 White Plains Public Schools
 Curricula

AP Calculus AB: This Advanced Placement course completes the study of the AB level of Advanced Placement Calculus. The students are required to pay the fee and take the Calculus AB 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
Limits and Their Properties
September
Section
Concepts
Objectives
Textbook
1.1
Introduction to Limits
Develop the concept of limits with instantaneous and average rate of change
Pages 4961
1.2
Finding Limits Graphically and Numerically
Estimate a limit using a numerical and graphical approach
Teacher generated
Learn different ways a limit can fail to exist
1.3
Evaluating Limits Analytically
Evaluate a limit using properties of limits
Pages 6268
Develop and use a strategy for finding limits
Evaluate a limit using dividing out and rationalizing techniques
Evaluate a limit using the Squeeze Theorem
1.4
Continuity and OneSided Limits
Determine continuity at a point and continuity on an open interval
Pages 54, 9097
Determine 1sided limits and continuity on a closed interval.
Use the properties of continuity
Use the Intermediate Value Theorem
1.5
Infinite Limits and Limits at Infinity
Determine infinite limits from the left and right
Pages 7178
Find the vertical asymptotes of the graph of a function
Determine limits at infinity
Determine horizontal asymptotes if they exist
1.6
Graphs of Limits and Discontinuities
Describe and draw graphs with varying continuity and discontinuities. Sketch vertical and horizontal asymptotes.
Teacher generated
Unit 2
Differentiation
Oct  Nov
Section
Concepts
Objectives
Textbook
2.1
Derivative and the Tangent Line
Find the slope of the tangent line to a curve at a point.
Pages 110121
Use the limit definition to find the derivative.
Understand the relationship between differentiability and continuity
2.2
Basic Differentiation Rules and Rates of Change
Find the derivative using the Constant, Power, Constant Multiple, Sum and Difference Rules.
Pages 134141
Use derivatives to find rates of change.
2.3
Product and Quotient rules and HigherOrder Derivatives
Find the derivative using the Product and Quotient Rule.
Pages 142147
Find the derivative of a trigonometric function
Find a higherorder derivative of a function
2.4
The Chain Rule
Find the derivative of a composite and trigonometric function using the Chain Rule
Pages 153160
2.5
Implicit Differentiation
Distinguish between implicit form and explicit form
Pages 161167
Use implicit differentiation to find the derivative of a function
2.6
Related Rates
Find a related rate
Pages 168174
Used related rates to solve reallife situations
End of Quarter 1
Unit 3
Applications of Differentiation
Nov  Dec
Section
Concepts
Objectives
Textbook
3.1
Extrema on an Interval
Understand the definition of extrema and relative extrema on an interval and open interval
Pages 216222
Find extrema on a closed interval
3.2
Rolle’s and Mean Value Theorem
Understand and use Rolle’s and Mean Value Theorem
Pages 252260
3.3
Increasing and Decreasing Functions and the First Derivative Test
Determine intervals of increasing and decreasing
Pages 187193
Use the First Derivative Test to find relative extrema of a function
3.4
Concavity and the Second Derivative Test
Determine intervals of concave up and down
Pages 197205
Find points of inflection
Use the Second Derivative Test to find extrema
3.5
Precurve Sketching
Summary of prerequisite skills needed for curve sketching
Teacher generated
3.6
Curve Sketching
Analyze and sketch the graph of a function
Pages 202204
3.7
Optimization Problems
Solved applied minimum and maximum problems
Pages 224233
3.8
Differentials
Compare value of the differential, dy w/ the actual change in y
Pages 175  180
Find the differential of a function using differentiation formulas
3.9
Graphs of Functions and their Derivatives
Analyze and understand the relationship between the graphs of functions and their derivatives
Teacher generated
Unit 4
Integration
Dec  Jan
Section
Concepts
Objectives
Textbook
4.1
Antiderivatives and Indefinite Integration
Write the general solution of a differential equation
Pages 271  278
Use basic integration rules to find antiderivative.
Find a particular solution of a differential equation
4.2
Integration by Substitution
Use a change of variables to evaluate an integral
Pages 281  285
4.3
Area and Riemann Sums
Understand and approximate the area of a plane region
Pages 265270,287297
Understand the definition of Riemann Sum
Evaluate a definite integral using limits
Approximate a definite integral using the Trapezoidal Rule
4.4
Fundamental Theorem of Calculus
Evaluate definite integral using the Fundamental Theorem of Calculus
Pages 300 319
Use the Mean Value Theorem for integrals
Use the average value of a function over a closed interval
Use the Second Fundamental Theorem of Calculus
4.5
Integration & Motion
Integration with rectilinear motion
Pages 322 329
End of Quarter 2
Unit 5
Applications of Integration
Feb
Section
Concepts
Objectives
Textbook
5.1
Area of a Region between Two Curves
Find the area of a region between intersecting curves using integration
Pages 347  353
5.2
Volume by Revolution: Disk and Washer Method
Find the volume of a solid of revolution using the disk method
Pages 358  362
Find the volume of a solid of revolution using the washer method
5.3
Volume by Revolution: Shells Method
Find the volume of a solid of revolution using the shells method
Pages 365  369
5.4
Volume by Cross Section
Find the volume of a solid with known cross sections
Pages 351, 355357
Unit 6
Logarithmic and Exponential Functions
Feb  Mar
Section
Concepts
Objectives
Textbook
6.1
Differentiation of the Natural Logarithmic Function
Find derivatives of functions involving the natural logarithmic function
Pages 420  423
6.2
Integration of the Natural Logarithmic Function
Use the Log Rule for integration to integrate a rational function.
Pages 423 425
6.3
Differentiation and Integration of Exponential Functions
Differentiate natural exponential functions. Integrate natural exponential functions.
Pages 427 – 428
Integrate natural exponential functions.
6.4
Bases other than e
Differentiate and integrate exponential functions that have bases other than e.
Pages 429 – 432
6.5
Differentials and Growth & Decay
Use differentials to derive the exponential growth & decay model
Teacher generated
6.6
Separation of Variables
Use initial conditions to find particular solutions of differential equations. Solve differential equations by separation of variables
Pages 568
6.7
Slope Fields
Sketch the slope field of a function
Pages 579
End of Quarter 3
Unit 7
Inverse Trigonometric Functions
April
Section
Concepts
Objectives
Textbook
7.1
Differentiation of Inverse Trigonometric Functions
Differentiate inverse trigonometric functions
Pages 462  467
7.2
Integration of Inverse Trigonometric Functions
Integrate functions whose antiderivatives involve inverse trigonometric functions.
Pages 467  470
7.3
Integrating Trigonometric Functions
Integrate trigonometric functions with positive integer powers
Pages 500  506
7.4
Indeterminant Forms & L'Hopital's Rule
Investigate the types of indeterminante form and use derivatives to find the limits using L'Hopital's Rule
Pages 441  447
Unit 8
AP Exam Review
Apr  May
Unit 9
Calculus Applied Problems Project
MayJune
End of Quarter 4