• 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