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

Honors Precalculus2017  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:
 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.
 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.
 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, yintercepts, 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.
 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 selfassess your progress, and it should help you to identify areas where you need additional practice.
