- White Plains Public Schools
- Curricula
- High School
- AP Calculus BC
-
AP Calculus BC: This Advanced Placement course completes the study of the BC level of Advanced Placement Calculus. The students are required to pay the fee and take the Calculus BC Advanced Placement Exam in order to receive the weighted final grade. The final exam is a departmental exam.
Please note that the timelines listed below are a guide. Teachers modify their pacing based on student needs in order to ensure concept mastery.Unit 1
Transcendental Functions- Trig Functions
September
Section
Concepts
Anton Resources
2.5
Find the limit of trig functions
2.5
Find derivatives of all six trig functions
2.5
Find anti-derivatives of all six trig functions
2.5
Find derivatives and evaluate integrals of trig based functions.
2.5
Find the derivatives of inverse sine/tangent functions.
Unit 2
Tools of Integration
Sep-Oct
Section
Concepts
Anton Resources
4.1
An Overview of the Area Problem
4.2
The Indefinite Integral
4.3
Integration by Substitution
4.4
The Definition of Area as a Limit
Pages 281-286
4.5
The Definite Integral
Pages 287-299
4.6
The Fundamental Theorem of Calculus – Parts I & II
4.7
Rectilinear Motion and Integration
Pages 309-321
4.8
Average Value of Function and its Applications
Pages 322-331
4.9
Evaluating Definite Integrals by Substitution
Pages 332-336
Pages
Unit 3
Applications of Integrals
October
Section
Concepts
Anton Resources
5.1
Area between two curves
Pages 347-354
5.2
Volume by Slicing – disks and washers
5.3
Volume by Cylindrical Shell
5.4
Length of a Plane Curve
5.5
Work
Optional: Find surface area of a solid of revolution.
Optional: Use integration methods to investigate fluid pressure.
Unit 4
Motion
October
Section
Concepts
Anton Resources
4.7
Motion
4.7
Find the velocity given position in terms of time
4.7
Find the acceleration from velocity
4.7
Find linear approximations by means of differentials
End of Quarter 1
Unit 5
Exponential, Logarithmic, and Inverse Trigonometric Functions
Nov-Dec
Section
Concepts
Anton Resources
6.1
Exponential and Logarithmic Functions
6.2
Derivatives and Integrals Involving Logarithmic Functions
6.3
Derivatives of Inverse Functions; Derivatives and Integrals Involving Exponential Functions
6.4
Graphs and Applications Involving Logarithmic and Exponential Functions
6.5
L’Hopital’s Rule; Indeterminate Form
6.6
Logarithms and other functions defined by integrals
6.7
Derivatives and Integrals involving Inverse Trig Functions
Unit 6
Integration Techniques
Dec-Jan
Section
Concepts
Anton Resources
7.1
Overview of Integration Methods
7.2
Integration by Parts
7.3
Integrating Trig Functions (powers of sine and cosine)
7.4
Trig Substitution
7.5
Integrating Rational Functions by Partial Fractions
7.7
Numerical Integration; Simpson’s Rule
7.8
Improper Integrals
End of Quarter 2
Unit 7
Series and Sequences
March
Section
Concepts
Anton Resources
10.1
Parametric Equations: Tangent Lines and Arc Length for Parametric Curves
10.2
Polar Coordinates
10.3
Tangent Lines, Arc length, and Area for Polar Curves
Unit 8
Modeling with Differential Equations
February
Section
Concepts
Anton Resources
8.1
Modeling with Differential Equations
8.2
Separation of Variables
8.3
Slope Fields, Euler’s Method
8.4
First-Order Differential Equations and Applications
End of Quarter 3
Unit 9
Series and Sequences
Feb-Mar
Section
Concepts
Anton Resources
9.1
Sequences
9.2
Monotone Sequences
9.3
Infinite Series
9.4
Convergence Tests
9.5
The Comparison, Ratio, and Root Tests
9.6
Alternating Series; Absolute and Conditional Convergence
9.7
Maclaurin and Taylor Polynomials
9.8
Maclaurin and Taylor Series; Power Series
9.9
Convergence of Taylor Series
9.10
Differentiating and Integrating Power Series; Modeling with Taylor Series
Unit 10
Parametric, Polar and Vector Calculus
April
Section
Concepts
Anton Resources
10.1
Parametric Equations
10.2
Polar Review
10.3
Area of Polar Curves
12.1
Vectors
12.6
Vector Valued Functions
Review for AP Exam
Final Exam