Mathematics+Topics+Scheduled

__Honors Precalc Math Topics __


 * Sequences (notation, rules, recursive definit ion, infinite sequence, geometric, arithmetic) **
 * Series (notation, summation notation, infinite series, convergence of geometric series) **


 * Exponential functions and logarithms **
 * 1) **  Vocabulary (base, exponent)  **
 * 2) **  Graphs of both functions, shifted up/down, reflected through y or x  **
 * 3) **  Understand that they are inverse functions  **
 * 4) **  Be able to use the rules of logs (eg. log(ab)=log(a) + log(b) and the other two.  **
 * 5) **  Understand ln(x) as the inverse of e x  **
 * 6) **  Be able to use the definition of log to evaluate basic logs without calculator  **
 * 7) **  Solve word problems involving exponential growth and decay and interest problems  **


 * Vectors (definition, operations, polar coordinates vs. rectangular, horiz.& vert.components) **


 * Functions and functional notation **
 * 1) **  Graph and evaluate basic nine functions  **
 * 2) **  Use functional notation f(x,y)=... and be able to evaluate compositions of functions  **
 * 3) **  Be able to define and understand piecewise functions  **
 * 4) **  Be able to state domain and range of basic functions  **
 * 5) **  Be able to determine whether functions are odd, even, and what kind of symmetry  **
 * 6) **  Be able to graph rational functions, determining intercepts and asymptotes  **
 * 7) **  Be able to define polynomial function, find number of roots, determine odd/even/neither  **
 * 8) **  Be able to find inverse functions and determine whether mappings are 1:1 or functions  **


 * Limits **
 * 1) **  right-hand vs. left-hand, limit as x goes to infinity  **
 * 2) **  rules for simplifying limits  **
 * 3) **  definition of continuity at a point  **
 * 4) **  special limits, limits that don’t exist, limits of trig functions  **
 * 5) **  extra (honors?) delta-epsilon definition of limit and its application  **


 * Trigonometry **
 * 1) **  Be able to use triangle-based trig to solve right-triangle problems  **
 * 2) **  Be able to use law of sines and law of cosines to solve other triangles  **
 * 3) **  Be able to find areas of SAS triangles  **
 * 4) **  Learn to evaluate trig functions of special angles using the unit circle  **
 * 5) **  Learn basic trig identities (pythagorean identities, sum and difference identity, double-angle)  **
 * 6) **  Learn graphs and properties of tan, cot, sec, csc, sin, cos (domain, range, intercepts)  **
 * 7) **  Learn graphs and properties of inverse trig functions (arcsin, arccos, arctan)  **
 * 8) **  Be able to solve trig equations eg. (sin3x)=1 without calculator  **
 * 9) **  Be able to describe period, amplitude, phase shift, etc.. from equation  **
 * 10) **  Be able to write the equation from the graph  **


 * Linear functions: examples, applications, standard form/slope-intercept form/point-slope form **
 * Conic functions (parabola, hyperbola, ellipse/circle) **
 * Know locus definitions and how to graph from equation **
 * Be able to find vertices, asymptotes, directrix (parabola), focus or foci, domain and range **
 * Be able to describe real-world examples for each of these conic functions **


 * //Might be included:// **
 * 1) **  Graphing, estimating, analyzing using technology  **
 * 2) **  SAT prep techniques and foundational algebra  **
 * 3) **  Problem-solving techniques  **
 * 4) **  Solving unfamiliar equations by symmetry and other methods  **
 * 5) **  Finding solutions to systems of equations by graphing and finding the intersections  **
 * 6) **  Nth powers and nth roots of complex numbers, argand diagram, De Moivre’s theorem  **
 * 7) **  Half-angle identity  **
 * 8) **  Product of sinx(siny) identity  **

//** Won’t be included:  **//
 * 1) **  Matrices and basic linear algebra  **
 * 2) **  Set theory  **
 * 3) **  Probability  **
 * 4) **  Statistics  **