MA 3178: Advanced Placement Calculus BC

Subject Area

Credits 1

Years

Level

High School

AP Calculus BC is more rigorous than AP Calculus AB. It meets the requirements set forth in the syllabus of the College Board. Topics include differentiation and integration techniques; vector functions and parametric equations; polar graphs and area bounded by polar curves; length of a path; work as an integral; improper integrals; and sequences and series. A satisfactory grade on the Advanced Placement BC test usually receives more college credit than a similar grade on the AB test.

Parent Docs

Advanced Placement Calculus BC Parent Doc 2021-2022

Storyboard

AP Calculus BC Essential Questions: How do I become a mathematical problem solver to better understand the world around me? In what ways can I communicate and represent my mathematical thinking?
Title	Limits: Foundation of Calculus	Differentiation: Solving the Tangent Line Problem	Integration: Solving the Area Proble	Beyond X and Y Parametrics, Polars, and Series
Focus of the Story	Have you ever wondered exactly how fast you are traveling through a tunnel such as the HRBT? We begin our story investigating if change can happen at an instant. Through application of limits, the foundation of calculus, we are able to determine how fast we travel through the tunnel and apply the concept to solve a variety of real-world problems. !	Now that you have arrived at your destination, how did your speed in the tunnel relate to the time it takes? The distance traveled? Through the mean value theorem, we will discover the relationship between average and instantaneous rates of change leading to the discovery of differentiation and how every point contributes to the behavior of the function.	Have you ever left your house only to realize that you left something and had to turn around? As we approach the end of our story, we will consider where objects begin and end their journey and wonder about the story in between. Through integration, we find the area under any curve and how it connects to where you are and where you have been. We end our journey by applying integration to generate models of solids.	What if we changed our perspective and viewed the world through different lenses?? For the last part of our story, we alter our perspective and view the world through Paremetrics, Polar, and Discrete sets. We apply the skills developed in this course through these new perspectives to better understand the world.
Transfer Goals	Explore: Make sense of the world mathematically by asking questions and making connections through inquiry.	Apply: Utilize effective strategies, processes, and tools to model new situations and/or real-world experiences.	Explain: Communicate mathematical thinking by justifying solutions using multiple representations while attending to precision.	Analyze: Investigate, formulate, and construct viable arguments by taking risks, persevering, and thinking flexibly.

Learning Targets

I can express and investigate limits in multiple ways, including graphically, numerically, and analytically.
I can explore how limits will allow me to solve problems involving change and to better understand mathematical reasoning about functions.

I can apply limits to define the derivative, become skillful at determining derivatives, and continue to develop mathematical reasoning skills.
I can master using the chain rule, develop new differentiation techniques, and be introduced to higher-order derivatives.
I can apply derivatives to set up and solve real-world problems involving instantaneous rates of change and use mathematical reasoning to determine limits of certain indeterminate forms.
I can explore relationships among the graphs of a function and its derivatives and learn to apply calculus to solve optimization problems.

I can apply limits to define definite integrals and determine how the Fundamental Theorem connects integration and differentiation. I can apply properties of integrals and practice useful integration techniques.
I can solve certain differential equations and apply that knowledge to deepen my understanding of exponential growth and decay.
I will make mathematical connections that will allow me to solve a wide range of problems involving net change over an interval of time and to find areas of regions or volumes of solids defined using functions.

I can solve parametrically defined functions, vector-valued functions, and polar curves using applied knowledge of differentiation and integration. I can also deepen my understanding of straight-line motion to solve problems involving curves.
I can explore convergence and divergence behaviors of infinite series and learn how to represent familiar functions as infinite series. I can also learn how to determine the largest possible error associated with certain approximations involving series.

AP Calculus BC: Assessment Matrix
Title	Unit	Rich Tasks:	Learning Target
	Unit 1: Limits and Continuity	Personal Progress Check 1 Can You Shoot Free Throws	I can express and investigate limits in multiple ways, including graphically, numerically, and analytically.
	Unit 1: Limits and Continuity	Many Coffee Beans 5-Star Uber Driver	I can explore how limits will allow me to solve problems involving change and to better understand mathematical reasoning about functions.
	Unit 2: Differentiation: Definition and Basic Derivative Rules	Personal Progress Check 2 Breaking the Sound Barrier Divide and Conquer	I can apply limits to define the derivative, become skillful at determining derivatives, and continue to develop mathematical reasoning skills.
	Unit 3: Differentiation: Composite, Implicit, and Inverse Functions	Personal Progress Check 3 How is Lindt Chocolate Made The Tangent Line Problem Calculus Round Table	I can master using the chain rule, develop new differentiation techniques, and be introduced to higher-order derivatives.
	Unit 4: Contextual Applications of Differentiation	Personal Progress Check 4 The Lovely Ladybug Birthday Balloons Close Enough is Good Enough	I can apply derivatives to set up and solve real-world problems involving instantaneous rates of change and use mathematical reasoning to determine limits of certain indeterminate forms.
	Unit 5: Analytical Applications of Differentiation	Personal Progress Check 5 Can Calculus Get You Fined? Canalysis	I can explore relationships among the graphs of a function and its derivatives and learn to apply calculus to solve optimization problems.
	Unit 6: Integration and Accumulation of Change	Personal Progress Check 6 How Much Snow Under Cover	I can apply limits to define definite integrals and determine how the Fundamental Theorem connects integration and differentiation. I can apply properties of integrals and practice useful integration techniques.
	Unit 7: Differential Equations	Personal Progress Check 7 Seeing is Believing Are you a Solution Seeker Coronavirus Spreading?	I can solve certain differential equations and apply that knowledge to deepen my understanding of exponential growth and decay.
	Unit 8: Applications of Integration	Personal Progress Check 8 Whitney’s Bike Ride Volume of a Pear Volume of a Bagel	I will make mathematical connections that will allow me to solve a wide range of problems involving net change over an interval of time and to find areas of regions or volumes of solids defined using functions.
	Unit 9: Parametric Equations, Polar Coordinates, and Vector Valued Functions	Personal Progress Check 9 Having a Ball The Lovely Ladybug (Part 2) Arctic Regions	I can solve parametrically defined functions, vector-valued functions, and polar curves using applied knowledge of differentiation and integration. I can also deepen my understanding of straight-line motion to solve problems involving curves.
	Unit 10: Infinite Sequences and Series	Personal Progress Check 10 How to Share a Pizza Uncommon Ratios A Better Approximation? Under the Right Conditions	I can explore convergence and divergence behaviors of infinite series and learn how to represent familiar functions as infinite series. I can also learn how to determine the largest possible error associated with certain approximations involving series.