In Precalculus, students extend their work with complex numbers begun in Algebra II to see that the complex numbers can be represented in the Cartesian plane and that operations with complex numbers have a geometric interpretation. They connect their understanding of trigonometry and the geometry of the plane to express complex numbers in polar form. Students begin working with vectors, representing them geometrically and performing operations with them. They connect the notion of vectors to complex numbers. Students also work with matrices, their operations, and find inverse matrices. They see the connection between matrices and transformations of the plane. Students use matrices to represent and solve linear systems.
Students extend their work with trigonometric functions, investigating the reciprocal functions secant, cosecant, and cotangent and their graphs and properties. They find inverse trigonometric functions by appropriately restricting the domains of the standard trigonometric functions and use them to solve problems that arise in modeling contexts.
Although students have worked previously with parabolas and circles, they now work with ellipses and hyperbolas. They also work with polar coordinates and curves defined parametrically and connect these to their other work with trigonometry and complex numbers.
Finally, students work with more complicated rational functions, graphing them and determining zeros, y-intercepts, symmetry, asymptotes, intervals for which the function is increasing or decreasing, and maximum or minimum points.
Students will develop a strong grasp of the Mathematical Practices:
Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
The Standards for Mathematical Practice complement the content standards so that students increasingly engage with the subject matter as they grow in mathematical maturity and expertise throughout the high school years.
Units of Study
Unit #1 = Functions and Their Graphs
Unit #2 = Linear Systems and Matrices
Unit #3 = Polynomial and Rational Functions
Unit # 4 = Conics
Unit #5 = Exponential and Logarithmic Functions
Unit #6 = Trigonometric Functions
Unit #7 = Graphs of Trigonometric Functions
Unit #8 = Analytic Trigonometry
Unit #9 = Vectors and Trigonometry
Unit #10 = Parametric
Unit #11 = Polar Functions and Graphs
Unit #12 = Complex Numbers in Polar Form