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CURRICULUM MAP COURSE TITLE: ____AP CALCULUS___ Sept Oct. Nov. Dec. Jan Essential Questions How can we extend our knowledge What is the relationship between a How do we integrate more complex How can we extend the How do we determine the of derivatives to analyze graphs and definite integral, Riemann sums and functions and how they relate to application of the definite integral technique of integration that is real world phenomena? the area of a region? applications? to area, volume and arc length? best suited for an integral? Differentiation: exponential, Anti-Differentiation and Integration by substitution Area of regions between two Review of elementary Content logarithmic, inverse trig. properties of the indefinite Trapezoidal rule curves integration techiniques Functions integral Volumes of solids of Integration by Parts Review of Curve Sketching Riemann summation and Slope fields revolution: discs, washers, applied to the above notation Integration of logarithmic, shells Trig Substitution Differentiation of Parametric Properties of definite integral exponential and inverse trig. Volumes of solids with Partial Fractions and Polar Curves functions known cross sections Logistic differential Fundamental Theorem of Separable differential equations Applications including Calculus (parts 1 - 2) equations and initial Arc Length differentials and error Accumulation Functions conditions Area bounded by polar Indeterminate Forms and curves L’Hopital’s rule Average Value Rectilinear motion Improper integrals Surface area Euler’s Method This may extend into the first week of February. Connect and apply Develop all basic rules for Discriminate the appropriate Analyze and formulate Using all new methods of logarithmic and exponential integration method of integration integrals to represent area integration and recognizing Skills rules to derivatives and Compare the definite integral Integration of exponential, between two curves when to use each new applications and area under a curve logarithms and inverse trig including polar curves method Synthesize information to Composing Riemann sums – functions Select the appropriate Combining partial fractions sketch graphs and optimize all right, left, midpoint Extend the knowledge of method (discs, washers, and knowledge of separable functions Riemann sums to using the shells) to find the volume of differential equations to Apply local linearization to Evaluate an accumulation Trapezoidal Rule with equal a solid of revolution solve logistic diff eq’s error analysis and derive function including a particular and unequal partitions Synthesize the knowledge Identify the type of Newton’s Method solution defined as an integral for area of a region, and indeterminate form and Identify, analyze and produce known geometric formulas evaluate their limits using slope fields to determine volumes of L’Hopital’s rule Apply integration and solids with known cross Extend the Fundamental solutions of differential sections Theorem using limits to equations to various Extend and apply the evaluate improper integrals applications distance formula and Riemann sums to find arc Apply local linearization to length of rectangular and develop Euler’ method parametric equations Surface Area C.H. 4.1.12C-1 4.2.12.B-4(bullets 2 and 3) 4.2.12B-4(bullets 2 and 3) 4.2.12A-1,3 4.1.12C-1 Standard/ 4.2.12D-2 4.2.12C-1 4.2.12C-1,2 4.2.12B-1,2,4 4.2.12E-1,2 Benchmarks 4.2.12E-2 4.2.12E-2 4.2.12E-2 4.2.12C-1 4.3.12B-1,2,4 4.3.12B-1,2,3,4 4.3.12A-1,2,3 4.3.12A-1,2,3 4.2.12E-1,2 4.3.12C-1 4.3.12C-1,2 4.3.12B-1,2,4 4.3.12B-1,2,4 4.3.12A-1 4.3.12D-3 4.3.12D-3 4.3.12C-1,2,3 4.3.12C-1,2,3 4.3.12B-1,2,3,4 4.5.A,B,C,D,E,F 4.4.12A2 4.3.12D-3 4.3.12D-3 4.5A,B,C,D,E,F 4.5.A,B,C,D,E,F 4.5.A,B,C,D,E,F 4.5.A,B,C,D,E,F Tests Tests Tests Tests Tests Assessments AP Problem of the Day AP Problem of the day AP Problem of the day AP Problem of the day AP Problem of the day CBL Lab: Fluids, Force and Graded worksheets / Graded worksheets / Graded worksheets / Graded worksheets / Pressure Explorations Explorations Explorations Explorations Graded worksheets / Internet Activities using Calculator Lab: Virus lab WinPlot Computer lab Explorations “Visual Calculus” Presentations: Fund Th. CBL Lab: Walk This Way CURRICULUM MAP COURSE TITLE: ______AP CALCULUS______ Feb. Mar. Apr. May June . Essential What methods are used to What techniques are used to REVIEW FOR AP EXAM How can we extend the REVIEW FOR FINAL Questions determine the convergence find and use the Taylor and most recent calculus topics or divergence of an infinite Maclaurin series? to practical applications in series? the laboratory? Sequences February topics may continue Most recent open-ended Topic exploration Content into early March and multiple choice CBL labs (Foerster, P) Infinite Series Taylor and Maclaurin questions Research writing Review packets for Nth term test for polynomials - Accumulation assignment (extension final exam divergence Power series f(x) of second semester Geometric and p-series Radius and interval of - Parametric topics) Integral test convergence f(x) Career investigations Comparison of Series Taylor and Maclaurin - Area, Volume, Alternating series test series Cross-Section Ratio and root tests Approximating the - Logistic D Eq Other topics of interest error bound using - Taylor/MacL Topics in italics Absolute and condit. Lagrange Hyperbolic trig. func., convergence - Curve Sketch etc. Recognize the Extending local Develop test-taking difference between a linearization to higher skills and strategies Skills sequence and a series degree polynomials to create Taylor and Decide what test is appropriate to Maclaurin polynomials Emphasize scoring rubrics determine the Representing functions convergence or as power series divergence of a series Determining the radius Mock AP exam and Computing sums of and the interval of scoring workshop (in- geometric series and convergence of a series school field trip) telescoping series Extend Taylor and Maclaurin polynomials to their series counterparts Support approximations by use of Lagrange error bound C.H. 4.2.12D-2 4.1.12C-1 Standard/ 4.2.12E-1 4.2.12D-2 Benchmarks 4.3.12A-1,2,3 4.2.12E-1 4.3.12B-1,2,3,4 4.3.12A-1,2,3 4.3.12C-1,2 4.3.12B-1,2,3,4 4.3.12D-3 4.3.12C-1,2 4.5.A,B,C,D,E,F 4.3.12D-3 4.5.A,B,C,D,E,F Tests Tests Graded AP Problems Graded AP Problems Final exam packets Assessments AP Problem of the day AP Problem of the day Practice AP Exam Reflection on AP Graded worksheets / Graded worksheet / exam Explorations Explorations CBL: Bouncing Ball Reflection CBL: Pendulum Lab Writing Assignment: Maclaurin, Taylor, etc.

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Calculus Basic Integration Worksheet document sample

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