Course Notes
  1. Prerequisites
  2. Functions
    1. Modeling
    2. Function properties
    3. Fundamental Functions
    4. Composition
    5. Parametric Functions
    6. Transformations
  3. Polynomial, Power, and Rational Functions
    1. Linear and Quadratic Models
    2. Modeling with Power Functions
    3. Modeling with Higher Order Polynomials
    4. Zeros (roots)
    5. Graphing Rational Functions
    6. Solving for a Single Variable
    7. Inequalities
  4. Exponents and Logarithms
    1. Exponential Functions
    2. Logarithmic Functions
    3. Finance
  5. Trigonometry
    1. Unit Circle
    2. Sine and Cosine
    3. Tangent
    4. Cosecant, Secant, and Cotangent
    5. Inverse Trig Functions
    6. Modeling with trig
  6. Analytic Trigonometry
    1. Fundamental Identities
    2. Proving Trig Identities
    3. Sum and Difference Identities
    4. Multiple Angle Identities
    5. Law of Sines
    6. Law of Cosines
  7. Applications of Trigonometry
    1. Vectors
  8. Systems and Matrices
    1. Systems of Equations
    2. Substitution
    3. Elimination
    4. The Matrix
  9. Discrete Math
    1. Σ Notation
  10. Calculus
    1. Limits
    2. Derivative
    3. Integral

Honors Precalculus

2017 - 2018

“The word "calculate" ... comes from the Latin word calculus, meaning a pebble used for counting. To enjoy working with numbers you don't have to be Einstein (German for "one stone"), but it might help to have rocks in your head.”
― Steven H. Strogatz, The Joy of x: A Guided Tour of Math, from One to Infinity
Instructor: Jed Williams
williamsj@npsk.org
Room 211
jedediyah.com/courses/precalculus

I. Rationale:

Precalculus combines the trigonometric, geometric, and algebraic techniques needed to prepare students for the study of calculus, and strengthens students’ conceptual understanding of problems and mathematical reasoning in solving problems. Facility with these topics is especially important for students intending to study calculus, physics, and other sciences, and/or engineering in college.

II. Course Aims and Outcomes:

By the end of this course, students will:
  1. extend work with complex numbers Students continue their work with complex numbers. They perform arithmetic operations with complex numbers and represent them and the operations on the complex plane. Students investigate and identify the characteristics of the graphs of polar equations, using graphing tools. This includes classification of polar equations, the effects of changes in the parameters in polar equations, conversion of complex numbers from rectangular form to polar form and vice versa, and the intersection of the graphs of polar equations.
  2. expand understanding of logarithms and exponential functions Students expand their understanding of functions to include logarithmic and trigonometric functions. They investigate and identify the characteristics of exponential and logarithmic functions in order to graph these functions and solve equations and practical problems. This includes the role of e, natural and common logarithms, laws of exponents and logarithms, and the solutions of logarithmic and exponential equations. Students model periodic phenomena with trigonometric functions and prove trigonometric identities. Other trigonometric topics include reviewing unit circle trigonometry, proving trigonometric identities, solving trigonometric equations, and graphing trigonometric functions.
  3. use characteristics of polynomial & rational functions to sketch graphs of those functions Students investigate and identify the characteristics of polynomial and rational functions and use these to sketch the graphs of the functions. They determine zeros, upper and lower bounds, y-intercepts, symmetry, asymptotes, intervals for which the function is increasing or decreasing, and maximum or minimum points. Students translate between the geometric description and equation of conic sections. They deepen their understanding of the Fundamental Theorem of Algebra.
  4. perform operations with vectors Students perform operations with vectors in the coordinate plane and solve practical problems using vectors. This includes the following topics: operations of addition, subtraction, scalar multiplication, and inner (dot) product; norm of a vector; unit vector; graphing; properties; simple proofs; complex numbers (as vectors); and perpendicular components.

III. Format and Procedures:

One of the most useful tools for your education is timely quality feedback on your work. That’s how we clear up any confusion and clarify things. That said, it is impossible for me to actually give quality feedback on ALL of my students’ work due to the number of students and the amount of work per student. So how do we resolve this? You will get plenty of feedback, but additionally we just treat it like the real world: you take responsibility for yourself! I am always available to answer questions and we will be constantly clarifying as we go, but it is incumbent upon you to ask questions and self reflect on your understanding.

IV. Grading Procedures

Grades for this course will be based on the quality of the work you produce! This will include assessments as well as projects and presentations. Homework, which is practice, will typically not be graded, but that does not make it unimportant. Homework is a way for you to practice and self-assess your progress, and it should help you to identify areas where you need additional practice.