Precalculus

Sets Functions Number Theory || 4 Weeks || How do we identify domains and relations between numbers? || Solving Absolute Value and Inequality Equation. Interval Notation. Set builder notation. Graphing absolute value functions. Functions vs. Relations || Handouts [|Logic Text] || Textbook Section (These are student created sections) Quiz Graph Project ||  ||   || Larson 8 || Textbook Section ||  ||   || Unit Circle Quiz Polar Graphing Project Quiz ||  ||   || What are the properties of trig functions? || Sine and Cosine Function Amplitude and stretching/compression. Asymptotes Graphs of Tan, Sec, Csc Graphs of Arcsin, Arccos || Larson 4.6, 4.7, 4.8 || Geogebra Project Textbook Section Quiz ||  ||   || Solving trig equations. || Larson 5, 6.1, 6.2 || Proofs of Identities Applied problem set. Test ||  ||   || Project Inverse Variation Word Problems ||  ||   || Rate of Change (Difference Quotient) || 9.1-9.4 || Textbook Section Function Art Project Quiz ||  ||   ||
 * ~ Topic ||~ Duration ||~ Essential Questions ||~ Content/Concepts/Skills ||~ Ch. ||~ Assessment ||~ Standards ||~ Plans ||
 * Inequalities and Absolute Values
 * Sequences Series || 2 Weeks || What is a set? How do we solve problems using properties of numbers? What is a series? How do we prove a pattern? || Sets, Number Theory, Summation Notation, Induction, Proof, || Redwood College Chapter 1
 * Circles and the Unit Circle, Polar Coordinates || 3 Weeks || What are different ways to define and analyze a circle? How does the Unit Circle work? How does our perspective change in a different coordinate system? || Equation of a Circle, Radius and Radians, Unit Circle, Polar Coordinates || Larson 9.1, 4.1, 4.2, 4.4 9.6 || Circle Word Problems/ Art Project
 * Graphs of Trigonometric Equations || 3 Weeks || How do we use the Unit Circle to generate the Sine and Cosine functions? How do use properties of graphing to graph tangent, sec, csc, arcsin, and arccos?
 * Trig Identities/ Solving Trig Equations || 2 Weeks || What are the methods and challenges of solving trig equations? How do we find an identity? How are they useful? || Describing identities, Prove the double angle and half angle identities, Law of Sines and Cosines
 * Ellipses and Inverse Variation || 1 Week || What is an ellipse? How is it related to our world? || Equation of an ellipse, minor/major axis, vertices, foci, elliptical orbit, constructing an ellipse || Larson 9.2 || Elliptical Art
 * Review ||  ||   ||   ||   || MIDTERM ||   ||   ||
 * Functions and Graphs || 2 Weeks || What is a function? How do the components of a function relate to its graph? || Domain, Range, Composite Function, Translations/ Reflections/ Dilations,
 * Linear Functions/ Models || 2 Week || How do we model our world with functions? What are applications of a linear model? || Slope, modeling. || 9.5-10.1 || Word Problem Set

What is Modeling Forum. ||  ||   || What is a parabola? How do construct them? Analyze them? Define them as a parametric? || Polynomials, Quadratics, Roots, Multiplicity, Long Run Behavior, Intercepts, Factoring, Parabolas Parametric Notation, Graphing Parametric. || 8.1-8.4 || Parabola Presentation or Textbook Section
 * Polynomial Functions/ Parabolas/ Parametric || 4 Weeks || What are the properties of polynomial functions?

Parametric Art Project

Test ||  ||   || What is a hyperbola? || Asymptotes Limits Graphing Rational Functions Hyperbolas- properties and equation of. || 8.5-8.7 || Graphing Project/ Textbook Sections for Rational / Functions Applied Hyperbola Problems Test ||  ||   || Graphs of Inverse Functions Exponential Equations Logarithms/ Log Identities and graphs || 11.1-11.5 || Exponential Word Problem Set Test ||  ||   || Find ways to solve for basic limits graphically and analytically. Finding Limits at infinity. || 11.1-11.4 || Take Home Test ||  ||   ||
 * Rational Functions/ Hyperbolas || 3 Weeks || How do rational numbers change as numerators or denominators approach infinite or 0?
 * Exponential Functions || 3 Weeks || How does a model change when the variable is in the exponent? || Inverse Functions
 * Limits || 2 Weeks || What is a limit? || Define and identify what a Limit is.