# 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

☐ Limits

☐ Evaluating limits

☐ Limits

☐ Formal definition of limits

☐ Limits

☐ Estimating limits (graphs and tables)

☐ Limits

☐ Continuity and Limits

☐ Limits

☐ Limits