Calculus 1 & 2 / AB / BC

This chapter begins your epic quest through differential calculus!  You will start with the concept and limit definition of the derivative before learning about differentiability and sketching graphs of the derivative of f(x).  From there, it is time to shine a light on differentiation rules so you can then tackle position, velocity, and acceleration – all very cool!  Then, it is off to master the Product, Quotient, and Chain Rules and then on to implicit differentiation.  The chapter rounds out with a rockin’ study of related rates and a host of Advanced Calculus AB and BC free response and multiple choice practice questions featuring all you learned about the derivative.  Time to dive in and get your blind blown by the beauty of the derivative!!!

Chapter 3 – Uses of the Derivative

This chapter is all about the awesome applications of derivatives!  You begin with absolute extrema and finding critical numbers.  Then it is off to Rolle’s and the Mean Value Theorems.  From there your quest takes you through using f ‘ to figure out where f is increasing and decreasing along with rocking the First Derivative Test!  The study of the second derivative, f “, and the concavity and points of inflection of f is the next important stop.  The 2nd derivative test is explored.  You will then learn how to sketch curves using all of the calculus rocked thus far.  You will master the fun and classic lesson on optimization and make easy work of tangent line approximations (local linearization) and differentials.  From there, you will make quick work of Newton’s method.  TONS of original AB and BC Exam practice problems all about the applications of the derivative close out the chapter!

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Chapter 4 – Integration

This chapter opens with rocking the antiderivative and a tour through all the basic integration rules and fundamental problem types.  Riemann sums, midpoint, and trapezoidal sums master you in the art of approximating area between the curve and the x-axis.  You will see the beauty of definite integrals and their properties along with finding area of graphs forming geometric figures.  The First Fundamental Theorem of Calculus will have you finding areas between the x-axis and a graph easily!  With this knowledge comes finding average value and the Second Fundamental Theorem of Calculus as you find derivatives of integrals.  The chapter begins to wind down with a fun exploration of “U” substitution or integration by substitution.  The final stop in this epic chapter consists of oodles of original AB and BC exam practice problems involving integration concepts.  Tons of free response and multiple choices questions await you!

Chapter 5 – Derivatives and Integrals of Exponential Functions, Logarithms, and Inverse Trigonometry

This chapter is all about derivatives and integrals of new functions, but also serves as a review of all Calculus applications you have learned!  You begin with the derivative of lnx or the natural log, before learning about integrals involving lnx.  From here, you will tackle derivatives of inverse functions.  Then, it is off to differentiate and integrate e^x.  After rocking the Calculus of e, you will learn how to take the derivatives and antiderivatives of exponential and logarithm functions of any base.  What follows is a fun journey into the derivatives and integrals of inverse trig functions (arcsin anyone?).  The chapter rounds out with a lesson on L’Hopital’s (L’Hospital) Rule and some original AB and BC exam practice problems.  A thorough review of precalculus knowledge is given in many lessons to ensure you are fresh on prior knowledge.  Let’s get on this!

Chapter 6 – Differential Equations and Exponential & Logistic Growth