•  

    calc
      

    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 49-61

    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 62-68

     

     

    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 One-Sided Limits

    Determine continuity at a point and continuity on an open interval

    Pages 54, 90-97

     

     

    Determine 1-sided 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 71-78

     

     

    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 110-121

     

     

    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 134-141

     

     

    Use derivatives to find rates of change.

     

    2.3

    Product and Quotient rules and Higher-Order Derivatives

    Find the derivative using the Product and Quotient Rule.

    Pages 142-147

     

     

    Find the derivative of a trigonometric function

     

     

     

    Find a higher-order derivative of a function

     

    2.4

    The Chain Rule

    Find the derivative of a composite and trigonometric function using the Chain Rule

    Pages 153-160

    2.5

    Implicit Differentiation

    Distinguish between implicit form and explicit form 

    Pages 161-167

     

     

    Use implicit differentiation to find the derivative of a function

     

    2.6

    Related Rates

    Find a related rate

    Pages 168-174

     

     

    Used related rates to solve real-life 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 216-222

     

     

    Find extrema on a closed interval

     

    3.2

    Rolle’s and Mean Value Theorem

    Understand and use Rolle’s and Mean Value Theorem

    Pages 252-260

    3.3

    Increasing and Decreasing Functions and the First Derivative Test

    Determine intervals of increasing and decreasing

    Pages 187-193

     

     

    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 197-205

     

     

    Find points of inflection

     

     

     

    Use the Second Derivative Test to find extrema

     

    3.5

    Pre-curve Sketching

    Summary of pre-requisite skills needed for curve sketching

    Teacher generated

    3.6

     Curve Sketching

    Analyze and sketch the graph of a function

    Pages 202-204

    3.7

    Optimization Problems

    Solved applied minimum and maximum problems

    Pages 224-233

    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 265-270,287-297

     

     

    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,  355-357

    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

    May-June

     End of Quarter 4