While it is advisable for students to study calculus concurrently with A.P. physics, there are certain calculus tools that are too important to wait for. In this unit students discover differentiation and integration of polynomials trig functions, and exponential functions in ways that are different enough from the standard methods so that the material will be complementary to (rather than a duplication of) the work that they do in their calculus course. Because it is important for students to develop these tools as they are needed, the material in this unit is distributed through the entire first semester.

**Topics include** The Law of Cosines and the Pythagoras Theorem, Differentiating Polynomials, The Derivative of a Product, The Bird and the Trains, Polynomial Approximations, Finding the Area of a Sphere without Calculus, Simple Integration, The Volume of a Pyramid or Cone without Calculus, Finding the Volume of a Sphere without Calculus, Integration for Beginners, Summary of Discoveries about Integration, Definite and Indefinite Integration, Sines and Cosines, The Area and Volume of a Sphere (calculus version), Introducing Exponential Functions, Discovering the Numerical Value of “e”, More About Exponential Functions, The Chain Rule, Separation of Variables, Integrating the Function y = x -1, Summary of Integration and Differentiation, Integrating sin3x by “Substitution”, Introducing Vector Products, Second-Order Differential Equations, The Gremlin Theory of Averaging, Integrating (A2 – x2)-1/2 (optional), More Polynomial Approximations (optional), Interpreting Imaginary Exponents (optional), Exponential Solutions to Second-Order Differential Equations (optional), More Examples of Integration by Substitution, Golden Trumpet & Dark Night Sky, Unit Vectors.

**Whole course with all units or more individual units available at ****https://www.teaching-point.net****.**