AP Calculus AB
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. 2019 Summer Assignment is to be completed prior to the 1st day of class 
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 
