Calculus+Standard

(January and February tests should be based on AB content only; March tests may contain up to 4 questions based on BC topics; State tests should contain only AB content; the exception is the BC topic test) A. January and February competitions – 27 of the test items should reflect up to 75% of those standards(1.01-10.02) and the remaining 3 items can be selected ‘at large’ from the course curriculum. B. For competitions held March 1 or later, all 30 items can reflect any topic area of the course curriculum.” 1.01 Identify the domain and range of a function. 1.02 Solve problems using the rules of sum; product; quotient; and composition of two functions. 1.03 Determine the inverse of a function. 1.04 Graph functions using symmetry and asymptotes.1.05 Determine the zeros of a function. 2.01 An intuitive understanding of the limiting process 2.02 Calculating limits using algebra 2.03 Estimating limits from graphs or tables of data 2.04 Define e. 3.01 Understanding asymptotes in terms of graphical behavior 3.02 Describing asymptotic behavior in terms of limits involving infinity 3.03 Comparing relative magnitudes of functions and their rates of change (for example, contrasting exponential growth, polynomial growth, and logarithmic growth) 4.01 An intuitive understanding of continuity. (The function values can be made as close as desired by taking sufficiently close values of the domain.) 4.02 Understanding continuity in terms of limits 4.03 Geometric understanding of graphs of continuous functions (Intermediate Value Theorem and Extreme Value Theorem)3. 5.01 Derivative presented graphically, numerically, and analytically 5.02 Derivative interpreted as an instantaneous rate of change 5.03 Derivative defined as the limit of the difference quotient 5.04 Relationship between differentiability and continuity 6.01 Slope of a curve at a point. 6.02 Tangent line to a curve at a point and local linear approximation 6.03 Normal line to a curve at a point 6.04 Instantaneous rate of change as the limit of average rate of change 6.05 Approximate rate of change from graphs and tables of values 7.01 Knowledge of derivatives of basic functions, including power, exponential, logarithmic, trigonometric, and inverse trigonometric functions 7.02 Derivative rules for sums, products, and quotients of functions 7.03 Chain rule and implicit differentiation 7.04 Find the derivative of the inverse of a function 7.05 Find higher order derivatives 8.01 Corresponding characteristics of graphs of ƒ and ƒ’ 8.02 Relationship between the increasing and decreasing behavior of ƒ and the sign of ƒ’ 8.03 The Mean Value Theorem and its geometric interpretation 8.04 Equations involving derivatives. Verbal descriptions are translated into equations involving derivatives and vice versa. 8.05 Corresponding characteristics of the graphs of ƒ, ƒ’, and ƒ’’ 8.06 Relationship between the concavity of ƒ and the sign of ƒ’’ 8.07 Points of inflection as places where concavity changes 9.01 Analysis of curves, including the notions of monotonicity and concavity 9.02 Optimization, both absolute (global) and relative (local) extrema 9.03 Modeling rates of change, including related rates problems 9.04 Use of implicit differentiation to find the derivative of an inverse function 9.05 Interpretation of the derivative as a rate of change in varied applied contexts, including velocity, speed, and acceleration 9.06 Geometric interpretation of differential equations via slope fields and the relationship between slope fields and solution curves for differential equations 9.07 Find basic antiderivatives based on known algebraic and trigonometric derivative rules 10.01 Basic properties of definite integrals (examples include additivity and linearity) 10.02 Numerical approximations to definite integrals. Use of Riemann sums (using left, right, and midpoint evaluation points) and trapezoidal sums to approximate definite integrals of functions represented algebraically, graphically, and by tables of values 10.03 Definite integral as a limit of Riemann sums 10.04 Definite integral of the rate of change of a quantity over an interval interpreted as the change of the quantity over the interval: 11.03 Antiderivatives following directly from derivatives of basic functions, including algebraic, trigonometric, inverse trigonometric, exponential, and logarithmic functions 11.04 Antiderivatives by substitution of variables (including change of limits for definite integrals) 12.01 Finding specific antiderivatives using initial conditions, including applications to motion along a line12.02 Solving separable differential equations and using them in modeling (including the study of the equation y’ = ky and exponential growth)12.03 Find the average value of a function12.04 Find the total distance traveled by a particle along a line 12.05 Find the accumulated change from a given rate of change 12.06 Find the area under a curve using integration 12.07 Find the volume of solids of revolution using disc, washer, or shell methods 12.08 Find the volume of solids with known cross sections 12.09 Use integration appropriately to model physical, biological, or economic situations or other similar applications L’Hospital’s Rule, including its use in determining limits and convergence of improper integrals and series  Parametric, polar, and vector functions The analysis of planar curves includes those given in parametric form, polar form, and vector form.  