| A Brief Overview of Pre-calculus |
Unit 1 – Exploring Functions
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- In what ways can we express mathematical ideas?
- How can a function help with analysis?
- Can anything be modeled mathematically? How and to what extent?
- Can anything be modeled with functions? How and to what extent?
- What factors can be used to determine whether an analytic or graphical strategy is most advantageous in solving a problem?
- How can analytic and graphical methods be used to support each other in the solution to a problem?
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| Unit 2 – Polynomial, Power, and Rational Functions |
- To what extent can we predict the future?
- Does change ever stop?
- How can infinity occur in reality?
- To what extent can technology be used to analyze a graph?
- How many solutions does a polynomial have?
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| Unit 3 – Exponential, Logarithmic, and Logistic Functions |
- How can exponential growth continue on forever?
- When is growth exponential versus logistic?
- To what extent can I use mathematics to prepare for my own financial success (or demise)?
- How are exponential and logarithmic functions related?
- Why is the natural base e natural?
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| Unit 4 – Trigonometric Functions |
- How does the periodic nature of the trigonometric functions affect their analytic values and graphical representations?
- When should we use degrees and when should we use radians for measuring angles?
- How are the trigonometric functions related to one another?
- To what extent can all periodic events in our world be modeled with trigonometric functions?
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| Unit 5 – Analytic Trigonometry |
- What do the transformations of the trig functions look like symbolically?
- To what extent can right triangle trigonometry be generalized to all triangles?
- How are the trigonometric identities helpful?
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| Unit 6 –Analytic Geometry / Conics |
- How are the different conic shapes related?
- In what ways does society take advantage of the reflective properties of the conic shapes?
- How does eccentricity connect the conics?
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| Unit 7 –Sequnces and Series |
- What is the relationship between arithmetic and geometric sequences?
- To what extent is an arithmetic sequence a linear function?
- To what extent is a geometric sequence an exponential function?
- How can an infinite number of numbers add up to a finite quantity?
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