Calculus Units
All of the units for the calculus curriculum are listed below. Click on the standard to get access to the video lesson, flipchart PDF, lesson questions, and homework practice. If you are looking for retake assignments please go to the retake request page in the Calculus drop down menu and look for the appropriate one.
Unit 1: Differentiation
Description: This unit will discuss what a derivative is and how to find one. You will learn a number of properties for different types of functions. These properties and skills will be pivotal to success in later units.
Big Idea: Derivatives provide the ability to calculate instantaneous rates of change.
Essential Questions:
Description: This unit will discuss what a derivative is and how to find one. You will learn a number of properties for different types of functions. These properties and skills will be pivotal to success in later units.
Big Idea: Derivatives provide the ability to calculate instantaneous rates of change.
Essential Questions:
- Describe the parts of the definition of a derivative and explain the reasoning behind them.
- What are the properties of calculating derivatives and when should they be used?
- How can derivatives be used in real life applications?
Unit 2: Applications of Derivatives
Description: This unit will discuss how derivatives are used to find critical parts of graphs and locating optimum results given certain conditions
Big Idea: Beyond being a means to calculate instaneous rates of change, derivatives are also critical in worldly extrema.
Essential Questions:
Description: This unit will discuss how derivatives are used to find critical parts of graphs and locating optimum results given certain conditions
Big Idea: Beyond being a means to calculate instaneous rates of change, derivatives are also critical in worldly extrema.
Essential Questions:
- Why is the use of derivatives essential to analyzing curves?
- Provide a scenario where using derivative calculus can help find the optimal result.
- How can the Mean Value Theorem be applied in the real world?
Unit 3: Integration
Description: This unit will discuss the uses of integration in calculus as it relates to derivative functions and finding areas and volumes.
Big Idea: Beyond simply reversing the derivative process, integration is a means to find displacement, areas, and volumes or reals world scenarios.
Essential Questions:
Description: This unit will discuss the uses of integration in calculus as it relates to derivative functions and finding areas and volumes.
Big Idea: Beyond simply reversing the derivative process, integration is a means to find displacement, areas, and volumes or reals world scenarios.
Essential Questions:
- Explain the use of integration when finding net and total change.
- Explain how integral calculus is used to calculate areas and volumes.
Unit 4: Transcendental Function Derivatives and Integrals
Description: This unit opens up derivative and integral mathematics to transcendental functions such as trig, logarithmic, exponential, and inverse functions
Big Idea: Extend calculus mathematics in to other function models.
Essential Questions:
Description: This unit opens up derivative and integral mathematics to transcendental functions such as trig, logarithmic, exponential, and inverse functions
Big Idea: Extend calculus mathematics in to other function models.
Essential Questions:
Unit 5: The Leftovers
Description: This unit covers a number or remaining topics in Calculus such as exponential growth and decay, separation of variables, slope fields, and volumes of solids of revolution.
Big Idea: Calculus is more than the study of rates of change. It can also be used to find volumes of shapes that are non common geometric figures.
Essential Questions:
Description: This unit covers a number or remaining topics in Calculus such as exponential growth and decay, separation of variables, slope fields, and volumes of solids of revolution.
Big Idea: Calculus is more than the study of rates of change. It can also be used to find volumes of shapes that are non common geometric figures.
Essential Questions:
- Describe how the sum of rectangles being used to help find definite integrals can be expounded to help find the volumes of solids of revolution.
- Show that if the rate of change of one variable with respect to another is proportional to itself, then it is the derivative of and exponential model.