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Unit 1: Modeling Polynomial and Rational Functions
How well can pure mathematics model messy, real-world situations?
When is the best mathematical answer not the best solution to a problem?
How does the graph of an equation help you better understand the function?
How can patterns, relations, and functions be used as tools to best describe and explain real-life situations?
What makes an algebraic algorithm both effective and efficient?
How are imaginary numbers useful?
How are patterns of change related to the behavior of functions?
Unit 2: Non-Polynomial Functions
What will happen next? How sure are you?
How can functions be used as mathematical models to describe and help explain real-life situations?
What real-life situations can be modeled by radical functions? by exponential functions? by sequences?
How does the graph of an equation help to better understand the function?
How can I continue working when I don't know the next step? What should I do when I get stuck?
Unit 3: Trigonometric Functions and Their Relationships
How can mathematics model real world situations that have cycles of repetition?
What do good problem solvers do, especially when they get stuck?
What are the limits of a mathematical model that uses trigonometric equations?
How are mathematical models used to describe physical relationships?
Compare trigonometric graphs and polynomial graphs. How are they the same? How are they different?
Unit 4: Probability and Statistics
How confident am I about my conclusion based on statistical evidence?
How can you describe data presented in tables, charts or graphs?
How is theoretical probability different from experimental probability?
When do the results of an experiment raise more questions?
What methods and tools will make the work efficient and precise?
What should I do when I get stuck?
How can I improve my performance?
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