# Qtr 3 Study Guide - AP Calculus AB

You are required to bring your own TI-84, pencil and eraser. It is a good idea to have a spare set of 4-AAA batteries (or a battery pack with a charger plug) with you in case your calculator needs it during the test.

The test 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 (8:00 AM May 5, 2020), but slightly less than half as long (the actual AP exam is 3 hours 15 minutes):
NO calculator Section (Which ust be turned in before Calculators are used):

• 14 Multiple choice questions (2 minutes a question= 28 min)
• 1 Free Response question - (15 minutes)
Calculator Section:
• Multiple choice (5 questions) - (15 minutes total)
• Free Response (2 questions) - (15 minutes each = 30 min )

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:

• 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)
• Slope if inverse functions
• Integration and Differentiation of Exponential and Logarithmic functions
• Indeterminate Forms and L'Hôpital's Rule
• Slope fields
• Recognizing when an equation is the solution of a Differential Equation
• Solving Separable Differential Equations
• Area between 2 functions
• Volume of functions rotated around axes and lines parallel to the axes
• Volume of solids that have a base area that is the area between 2 functions

It would be good to go over the Free Response and Multiple choice questions that we started working after the Chapter 7 Test, the PPC's at myAp.collegeBoard.org, and the AP Calc AB at Khan Academy (In particular the solved exams section), homework and tests; review what you did well, and learn from any mistakes. Another worksheet that might be helpful is a strategy review: AP Calculus:When you see the words....

. The exam category is worth 20% of your grade, and will be curved. (There is a grade calculator in the Syllabus)

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

Good Luck!