Week 1: Fundamental Skills for Calculus
Getting to know each other, recall some math skills learned in previous courses, and get familiar with the course.
Week 2: A review of functions.
Get to know each other and to review.
Week 3: An introduction to limits.
Explore the concept of limits.
Week 4: Continuity
A look at the definition, properties, and geometric representation of functions that are continuous and discontinuous.
Week 5: Secants and tangents and lines, oh my.
A look at one interpretation of the derivative of a function at a point.
Week 6: Exponents, Radicals and the Power Rule.
Rules for solving exponents and finding the derivatives by Power rule.
Week 7: Reversing exponential Functions.
Simplification of logarithms, exponents and their derivatives, finding inverses.
Week 8: Driving Your Quad Over The Line.
Solving Quadratic Equations and finding the derivative of polynomials using sum and difference rules.
Week 9: Factors And The Product Rule.
Chain rule and Product rule for finding the derivatives, solving Quadratics by Factorization.
Week 10: Use Your DQ Derivative Quotient
Rational functions and introduction of Quotient rule for finding their derivatives.
Week 11: Trig Functions And Their Derivatives.
Guide to trigonometric functions and finding their derivatives.
Week 12: Good Golly Geometry
Step into Geometry with areas, volumes and more of derivatives.
Week 13: Rates Of Change
More about derivatives and their applications in finding rates of change.
Week 14: Other Uses Of Derivatives
Cost, revenue and profit analysis, just some of the applications od derivatives to business and economics.
Week 15: Wrapping it Up
Final exam, final thoughts about the course.
This course follows the Topical Outline and objectives of the College Board as described for the first semester of Calculus AB.
A complete listing is available online at www.collegeboard.org.
analyze graphs geometrically and analytically
estimate and calculate limits of functions
describe asymptotic behavior in terms of limits involving infinity
determine continuity geometrically and in terms of limits
compute the derivative at a point
describe and analyze rates of change
compute the derivative of a function
analyze the derivatives of trigonometric functions
apply the derivative to optimization, related rates, and marginals
interpret the derivative as a rate of change
compute the derivative through a variety of methods