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* What is the roll of deductive reasoning in mathematics?
* What is proof?
* What is a function and what can you do with it?
* How can functions be represented numerically, graphically, and analytically?
* What are the connections between Algebra and Geometry?
* How can we extend our knowledge of basic algebra to investigate more advanced relationships?
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* Definition, graphs, and transformations of functions
* Linear, quadratic, polynomial, radical, exponential, logarithmic, rational, absolute value, greatest integer, and piecewise functions
* Domain and range of functions
* Inverse and composition of functions
* Geometric inverses and transformations
* Solving systems of equations with three variables
* Matrices
* Congruence in geometric figures
* Geometric proofs
* Coordinate Geometry proofs
* Algebraic proofs
* Geometric sequences
* Complex numbers
* Real-life applications of functions
* Modeling growth and decay
* Problem solving strategies
* Definitions and properties of three-dimensional figures
-pyramids
-cylinders
-prisms
-spheres
-cones
* Joint and inverse variation
* Proportion and similarity in geometric figures
* Basic probability and permutations and combinations
* Properties of circles |
* recognize arithmetic and geometric sequences
* recognize and write recursive formulas for geometric sequences
* recognize graphs of all functions listed under Declarative Knowledge
* create graphs of all functions listed under Declarative Knowledge
* write the equation of a function, given its graph
* use transformations of functions to graph a new function or write its equation
* determine horizontal and vertical asymptotes
* solve equations, inequalities, and systems of equations and inequalities involving the types of functions listed under Declarative Knowledge
* perform operations with matrices
* solve matrix equations and use matrices to solve systems of equations
* model data using exponential growth and decay models
* simplify algebraic expressions that involve complex number, exponential, radical, and fractional expressions
* add, subtract, multiply, divide, and simplify polynomials, rational expressions, and radical expressions
* factor polynomial expressions
* determine angles between faces in a geometric solid
* calculate volumes and surface areas of three-dimensional figures
* apply properties of three-dimensional shapes to solve numerical problems involving geometric figures
* prove geometric and algebraic properties and theorems
* translate word problems into algebraic language and solve
* solve elementary problems involving probability, permutations, and combinations
* use a graphing calculator, computer, or paper and pencil to perform a variety of tasks involving the topics listed under Declarative Knowledge
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* Tests
* Quizzes
* Projects
* Homework
* Class Participation |
TI-83 or TI-84 graphing calculator
Geometer's Sketchpad Software (published by Key Curriculum Press)
Fathom Dynamic Data Software (published by Key Curriculum Press)
laptop computer
Discovering Geometry: An Investigative Approach, 4th edition, by Michael Serrra
Discovering Advanced Algebra: An Investigative Approach, by Murdock, Kamischke, and Kamischke |
* Mathematics is inherently multicultural because it is a universal language
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