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Advance d Place me nt AP Calculus ABIn AP Calculus AB, students learn to understand change geometrically and visually (by studying graphs of curves),analytically (by studying and working with mathematical formulas), numerically (by seeing patterns in sets of numbers), andverbally. Instead of simply getting the right answer, students learn to evaluate the soundness of proposed solutions and toapply mathematical reasoning to real-world models. Calculus helps scientists, engineers, and financial analysts understandthe complex relationships behind real-world phenomena. The equivalent of an introductory college-level calculus course, APCalculus AB prepares students for the AP exam and further studies in science, engineering, and mathematics.This course has been authorized by the College Board to use the AP designation.*Advanced Placement and AP are registered trademarks and/or owned by the College Board, which was not involved inthe production of, and does not endorse this product.Length: Two semestersUNIT 1: PRECALCULUS REVIEWUNIT 2: BRIDGE TO CALCULUSLESSON 1: INT RO T O CALCULUSStudy: What Is Calculus ?Explore calculus as the mathematical study of change, which can help us understand and model change in our world.See some specific examples of uses for calculus.Duratio n: 0 hrs 30 minsPractice: What Is Calculus ?Explore calculus as the mathematical study of change, which can help us understand and model change in our world.See some specific examples of uses for calculus.Duratio n: 0 hrs 30 mins S co ring: 0 po intsDis cus s : IntroductionsBefore exploring the details of calculus, discuss its definition with your classmates.Duratio n: 0 hrs 30 mins S co ring: 10 po intsLESSON 2: FUNCT IONSStudy: FunctionsExplore the concepts of domain, range, zeros (roots) of a function, and asymptotes, including the idea that a functiongives a unique value for a given domain value.Duratio n: 0 hrs 30 minsPractice: FunctionsExplore the concepts of domain, range, zeros (roots) of a function, and asymptotes, including the idea that a functiongives a unique value for a given domain value.Duratio n: 0 hrs 30 minsQuiz : As ymptotes and Domain Res trictionsPractice finding asymptotes and domain restrictions.Duratio n: 0 hrs 45 mins S co ring: 12 po intsPractice: How to Us e Your Graphing CalculatorUse your graphing calculator to graph a function to an arbitrary viewing window.Duratio n: 1 hrAP Calculus ABCopyright 2019 Apex Learning Inc. Apex Learning and the Apex Learning logo are registered trademarks of Apex Learning Inc.1 of 22
Practice: Finding Z eroes with Your Graphing CalculatorUse your graphing calculator to find the zeroes of a function.Duratio n: 0 hrs 45 minsPractice: Graphing Functions and Finding RootsGraph various functions and find roots for those functions.Duratio n: 1 hrStudy: Functions From Functions 1Learn about adding, subtracting, multiplying, and dividing functions to create new functions. Notice what happens totheir domains.Duratio n: 0 hrs 30 minsPractice: Functions From Functions 1Learn about adding, subtracting, multiplying, and dividing functions to create new functions. Notice what happens totheir domains.Duratio n: 0 hrs 30 minsPractice: Exploring Functions With Your Graphing CalculatorUse your graphing calculator to explore combinations of functions.Duratio n: 0 hrs 45 minsStudy: Functions From Functions 2Explore functions created from composites and inverses of other functions. Notice what happens to their domains.Duratio n: 0 hrs 30 minsPractice: Functions From Functions 2Explore functions created from composites and inverses of other functions. Notice what happens to their domains.Duratio n: 0 hrs 30 minsQuiz : Finding Function CombinationsPractice finding functions that are combinations of other functions.Duratio n: 1 hr S co ring: 10 po intsPractice: Concepts in FunctionsAnswer questions and solve problems that relate the concepts covered in the study of functions.Duratio n: 1 hrLESSON 3: