Course Content. Phillips Academy was one of the first schools to teach AP®︎ nearly 60 years ago. 4.2 Straight-Line Motion: Connecting Position, Velocity, 4.3 Rates of Change in Applied Contexts Other Than, 4.6 Approximating Values of a Function Using Local, 4.7 Using L'Hopital's Rule for Determining Limits of, 5.2 Extreme Value Theorem, Global Versus Local, 5.3 Determining Intervals on Which a Function is, 5.4 Using the First Derivative Test to Determine Relative, 5.5 Using the Candidates Test to Determine Absolute, 5.6 Determining Concavity of Functions over Their, 5.7 Using the Second Derivative Test to Determine, 5.8 Sketching Graphs of Functions and Their Derivatives, 5.9 Connecting a Function, Its First Derivative, and Its, 5.10 Introduction to Optimization Problems, 5.12 Exploring Behaviors of Implicit Relations, 2.3 Differentiability [Calculator Required], 8.2 Fundamental Theorem of Calculus (part 1), 8.3 Antiderivatives (and specific solutions), 10.2 u-Substitution (indefinite integrals). 2. The Course challenge can help you understand what you need to review. The framework also encourages instruction that prepares students for advanced coursework in mathematics or other fields engaged in modeling change (e.g., pure sciences, engineering, or economics) and for creating useful, reasonable solutions to problems encountered in an ever-changing world. Learn more about the CED in this interactive walk-through. Determining limits using algebraic properties of limits: limit properties, Determining limits using algebraic properties of limits: direct substitution, Determining limits using algebraic manipulation, Selecting procedures for determining limits, Determining limits using the squeeze theorem, Connecting infinite limits and vertical asymptotes, Connecting limits at infinity and horizontal asymptotes, Working with the intermediate value theorem, Defining average and instantaneous rates of change at a point, Defining the derivative of a function and using derivative notation, Estimating derivatives of a function at a point, Connecting differentiability and continuity: determining when derivatives do and do not exist, Derivative rules: constant, sum, difference, and constant multiple: introduction, Derivative rules: constant, sum, difference, and constant multiple: connecting with the power rule, Derivatives of cos(x), sin(x), ˣ, and ln(x), Finding the derivatives of tangent, cotangent, secant, and/or cosecant functions, Differentiating inverse trigonometric functions, Selecting procedures for calculating derivatives: strategy, Selecting procedures for calculating derivatives: multiple rules, Further practice connecting derivatives and limits, Interpreting the meaning of the derivative in context, Straight-line motion: connecting position, velocity, and acceleration, Rates of change in other applied contexts (non-motion problems), Approximating values of a function using local linearity and linearization, Using L’Hôpital’s rule for finding limits of indeterminate forms, Extreme value theorem, global versus local extrema, and critical points, Determining intervals on which a function is increasing or decreasing, Using the first derivative test to find relative (local) extrema, Using the candidates test to find absolute (global) extrema, Determining concavity of intervals and finding points of inflection: graphical, Determining concavity of intervals and finding points of inflection: algebraic, Using the second derivative test to find extrema, Sketching curves of functions and their derivatives, Connecting a function, its first derivative, and its second derivative, Exploring behaviors of implicit relations, Riemann sums, summation notation, and definite integral notation, The fundamental theorem of calculus and accumulation functions, Interpreting the behavior of accumulation functions involving area, Applying properties of definite integrals, The fundamental theorem of calculus and definite integrals, Finding antiderivatives and indefinite integrals: basic rules and notation: reverse power rule, Finding antiderivatives and indefinite integrals: basic rules and notation: common indefinite integrals, Finding antiderivatives and indefinite integrals: basic rules and notation: definite integrals, Integrating functions using long division and completing the square, Integrating using linear partial fractions, Modeling situations with differential equations, Verifying solutions for differential equations, Approximating solutions using Euler’s method, Finding general solutions using separation of variables, Finding particular solutions using initial conditions and separation of variables, Exponential models with differential equations, Logistic models with differential equations, Finding the average value of a function on an interval, Connecting position, velocity, and acceleration functions using integrals, Using accumulation functions and definite integrals in applied contexts, Finding the area between curves expressed as functions of x, Finding the area between curves expressed as functions of y, Finding the area between curves that intersect at more than two points, Volumes with cross sections: squares and rectangles, Volumes with cross sections: triangles and semicircles, Volume with disc method: revolving around x- or y-axis, Volume with disc method: revolving around other axes, Volume with washer method: revolving around x- or y-axis, Volume with washer method: revolving around other axes, The arc length of a smooth, planar curve and distance traveled, Defining and differentiating parametric equations, Second derivatives of parametric equations, Finding arc lengths of curves given by parametric equations, Defining and differentiating vector-valued functions, Solving motion problems using parametric and vector-valued functions, Defining polar coordinates and differentiating in polar form, Finding the area of a polar region or the area bounded by a single polar curve, Finding the area of the region bounded by two polar curves, Defining convergent and divergent infinite series, Determining absolute or conditional convergence, Finding Taylor polynomial approximations of functions, Radius and interval of convergence of power series, Finding Taylor or Maclaurin series for a function, See how our content aligns with AP®︎ Calculus BC standards.

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