• AP Calculus BC

SCOPE AND SEQUENCE-AP CALCULUS BC 2008-2009

First Quarter ** NOTE: Include AP review throughout each quarter.

Number of

Blocks Concept Text Reference

2 LIMITS & THEIR PROPERTIES Chapter 1

Limits--Graphically, Numerically & Analytically 1.2/1.3

Continuity, One-Sided Limits, Infinite Limits 1.4/1.53 DERIVATIVES Chapter 2

Derivative, Tangent Line Problem, Differentiation Rules, Rates of Change 2.1/2.2/2.3

Chain Rule, Implicit Differentiation & Quiz 2.4/2.5

Related Rates 2.65 APPLICATIONS OF DIFFERENTIATION Chapter 3

Extrema, Rolle's Theorem, Mean Value Theorem, First Derivative Test 3.1/3.2/3.3

Quiz, Second Derivative Test, Concavity, Limits at Infinity, Curve Sketching 3.4/3.5/3.6

Review

Optimization, Newton's Method, Differentials 3.7/3.8/3.9

Test Chapter 3 3.105 INTEGRATION Chapter 4

Antiderivatives, Indefinite Integrals, Area 4.1/4.2

More Area, Riemann Sums, Definite Integrals 4.2/4.3

Fundamental Theorem of Calculus 4.4

Integration by Substitution 4.5

Numerical Integration 4.69 LOGARITHMIC & EXPONENTIAL FUNCTIONS Chapter 5

Natural Log & Derivatives 5.1

Ln x & Integration, Inverse Functions 5.2/5.3

Exponential Functions, Derivative & Integration 5.4

Other Bases & Applications 5.5

48 days Growth & Decay, Differential Equations 5.6

Separable Differential Equations 5.7

Slope Fields/Euler’s Method

Inverse Trig Functions & Derivatives 5.8

Inverse Trig Functions & Integrations 5.924 blocks in Quarter

Second Quarter ** NOTE: Include AP review throughout each quarter.

Number of

Blocks Concept Text Reference

1 Test Chapter 5, Area Between Two Curves 6.18 AREA & VOLUME Chapter 6

Discs Method & Volume with Cross Sections 6.2

Shell Method 6.3

Review

Arc Length & Surfaces of Revolution 6.4WORK 6.5

Moments, Centers of Mass, Centroids (optional) 6.7

Review (torus)

Test Chapter 69 INTEGRATION, L'HOPITAL'S RULE, & IMPROPER INTEGRALS Chapter 7

Basic Integration 7.1

Integration by Parts 7.2TRIGONOMETRIC INTEGRALS 7.3

Trigonometric Substitution 7.4

Partial Fractions 7.5

Logistics Worksheet

Indeterminate Forms, L'Hopital's Rule 7.7

41 days Improper Integrals 7.8

Test Chapter 72 INFINITE SERIES Chapter 8

Sequences 8.1

Series & Convergence 8.218 Blocks in this quarter (2 blocks for Semester Exams)

SCOPE AND SEQUENCE-AP CALCULUS BC 2008-2009

Third Quarter ** NOTE: Include AP review throughout each quarter.

Number of

Blocks Concept Text Reference

12 INFINITE SERIES Chapter 8

Integral Test & p-series 8.3

Comparisons of Series 8.4

Quiz

Alternating Series 8.5

Ratio & Root Tests 8.6

Review 8.1-8.6

Taylor Polynomials & Approximations 8.7

Power Series 8.8

Representation of Functions by Power Series 8.9

Taylor & Maclaurin Series 8.10

Review 8.5-8.10

Test Chapter 84 PARAMETRIC EQUATIONS & POLAR COORDINATES Chapter 9

Conics & Calculus, Plane Curves & Parametric Equations 9.1/9.2

(may review conics with section 9.1)

Parametric Equations & Calculus 9.3

Polar Coordinates & Graphs 9.4

Area & Arc Length in Polar Coordinates 9.51 VELOCITY & ACCELERATION VECTORS & SPEED Chapter 11

Vector-Valued Functions, Differentiation & Integration of Vector-Valued 11.1/11.2/11.3

Functions, Velocity & Acceleration (supplement background info on vectors

52 days with 11.1 & 11.2)2 Logistics Models Supplement (Theme Book, etc)26 Blocks in this quarter

Fourth Quarter ** NOTE: Include AP review throughout each quarter.

Number of

Blocks Concept Text ReferenceReview for the Test Use AP Problems All Year.

Practice old AP problems.

Centers of Mass and Fluid Pressure (if possible) 6.6 & 6.7EXAM May 3, 2008-AM

19 Blocks in this quarter (2 blocks for Semester Exams)42 daysSCOPE AND SEQUENCE-AP CALCULUS BC 2008-2009

Themes for Advanced Placement Calculus Book

Section Theme Topic

P.4 1

1.5 2

2.3 3

3.4 4

4.4 5

4.4 6

4.4 8

5.7 10

5.8 9

6.5 7

7.5 11

7.2 12

8.1 13

9.6 14

11.3 15 Parametric & Vector Functions

Polar Coordinates & Applications

Taylor Polynomials

Euler’s Method

LOGISTICS Equations & SLOPE FIELDS (uses partial fractions)

Integration Applications

Inverses

Differential Equations (LOGISTICS)

Derivative as a Function

Limits & Continuity

Modeling Functions

Rectilinear Motion

Integral as Accumulator Function

Total Change

Geometry of Derivatives