GRAPHICAL SYMMET RYStudy: SymmetryExplore what symmetry is present in the cases of odd, even, and inverse functions. Look at ways to identify the varioussymmetry cases graphically and algebraically.Duratio n: 0 hrs 30 minsPractice: SymmetryExplore what symmetry is present in the cases of odd, even, and inverse functions. Look at ways to identify the varioussymmetry cases graphically and algebraically.Duratio n: 0 hrs 30 minsQuiz : Symmetry of EquationsAfter determining the type of symmetry for various equations that may be given graphically, algebraically, or as a tableof values, answer questions about symmetry.Duratio n: 1 hr S co ring: 11 po intsPractice: Writing Symmetrical FunctionsPractice with functions by writing functions for situations and situations for functions.Duratio n: 1 hr S co ring: 25 po intsLESSON 4 : PAT T ERNS IN GRAPHS: PARAMET ERSAP Calculus ABCopyright 2019 Apex Learning Inc. Apex Learning and the Apex Learning logo are registered trademarks of Apex Learning Inc.2 of 22
Study: Families of Functions and T heir GraphsExplore how to use information about one graph to quickly draw the graphs of other, related functions.Duratio n: 0 hrs 30 minsPractice: Families of Functions and T heir GraphsExplore how to use information about one graph to quickly draw the graphs of other, related functions.Duratio n: 0 hrs 30 minsPractice: Exploring Shif ting and Dis torting GraphsUse your graphing calculator to explore shifting and distorting graphs.Duratio n: 0 hrs 45 minsPractice: Pattern RecognitionWork on pattern recognition for the various forms, and sharpen your skills with parameters and how they relate tofamilies of functions.Duratio n: 1 hrLESSON 5: BRIDGE T O CALCULUS WRAP-UPReview: Bridge to CalculusReview your studies of functions, graphical symmetry, and patterns in graphs.Duratio n: 5 hrsT es t (CS): Bridge to CalculusTake a 25-minute test, modeled after the AP Exam, covering the concepts of functions, graphical symmetry, andpatterns in graphs.Duratio n: 0 hrs 25 mins S co ring: 20 po intsT es t (T S): Bridge to CalculusTake a 35-minute test, modeled after the AP Exam, covering the concepts of functions, graphical symmetry, andpatterns in graphs.Duratio n: 0 hrs 35 mins S co ring: 30 po intsUNIT 3: LIMITS AND CONTINUITYLESSON 1: LIMIT S AND CONT INUIT YDis cus s : Coming to T erms With Inf inityDiscuss Zeno's paradox of Achilles and the tortoise (and maybe some other paradoxes) in preparation for studying theinfinite.Duratio n: 0 hrs 30 mins S co ring: 10 po intsStudy: Limits of FunctionsExplore how to estimate limits from graphs or tables of data.Duratio n: 0 hrs 30 minsPractice: Limits of FunctionsExplore how to estimate limits from graphs or tables of data.Duratio n: 0 hrs 30 minsQuiz : Limits PracticeAnswer questions about whether (and where!) limits exist.Duratio n: 1 hr S co ring: 9 po intsStudy: Determining Limits AnalyticallyExamine the basic properties of limits and how to calculate limits using algebra; explore the limits of functions thatinclude trig functions.Duratio n: 0 hrs 30 minsPractice: Determining Limits AnalyticallyExamine the basic properties of limits and how to calculate limits using algebra; explore the limits of functions thatAP Calculus ABCopyright 2019 Apex Learning Inc. Apex Learning and the Apex Learning logo are registered trademarks of Apex Learning Inc.3 of 22
include trig functions.Duratio n: 0 hrs 30 minsPractice: Limits in T rigonometric FunctionsPractice determining limits, including limits of trigonometric functions.Duratio n: 0 hrs 45 minsLESSON 2: ASYMPT OT IC AND UNBOUNDED BEHAVIORStudy: As ymptotes as LimitsExamine asymptotes in terms of graphical behavior, and asymptotic behavior in terms of limits involving infinity.Duratio n: 0 hrs 30 minsPractice: As ymptotes as LimitsExamine asymptotes in terms of graphical behavior, and asymptotic behavior in terms of limits involving infinity.Duratio n: 0 hrs 30 minsPractice: Determining Graphs When Given LimitsApply given information about limits, when