutions here)
  4. 88 MC Questions from the Textbook (solutions at the end of the pdf)
  5. DeltaMath Has Practice Problems with solutions and video links
  6. Fr. Chris's Podcast has 10 Chapter 1 videos and 22 Chapter 2 Videos explaining the difficult Homework Problems
  7. Mr O'Connor's videos Which explain many examples with geometer's sketchpad.
  8. AP Calculus: "Stuff you MUST Know Cold"
  9. Stuff to know cold-fill in the blank version (we have only covered most of side 1)
  10. The Packet that summarizes everything you need for this course
  11. Example Multiple choice and Free response questions are in the AP Course Description (for AB Questions from Qtr 1 topics you should be able to answer MCQ 2,3,5 on page 48f as well as FRQ 2 parts (a) and (b) on page 68)
  12. Khan Academy's AP Calculus AB (Where you need to get at least 80% Mastery in "Get Ready for AP Calculus" by December 16)

Other Links

  1. myAP.collegeboard.org AP Classroom personal progress checks
  2. Past Exam Questions from the College Board.
  3. Past AP Exam Answers from Mr Calculus.
  4. Past Exam Answers from Skylit.com.
  5. Exam Information from the College Board
  6. AP Exam Info
  7. MC questions from 1969-1998
  8. MC Questions from 2003
  9. 2008 Complete Exam
  10. Video Links from the homework page
  11. Worksheet links from the homework page

It would be good to go over your 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

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

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

Good Luck!