MCV4U (Grade 12 Calculus and Vectors Course)

Unit #1: Rates of Change

Please make me a "cheat cheat" for me to study off for my unit 1 test of the following concepts. Please try to provide clear detail such as; explanation, definition, examples?, formulas... and any extra information you think may help me. I know its a lot, but I'd really appreciate it (and I'll be sure to provide a good review).

• Pascals Triangle and Binomial Theorem:

- Binomial theorem using pascals triangle (and applying to equations):

- simplifying radicals:

- rationalizing the denominator:

• Rates of change and the slope of the curve:

- secants:

- tangents:

- slope of tangent (tangency):

- independent variable:

- dependent variable:

• Average rate of change: (provide formula, when you'd use it, why'd you use it, how you'd use it...)
• Instantaneous rate of change: (provide formula, when you'd use it, why'd you use it, how you'd use it...)

-explain how intervals, for example: tE [2,8], can be used for AROC and IROC:

• Rates of change using equations:

- explain how the interval between two points on the x-axis can be expressed as:

- explain then average rate of change relation with the slope of the secant line:

- explain then Instantaneous rate of change relation with the slope of the secant line:

• Difference quotient:
• Limits:

- provide formulas:

- when/why you'd use it:

-key concepts:

- relation to anything else such as average rate of change and instantaneous rate of change:

- left hand limit:

- right hand limit:

-limit of a function:

- continous function:

- sequence:

-continuity at a point:

• Limits and continuity:

- discontinuous:

- removable discontinuity:

- indeterminate form:

- infinite discontinuity:

- jump discontinuity:

• limits properties:
• introduction to derivatives:

- derivative:

- principles:

- differentiate:

- what does f'(x) mean? f'(x) (the apostrophe)