Differential Equations-Modeling situations with differential equations, verifying solutions for differential equations, sketching slope fields, and using separation of variables.Integration and Accumulation of Change-Finding accumulations of change, Reimann sums, and definite integrals, understanding the Fundamental Theorem of Calculus, interpreting accumulation functions, finding anti-derivatives and indefinite integrals, and integrating using substitutions, long division, and completing the square.Analytical Applications of Differentiation-Understanding the Mean Value Theorem, using the Extreme Value Theorem, finding global and local extrema, applying the First Derivative Test and Second Derivative Test, finding intervals of increase and decrease, understanding concavity, sketching graphs, solving optimization problems, and using implicit relations.Contextual Applications of Differentiation-Interpreting derivatives in context, using rates of change in motion and other context, applying related rates, approximating using linearization, and applying L’Hospital’s Rule.
Differentiation: Composite, Implicit, and Inverse Functions-Applying the Chain Rule, using implicit differentiation, differentiating inverse functions, and calculating higher order derivatives.Differentiation: Definition and Basic Rules-Defining average and instantaneous rates of change, defining the derivative of a function, estimating derivatives at a point, connecting differentiability and continuity, applying the Power Rule, the Product Rule, and the Quotient Rule, and determining derivatives of constants, sums, differences, and constant multiples, trigonometric functions, e x, and ln x.Limits and Continuity-Defining limits, estimating limits from graphs and tables, determining limits using algebraic properties and manipulation, applying the Squeeze Theorem, Determining types of discontinuities, understanding asympototes, and the applying Intermediate Value Theorem.You should be familiar with the following topics: The College Board is very detailed in what they require your AP teacher to cover in his or her AP Calculus AB course. If you score high enough on the exam, your AP Calculus score could earn you college credit!Ĭheck out our AP Calculus AB Guide for the essential information you need for the exam: Private Tutoring with Pass Assurance NEWĪre you familiar with the Mean Value Theorem? Can you calculate derivatives? The AP ® Calculus AB exam tests topics and skills discussed in your AP Calculus AB course.
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