Calculus Curriculum

Below are skills needed, with links to resources to help with that skill. We also encourage plenty of exercises and book work. Curriculum Home

Important: this is a guide only.
Check with your local education authority to find out their requirements.

Calculus | Functions
☐ Introduction to continuity
☐ Intermediate Value Theorem
☐ How Polynomials Behave
☐ Intermediate Value Theorem and Extreme Value Theorem
☐ Intermediate Value Theorem
☐ Understand how the behavior of the graphs of polynomials can be predicted from the equation, including: continuity, whether the leading term has an even or odd exponent, the size of the factor of the leading term, the number of turning points, and end behavior.
☐ Polynomials: Bounds on Zeros
☐ How Polynomials Behave
☐ Polynomials: The Rule of Signs
☐ Understand what is meant by saying that a function is increasing, strictly increasing, decreasing or strictly decreasing.
☐ Increasing and Decreasing Functions
☐ Understand what is meant by the following terms for a function: Local Maximum, Local Minimum, Global Maximum and Global Minimum.
☐ Maxima and Minima of Functions
☐ Graph of an Equation
☐ Activity: Soup Can
☐ Understand what is meant by a continuous function and how continuity can depend upon the domain.
☐ Continuous Functions
☐ Piecewise Functions
☐ Asymptote
Calculus | Derivatives
☐ Introduction to derivatives
☐ Derivatives as dy/dx
☐ Introduction to Derivatives
☐ Introduction to Calculus
☐ From average rate of change to instantaneous rate of change
☐ Derivatives as dy/dx
☐ Derivatives and continuity
☐ Increasing and Decreasing Functions
☐ Maxima and Minima of Functions
☐ Intermediate Value Theorem
☐ How Polynomials Behave
☐ Approximating rate of change (graphs and tables)
☐ Function Grapher and Calculator
☐ Differentiate functions using the Derivative Rules
☐ Derivative Rules
☐ Introduction to Derivatives
☐ Derivatives as dy/dx
☐ Find the second derivative of a function using the rules of differentiation
☐ Second Derivative
☐ Introduction to Derivatives
☐ Derivative Rules
Calculus | Integrals
☐ Introduction to Integration. Understand that integration is the inverse of differentiation, and recognize the importance of the constant of integration.
☐ Introduction to Integration
☐ Integrate functions using the Integration rules.
☐ Introduction to Integration
☐ Integration Rules
☐ Integration by Parts
☐ Integration by Substitution
☐ Integrate products of functions using Integration by Parts, and know how this method can sometimes be applied to integrating single functions.
☐ Integration by Parts
☐ Integration by Substitution
☐ Integration by Substitution
☐ Calculate definite integrals and know how they relate to areas.
☐ Definite Integrals
Calculus | Limits
☐ Introduction to limits
☐ Limits (An Introduction)
☐ Evaluating limits
☐ Limits - Evaluating
☐ Limits to Infinity
☐ Introduction to Derivatives
☐ Limits (An Introduction)
☐ Formal definition of limits
☐ Limits (Formal Definition)
☐ Introduction to Derivatives
☐ Estimating limits (graphs and tables)
☐ Function Grapher and Calculator
☐ Continuity and Limits
☐ How Polynomials Behave
☐ What is Infinity?
☐ Limits (An Introduction)
☐ Limits to Infinity