# Semester 1 Study Guide - AP Calculus AB

The Semester exam will have about 30 multiple choice questions (2 min each), and 2 free response questions (10 min each). The exam covers all the material we covered from Chapters P-4. Of the 30 questions, 16 will be without calculator and 14 permit the use of a calculator (even though a good number of the calculator section can be solved without one). The review packets are at hw.mathorama.com and the solutions are on plus portal. The material in the review packet includes multiple choice questions covering all chapters on the exam. The review packets will refresh your memory of all the concepts covered and will help you practice working on multiple choice type questions. Additional practice can be found on myAp.collegeboard.com.

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 Calculus AB exam is on Friday, December 20 from 10:15-11:45. You will need a calculator and a couple of # 2 pencils with erasers.

Good luck on the exam and have a great Christmas vacation.

The Actual AP Exam is on May 5, 2020 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. 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. Store intermediate values ([STO] [Alpha] A) is a fast and accurate way to do this.
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:
• limits
• The definition of continuity
• The Intermediate Value Theorem (IVT)
• The definition of differentiability
• The limit process for finding a derivative
• Differentiating using the power
• Product, quotient, and chain rules
• Implicit differentiation
• Related rates
• Extreme Value Thm (EVT)
• Candidates Test for extrema on a closed interval
• Rolle's Thm, Mean Value Theorem (MVT) for derivatives
• Mean Value Thm (MVT) for integrals
• 1st Derivative and 2nd Derivative Test for extrema
• Curve sketching, limits at infinity
• Optimization Problems
• Antiderivatives and Indefinite Integrals
• Riemann Sums and Definite Integrals
• The Fundamental Theorem of Calculus
• Integration by Substitution (u-sub)
You need to know the derivatives and antiderivatives of polynomials and the six trig functions (Some review materials from Khan Academy might have ex or ln x, but these are not on the Semester 1 Exam).

Math is always cumulative and knowledge of the material covered in earlier chapters could be incorporated in solutions of problems in later chapters.

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

1. 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
2. Khan Academy's AP Calculus AB (Join UCE8NZHF for Block A, and join TYSB6SVP for Block B)
3. myAP.collegeboard.org AP Classroom (6XRDNG for Block A, AEEAEX for Block B)
4. Past Exam Questions from the College Board.
5. Past Exam Answers from Mr Calculus.
6. Past Exam Answers from Skylit.com.
7. Exam Information from the College Board
8. AP Exam Info
9. Example Multiple choice and Free response questions are in the AP Course Description (Exam questions begin around page 228)
10. MC questions from 1969-1998
11. MC Questions from 2003
12. 2008 Multiple choice Questions and answers
13. Video Links from the homework page
14. Worksheet links from the homework page
15. Worksheets from the class Google classroom page.
16. Syllabus has a grade calculator.

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!