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 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