Course Description
A course designed to develop higher order thinking processes. The concepts covered address sequences and series, Exponential and Logarithmic Functions, Matrices and Determinants, Conic Sections and Trigonometry.
Credits: 5
Released: 2005
Course Content
Sequences and Series Unit 6
- Define, describe, and apply sequences
- Find terms of sequences
- Define, describe, and apply series
- Find terms of series
- Find sums of series
- Define, describe, and apply arithmetic sequences and series
- Find common difference
- Find terms of arithmetic sequences
- Find sums of arithmetic sequences
- Solve applications using arithmetic series
- Define, describe, and apply geometric sequences and series
- Find common ratio
- Find terms of geometric sequences
- Find sums of geometric sequences
- Applications using geometric series
- Apply the Fundamental Counting Principle
- Compute permutations
- Compute combinations
- Find the probability of events
- Apply understanding of sequences and series to real problems
- Explore patterns using Pascal's Triangle
- Use the binomial theorem
Exponential and Logarithmic Functions Unit 7
- Develop vocabulary and symbolic notations for exponential and logarithmic functions
- Develop skills and evaluate natural base e and base 10 problems
- Sketch graphs of exponential and logarithmic functions
- Use and apply properties of logarithms
- Solve logarithmic problems by changing bases.
- Solve real world applications relating to exponential and logarithmic functions
- Express understanding through writing exercises
- Demonstrate higher level learning through evaluation and presentations of reports
Matrices and Determinants Unit 8
- Develop vocabulary and symbolic notations for matrices
- Develop skills in matrix operations
- Evaluate determinants
- Solve equations and systems of equations using Cramer's Rule and inverse matrices
- Use matrices to solve real world applications
- Express understanding through writing exercises
- Demonstrate higher level learning through evaluation and presentations of reports
Conic Sections Unit 9
- Develop vocabulary for conic sections
- Sketch graphs and determine formulas for conic sections
- Write standard equations and classify conic sections
- Find equations of conic sections
- Use conic sections to solve real world applications
- Express understanding through writing exercises
Trigonometry Unit 10
- Develop vocabulary for trigonometry
- Develop mathematical skills relating to the unit circle and radian measures
- Graph and interpret circular and inverse trigonometric functions
- Compute values of circular and inverse trigonometric functions
- Use Laws of Sines and Cosines
- Use trigonometry and the geometry of right triangles to find unknown measures and areas.
- Use trigonometry to solve real world applications
- Express understanding through writing exercises