determining graphsDuratio n: 1 hr S co ring: 25 po intsStudy: Comparing Relative Magnitudes of FunctionsSee how relative magnitudes of functions can help you determine limits quickly.Duratio n: 0 hrs 30 minsPractice: Comparing Relative Magnitudes of FunctionsSee how relative magnitudes of functions can help you determine limits quickly.Duratio n: 0 hrs 30 minsQuiz : LimitsPractice calculating limits as x goes to infinity.Duratio n: 1 hr S co ring: 13 po intsStudy: Limits T hat Do Not Exis tLearn about some nonexistent limits and the reasons for their nonexistence.Duratio n: 0 hrs 30 minsPractice: Limits T hat Do Not Exis tLearn about some nonexistent limits and the reasons for their nonexistence.Duratio n: 0 hrs 30 minsDis cus s : Nonexis tent Limits in NatureConsider nonexistent limits in nature using a predator/prey model.Duratio n: 1 hr S co ring: 10 po intsPractice: Overview of LimitsApply your knowledge of limits as you determine limits that require algebraic manipulation.Duratio n: 1 hrLESSON 3: CONT INUOUS FUNCT IONSStudy: ContinuityExplore the central idea of continuity (close values of the domain lead to close values of the range) and understandcontinuity in terms of limits.Duratio n: 0 hrs 30 minsPractice: ContinuityExplore the central idea of continuity (close values of the domain lead to close values of the range) and understandcontinuity in terms of limits.Duratio n: 0 hrs 30 minsAP Calculus ABCopyright 2019 Apex Learning Inc. Apex Learning and the Apex Learning logo are registered trademarks of Apex Learning Inc.4 of 22
Quiz : Domains of ContinuityPractice determining domains of continuity for functions, given either the graph or the algebraic expression (includingasymptotes).Duratio n: 0 hrs 30 mins S co ring: 11 po intsPractice: Continuity ProblemsAs you examine functions for discontinuities and examine their types, recognize the properties of functions that areimportant in describing functions.Duratio n: 1 hr 15 mins S co ring: 25 po intsStudy: T he Intermediate Value T heorem and the Extreme Value T heoremExplore the existence of absolute extrema of a continuous function on a closed interval [a,b] and the possiblenonexistence on an open interval (a,b) look at geometric understanding of graphs of continuous functions.Duratio n: 0 hrs 30 minsPractice: T he Intermediate Value T heorem and the Extreme Value T heoremExplore the existence of absolute extrema of a continuous function on a closed interval [a,b] and the possiblenonexistence on an open interval (a,b) look at geometric understanding of graphs of continuous functions.Duratio n: 0 hrs 30 minsDis cus s : Unbounded Behavior and ContinuityBrainstorm solutions to problems that show the relationship between unbounded behavior and continuity. Respond toyour classmates ideas.Duratio n: 1 hr S co ring: 10 po intsLESSON 4 : LIMIT S AND CONT INUIT Y WRAP-UPReview: Limits and ContinuityReview your studies of limits and continuity.Duratio n: 5 hrsT es t (CS): Limits and ContinuityTake a 25-minute test, modeled after the AP Exam, covering the concepts of limits and asymptotes and continuity.Duratio n: 0 hrs 25 mins S co ring: 20 po intsT es t (T S): Limits and ContinuityTake a 35-minute test, modeled after the AP Exam, covering the concepts of limits and asymptotes and continuity.Duratio n: 0 hrs 35 mins S co ring: 30 po intsUNIT 4: DERIVATIVESLESSON 1: DERIVAT IVES AT A POINTStudy: Rates of Change as Slopes and LimitsExamine approximate rate of change from graphs and tables of values, the tangent line to a curve at a point, and locallinear approximation.Duratio n: 0 hrs 30 minsPractice: Rates of Change as Slopes and LimitsExamine approximate rate of change from graphs and tables of values, the tangent line to a curve at a point, and locallinear approximation.Duratio n: 0 hrs 30 minsQuiz : Slope Es timatesAnswer questions by estimating slope from graphs and tables of data. Find instantaneous rates of change byestimations.Duratio n: 1 hr S co ring: 7 po intsStudy: T he Derivative at a PointExamine the derivative defined as the limit of the difference quotient. See examples, including points at which there arevertical tangents and points at which there are no tangents.AP Calculus ABCopyright 2019 Apex Learning Inc. Apex Learning and the Apex Learning logo are registered trademarks of Apex Learning Inc.5 of 22
