Course Map for

BC Calculus and Lab

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)



Be able to define integration

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

Eulerís Method

Differential Equations

Logistic Equations



Be able to integrate by separation of variables.

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 Eulerís 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 by parts

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 series/polynomials/approximations

Taylor and Maclaurin series

Parametric equations

Polar Coordinates (arc length)

Parametric equations

 



Identify series, sequences, nth terms, and summation

 

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.) Ė Chapter 11, Making connections

Calculus of parametric equations

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