Analysis of planar curves given in parametric form, polar form, and vector form, including velocity and acceleration  Area of regions bounded by polar curves  Numerical solution of differential equations using Euler’s method  Derivatives of parametric, polar, and vector functions  Antiderivatives by substitution of variables (including change of limits for definite integrals), parts, and simple partial fractions (non-repeating linear factors only)  Improper integrals (as limits of definite integrals)  Solving logistic differential equations and using them in modeling Polynomial Approximations and Series  Motivating examples, including decimal expansion  Geometric series with applications  The harmonic series  Alternating series with error bound  Terms of series as areas of rectangles and their relationship to improper integrals, including the integral test and its use in testing the convergence of p-series  The ratio test for convergence and divergence <span style="font-family: 'Times New Roman',helvetica,sans-serif; font-size: 12px; line-height: normal;"> Comparing series to test for convergence or divergence <span style="font-family: 'Times New Roman',helvetica,sans-serif; font-size: 12px; line-height: normal;"> Taylor polynomial approximation with graphical demonstration of convergence (for example, viewing graphs of various Taylor polynomials of the sine function approximating the sine curve) <span style="font-family: 'Times New Roman',helvetica,sans-serif; font-size: 12px; line-height: normal;"> Formal manipulation of Taylor series and shortcuts to computing Taylor series, including substitution, differentiation, antidifferentiation, and the formation of new series from known series <span style="font-family: 'Times New Roman',helvetica,sans-serif; font-size: 12px; line-height: normal;"> Functions defined by power series <span style="font-family: 'Times New Roman',helvetica,sans-serif; font-size: 12px; line-height: normal;"> Radius and interval of convergence of power series <span style="font-family: 'Times New Roman',helvetica,sans-serif; font-size: 12px; line-height: normal;"> Lagrange error bound for Taylor polynomials <span style="font-family: 'Times New Roman',helvetica,sans-serif; font-size: 12px; line-height: normal;"> Maclaurin series and the general Taylor series centered at x = a <span style="font-family: 'Times New Roman',helvetica,sans-serif; font-size: 12px; line-height: normal;"> Maclaurin series for the functions ex, sinx, cosx , and **Error! 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 * //AP Calculus AB Standards//**
 * //1. Demonstrate the ability to identify and apply properties of algebraic; trigonometric; exponential; and logarithmic functions.//**
 * //2. Demonstrate the ability to apply the concept of limits to functions.//**
 * //3. Demonstrate the ability to identify asymptotic and unbounded behavior.//**
 * //4. Demonstrate an understanding of continuity.//**
 * //5. Apply the concept of the derivative.//**
 * //6. Demonstrate the ability to apply derivatives to find the slope of a curve and tangent and normal lines to a curve and as an instantaneous rate of change.//**
 * //7. Demonstrate the ability to compute derivatives of algebraic; trigonometric; exponential; and logarithmic functions.//**
 * //8. Demonstrate the ability to identify increasing and decreasing functions; relative and absolute maximum and minimum points; concavity; and points of inflection.//**
 * //9. Demonstrate an understanding of applications of the derivative.//**
 * //10. Demonstrate the ability to interpret definite integrals and use properties of definite integrals//**
 * //11. Demonstrate the ability to use the techniques of integration .//** 11.01 Use of the Fundamental Theorem to evaluate definite integrals 11.02 Use of the Fundamental Theorem to represent a particular antiderivative, and the analytical and graphical analysis of functions so defined
 * //12. Demonstrate the ability to apply antiderivatives to solve problems including growth and decay, particle motion, and finding areas and volumes//**
 * //Calculus BC Topics//** for use only on March or State BC Topic tests. These topics should not be tested on January or February tests.