Duratio n: 0 hrs 30 minsPractice: T he Derivative at a PointExamine the derivative defined as the limit of the difference quotient. See examples, including points at which there arevertical tangents and points at which there are no tangents.Duratio n: 0 hrs 30 minsPractice: Practice Finding SlopesPractice finding slopes using easy examples of limits, some using real-world examples.Duratio n: 1 hrPractice: Us e of nDeriv or d (dif f erentiate)Use nDeriv or d (differentiate) on your calculator to compute the derivative at a point.Duratio n: 1 hrQuiz : nDeriv ExamplesOn real-world examples, use nDeriv on points to find slopes.Duratio n: 1 hr S co ring: 9 po intsStudy: T he Derivative as a FunctionExplore the use of the derivative as a function to find the original function's slope at any x value.Duratio n: 0 hrs 30 minsPractice: T he Derivative as a FunctionExplore the use of the derivative as a function to find the original function's slope at any x value.Duratio n: 0 hrs 30 minsPractice: Comparing Calculator Derivatives to Real OnesUse the limit definition to find a function, then compare that to y2 nDeriv(y1,x,x) (graphical analysis). Graph a functionthat you found using the limit and compare that to the calculator derivative graph y2 nDeriv(y1,x,x)Duratio n: 0 hrs 45 mins S co ring: 20 po intsLESSON 2: COMPUT ING DERIVAT IVESDis cus s : Shortcut RulesCreate a shortcut to the derivative, and make suggestions to your classmates.Duratio n: 1 hr S co ring: 10 po intsStudy: Computing DerivativesSee basic shortcuts for finding derivatives of power functions and of sine and cosine functions.Duratio n: 0 hrs 30 minsPractice: Computing DerivativesSee basic shortcuts for finding derivatives of power functions and of sine and cosine functions.Duratio n: 0 hrs 30 minsPractice: Practice on DerivativesPractice the power rule and simple trig derivatives. Find slopes and simple applications. Come up with the originalfunction and answer some questions based on the derivative.Duratio n: 1 hrStudy: Derivatives of Sums , Products , and Quotients of FunctionsSee how to take derivatives of functions defined as a combination of other functions. The rule for doing this will helpdetermine derivatives for all sorts of functions.Duratio n: 0 hrs 30 minsPractice: Derivatives of Sums , Products , and Quotients of FunctionsSee how to take derivatives of functions defined as a combination of other functions. The rule for doing this will helpdetermine derivatives for all sorts of functions.Duratio n: 0 hrs 30 minsAP Calculus ABCopyright 2019 Apex Learning Inc. Apex Learning and the Apex Learning logo are registered trademarks of Apex Learning Inc.6 of 22
Quiz : Product and Quotient Rule PracticeAnswer questions using the product and quotient rules.Duratio n: 1 hr S co ring: 10 po intsPractice: Determining SlopeUse the rules for finding derivatives to answer questions about curves.Duratio n: 1 hr S co ring: 20 po intsLESSON 3: DERIVAT IVE AS A FUNCT IONDis cus s : Graphs of DerivativesExplore derivatives and their graphs.Duratio n: 0 hrs 30 mins S co ring: 10 po intsStudy: Relating the Graph of a Function and Its DerivativeExamine the corresponding characteristics of graphs of f and f''. and the relationship between the increasing anddecreasing behavior of f and the sign of f''.Duratio n: 0 hrs 30 minsPractice: Relating the Graph of a Function and Its DerivativeExamine the corresponding characteristics of graphs of f and f''. and the relationship between the increasing anddecreasing behavior of f and the sign of f''.Duratio n: 0 hrs 30 minsPractice: Derivatives and GraphsPractice recognizing derivatives by looking at graphs.Duratio n: 0 hrs 45 minsStudy: T he Relations hip