# 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 and Extreme 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.
☐ Understand what is meant by saying that a function is increasing, strictly increasing, decreasing or strictly decreasing.
☐ Understand what is meant by the following terms for a function: Local Maximum, Local Minimum, Global Maximum and Global Minimum.
☐ Understand what is meant by a continuous function and how continuity can depend upon the domain.
Calculus | Derivatives
☐ Introduction to derivatives
☐ From average rate of change to instantaneous rate of change
☐ Derivatives and continuity
☐ Slope of a curve at a point: where there is a vertical tangent, or no tangents
☐ Approximating rate of change (graphs and tables)
☐ Differentiate functions using the Derivative Rules
☐ Find the second derivative of a function using the rules of differentiation
Calculus | Integrals
☐ Introduction to Integration. Understand that integration is the inverse of differentiation, and recognize the importance of the constant of integration.
☐ Integrate functions using the Integration rules.
☐ Integrate products of functions using Integration by Parts, and know how this method can sometimes be applied to integrating single functions.
☐ Integration by Substitution
☐ Calculate definite integrals and know how they relate to areas.
Calculus | Limits
☐ Introduction to limits
☐ Evaluating limits
☐ Formal definition of limits
☐ Estimating limits (graphs and tables)
☐ Continuity and Limits