# Calculus Basic Integration Worksheet - DOC

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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
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