Between Continuity and Dif f erentiabilityExplore the relationship between differentiability and continuity.Duratio n: 0 hrs 30 minsPractice: T he Relations hip Between Continuity and Dif f erentiabilityExplore the relationship between differentiability and continuity.Duratio n: 0 hrs 30 minsPractice: More ExplorationAnswer questions while exploring the relationship between differentiability and continuity.Duratio n: 1 hr S co ring: 25 po intsStudy: T heorems : Rolle and Mean ValueExplore Rolle's Theorem and the Mean Value Theorem and their geometric consequences.Duratio n: 0 hrs 30 minsPractice: T heorems : Rolle and Mean ValueExplore Rolle's Theorem and the Mean Value Theorem and their geometric consequences.Duratio n: 0 hrs 30 minsPractice: Mean Value T heoremAnswer free-response questions by finding x values that satisfy the Mean Value Theorem and looking at situations thatcall for the Mean Value Theorem.Duratio n: 1 hr 30 minsLESSON 4 : HIGHER-ORDER DERIVAT IVESPractice: Higher-Order DerivativesExplore patterns in sin/cos/-sin/-cos/sin. Look for patterns in higher-order derivatives; learn notation for showing thesecond, third, etc. derivatives.Duratio n: 1 hrQuiz : Multiple Derivatives of FunctionsAP Calculus ABCopyright 2019 Apex Learning Inc. Apex Learning and the Apex Learning logo are registered trademarks of Apex Learning Inc.7 of 22
Practice finding some multiple derivatives of functions.Duratio n: 1 hr S co ring: 10 po intsStudy: T he Second Derivative and ConcavityExplore the steps to find and use concavity. Examine the relationship between the concavity of f and the sign of f'', andpoints of inflection as places where concavity changes.Duratio n: 0 hrs 30 minsPractice: T he Second Derivative and ConcavityExplore the steps to find and use concavity. Examine the relationship between the concavity of f and the sign of f'', andpoints of inflection as places where concavity changes.Duratio n: 0 hrs 30 minsPractice: ConcavityPractice finding and using concavity. This activity is mostly graphical and numerical, with only a few analytical cases.Duratio n: 1 hr S co ring: 25 po intsPractice: Identif ying Functions and T heir DerivativesPractice associating the features of a graph (a maximum or minimum point, an inflection point, an asymptote, uphill anddownhill parts) with features on the graph of the derivative and the second derivative.Duratio n: 0 hrs 45 minsLESSON 5: CHAIN RULE AND IMPLICIT DIFFERENT IAT IONStudy: T he Chain RuleSee when and how to use the Chain Rule to find derivatives of composite functions.Duratio n: 0 hrs 30 minsPractice: T he Chain RuleSee when and how to use the Chain Rule to find derivatives of composite functions.Duratio n: 0 hrs 30 minsPractice: Chain Rule PracticePractice with the Chain Rule in a couple of applications to see the relationship to units.Duratio n: 1 hr 30 minsPractice: Finding the Slope of a CurveUsing algebra, find the slope of a curve at several places.Duratio n: 1 hr S co ring: 20 po intsStudy: Implicit Dif f erentiationExplore how to use a powerful tool, implicit differentiation, to find the slope of a curve that isn't a function.Duratio n: 0 hrs 30 minsPractice: Implicit Dif f erentiationExplore how to use a powerful tool, implicit differentiation, to find the slope of a curve that isn't a function.Duratio n: 0 hrs 30 minsPractice: Conic SectionsAnswer questions using implicit differentiation. Practice using conic sections and new types of curves.Duratio n: 1 hr 15 minsLESSON 6: DERIVAT IVES WRAP-UPReview: DerivativesReview your studies of derivatives, concavity, the Chain Rule, and implicit differentiation.Duratio n: 5 hrsT es t (CS): DerivativesTake a 25-minute test, modeled after the AP Exam, covering the concepts of derivatives, concavity, the Chain Rule, andimplicit differentiation.AP Calculus ABCopyright 2019 Apex Learning Inc. Apex Learning and
Advanced Placement AP Calculus AB In AP Calculus AB, students learn to understand change geometrically and visually (by studying graphs of curves),
