Course Map for
Month |
Core Standard |
Learning Activity |
Assessment |
August- September |
Chapter P-Chapter 1 Pre Calculus Review Limits Graphically Analytically Numerically Infinite Limits |
Review Pre Calculus skills Finds limits graphically, analytically, numerically Be able to predict end behavior of a function |
Random check of homework Random quizzes Classroom discussions and review of topics Exams over core standards Labs over core standards or to introduce topics |
October |
Chapter 2-3 Secant vs Tangent Line Rate of change Instantaneous vs average Derivatives (limit definition) Basic rules Chain rule Implicit Differentiation Related Rates Extrema (Extreme value therom) Rolle's and Mean Value Therom 1st derivative test/critical pnts/ increasing / decreasing 2nd derivative test /inflection pnts/ concavity Curve sketching Optimization Newton's Method Differentials and Linearization |
Define secant and tangent lines Find average rate of change and instantaneous rate of change Derive basic integration rules using the definition. Know and apply chain rule Solve related rate problems Find maximums and minimums of functions Know and apply Rolle's and Mean Value therom Be able to describe the behavior of function using 1st and 2nd derivative tests, and precalculus items. Approximate values |
Random check of homework Random quizzes Classroom discussions and review of topics Exams over core standards Labs over core standards or to introduce topics |
November |
Chapter 4-Chapter 5 Antiderivatives Area Riemann sums- Definite integrals Chain rule in reverse Fundamental Therom of Calculus Integration by substitution Numerical integration Natural logs (differentiation/integration) Inverse functions Exponential functions (growth/decay) |
Find area under a curve Know and apply the definiton of an integral. Be able to explain and use the Fundamental Therom of Calculus Review logarithms and know the integration and derivative rules Review Inverse functions Be able to find growth and decay models based on exponential growth or decay |
Random check of homework Random quizzes Classroom discussions and review of topics Exams over core standards Labs over core standards or to introduce topics |
December |
Chapter 5(cont) - Chapter 6 Seperation of variables Inverse Trig functions (differentiation/ integration) Slope Fields Euler’s Method Differential Equations Logistic Equations |
Know and be able to apply the rules of inverse trig functions Be able to generate slope fields by hand and on calculator Estimate curvature and tangent lines using Euler’s Method Be able to solve first order differential equations Apply differential equations to logistic methods |
Random check of homework Random quizzes Classroom discussions and review of topics Exams over core standards Labs over core standards or to introduce topics |
January |
Chapter 7- Chapter 8 Area between curves Volume (shell and disk) Arc length/ surface area Work Average Integration by parts Trig substitution Partial Fractions Integration by tables L'Hopitals rule for limits Improper integrals |
Find the area between to curves, volume of objects, arc lengths of curves, and surface areas using integrals. Compute work done by a varying force. Calculate averages of functions
Be able to integrate using tables and trig substitution Decompose rational functions into partial fractions for integration Use L'hopital's rule to find limits Integration with infinite limits |
Random check of homework Random quizzes Classroom discussions and review of topics Exams over core standards Labs over core standards or to introduce topics |
February |
Chapter 9 - Chapter 10 Series/sequences Convergence Tests for convergence Comparison test/ Alternating / Ratio / Root / P series/ Limit comparison/ integral test Taylor and Maclaurin series Parametric equations Polar Coordinates (arc length) Parametric equations |
Be able to tell if a series converges by using Comparison test, Limit Comparison test, Ratio test, Root test, p-series test, nth term test, Integral test, and Alternating series test Build Talyor and MacClaurin polynomials to estimate values of functions Graph parametric and polar equations using techniques discussed in chapter 3 |
Random check of homework Random quizzes Classroom discussions and review of topics Exams over core standards Labs over core standards or to introduce topics |
March |
Chapter 10 (cont.) – Chapter 11, Making connections Polar Coordinates (arc length) Vectors |
Find arc length and surface area using parametric and polar equations. Find slopes of tangent lines to parametric and polar equations Use vector-valued functions Calculate position, velocity, and acceleration using vectors Be able to take methods of integration and rules of derivatives and apply them in story problem settings. |
Random check of homework Random quizzes Classroom discussions and review of topics Exams over core standards Labs over core standards or to introduce topics |
April |
Review |
Be able to pass AP test |
Practice AP tests Free Response Multiple choice with calculator Multiple choice without calculator |
May-June |
AP TEST Additional topics and/or project |
Discuss related topics in math |
Take AP test (date to be announced) Projects |