UTAustinX: Discovery Precalculus: A Creative and Connected Approach

• How to make conjectures, construct logical arguments, and justify your reasoning
• The concept of function in mathematics, function characteristics and properties, and rate of change of functions
• Modeling of common relations and functions such as linear, power, exponential, and logarithmic functions using statistical regression and matrix methods
• An exploration of algebra and geometry, and the connections between the two in analytic geometry
• Properties and applications of exponential and logarithmic functions including exponential growth and decay and The Logistic Function
• The development of the trigonometric functions and identities along with applications of trigonometry
• Limits and rate of change of functions as a precursor to Calculus
• Other Coordinates Systems – an investigation of parametrization of the plane and the polar coordinate system along with exploration and use of vectors
• Sequences and Series including The Method of Induction
• Basic probability and combinatorics used in an investigation and development of the Binomial Theorem and its connections to Pascal’s Triangle

The course is organized around the following seven units:

1. Functions, Rates, and Patterns
2. Algebra and Geometry
3. Exponential and Logarithmic Functions
4. Trigonometry
5. Limits and Rate of Change of Functions
6. Exploring Other Coordinate Systems
7. Sequences and Series