Critical Areas of Advanced Algebra & Trigonometry
- Expressions and equations generalize patterns based on the ways that numbers operate. Inductive reasoning helps us connect concrete examples with algebraic generalizations.
- Familiar operations with numbers can be extended to more complex situations. For instance, the laws of integer exponents can be extended to rational exponents and to the concept of logarithm.
- Key types of functions can be used to represent important real life situations. They can be modeled with algebraic descriptions, tables and graphs, which show the characteristics of the function.
- The trigonometry of right triangles can be extended to the coordinate plane, where it provides a new way to specify points. Symmetry plays a big role in this new method.
- Develop fluency in working with basic skills of algebra, extending them to new domains.
- Use the language and notation of algebra with increasing sophistication in a variety of different classroom settings: individual work, small group tasks, and whole class activities
- Use and connect numerical, algebraic, and graphical representations of a wide variety of relations and functions.
- Understand the concept of function, relate it to relationships previously studied (linear, exponential, quadratic) and extend it to new types of functions (variation, power, logarithmic, trigonometric, and polynomial) and to the ideas of composite and inverse.
- Expand the study of right triangle trigonometry to the general triangle and to rotations on the coordinate plane
Semester 1:
Chapter 1: Functions
Chapter 2: Variation and Graphs
Chapter 3 Linear Functions
Chapter 4: Matrices (Lessons 4.2 and 4.3)
Chapter 5: Systems (omit Lessons 5-9 and 5-10)
Chapter 6: Quadratic Functions (omit Lesson 6-6)
Chapter 11: Polynomials (omit Lessons 11-3 and 11-6 thru 11-10)
Semester 2:
Chapter 7: Powers
Chapter 8: Inverses and Radicals
Chapter 9: Exponential and Logarithmic Functions (omit Lesson 9-9)
Chapter 10: Trigonometry (based largely on packets, omit Lesson 10-10)
- Text: UCSMP Advanced Algebra 2nd edition published by Scott, Foresman, copyright 1996