Units Covered and Essential Outcomes (not necessarily taught in this order):
· Unit 1: Beginning Trigonometry and Trig Graphs
o Use the unit circle to find exact values of trig functions with special reference angles for not only sin, cos, and tan but also their reciprocal functions. [PC.F.2.1]
o Identify the symmetry of the unit circle to help determine whether trig functions are odd or even as well as the period of the functions. [PC.F.2.2]
o Identify the key features and graphs of all six trig functions including phase shift and frequency. [PC.F.1.1, PC.F.1.2]
o Use key feature information to create trig functions in standard form. [PC.F.1.3]
· Unit 2: Trigonometry Identities, Inverse Trigonometry, and Trigonometry Equations
o Derive and use the Pythagorean Identities to find the value of trig functions. [PC.F.3.3]
o Use identities and inverse trig to solve problems. [PC.F.3.1, PC.A.2.3]
o Use key features of trig functions to solve equations and inequalities. [PC.F.1.4]
· Unit 3: Triangle Trigonometry
o Use the Law of Sines and Law of Cosines to solve problems. [PC.F.3.2]
· Unit 4: Vectors and Matrices
o Represent vectors using magnitude and direction and vector notation. [PC.N.3.1]
o Add and subtract vectors to combine into one new vector. [PC.N.3.2]
o Add and subtract matrices [PC.N.2.1]
o Execute commutative, associative and distributive property of matrices. [PC.N.2.2, PC.N.2.3]
o Multiply a matrix by a scalar. [PC.N.2.4]
o Multiply matrices together, understand the requirements, what the expected dimensions should be, and how to calculate each element. [PC.N.2.5]
· Unit 5: Parametric, Polar, and Complex Numbers
o Model using parametric equations. [PC.F.7.1]
o Use technology to solve parametric equations. [PC.F.7.1]
o Eliminate parameters to rewrite parametric equations into cartesian form (in terms of x and y) [PC.A.2.4]
o Add and subtract complex numbers [PC.N.1.1]
o Multiply complex numbers [PC.N.1.2]
· Unit 6: Exponentials and Logarithms
o Build exponential functions to model growth or decay [PC.F.4.2]
o Identify key features of exponential functions (domain/range, intercepts, asymptotes, increasing/decreasing intervals, positive/negative intervals, end behavior, concavity, continuity, and limits) both graphically and algebraically [PC.F.4.1]
o Identify key features of logarithmic functions (domain/range, intercepts, asymptotes, increasing/decreasing intervals, positive/negative intervals, end behavior, concavity, continuity, and limits) both graphically and algebraically [PC.F.4.3]
o Use properties of logarithms to rewrite expressions. [PC.A.2.1]
o Use properties of exponentials and logarithms to solve equations. [PC.A.2.2]
o Use properties of exponentials and logarithms to solve real-world problems with and without technology [PC.F.4.4]
· Unit 7: Functions Toolkit: Extending Polynomial and Rational Functions
o Review transformation of functions and apply to power, exponential and logarithmic functions [PC.F.4.7]
o Model optimization problems with polynomial and rational functions (PRF), solve graphically, and solve algebraically [PC.F.4.6]
o Identify key features of rational functions (domain/range, intercepts, asymptotes, increasing/decreasing intervals, positive/negative intervals, end behavior, concavity, continuity, and limits) both graphically and algebraically [PC.F.4.5]
o Use graphical methods to solve inequalities of PRF [PC.A.1.2]
o Use sign charts to solve inequalities of PRF algebraically [PC.A.1.1]
· Unit 8: Composition and Inverse Function
o Use the operation of composition of two or more functions. [PC.F.5.1]
o Evaluate the value of a composite function using algebraic, graphical, tabular representations. [PC.F.5.2]
o Find the domain of a composite function. [PC.F.5.3]
o Build algebraic models involving function composition. [PC.F.5.4]
o Decompose the composition of functions into two functions. [PC.F.5.5]
o Find the inverse of a function algebraically and graphically. [PC.F.5.6]
o Determine if (or verify) one function is the inverse of another [PC.F.5.7]
· Unit 9: Sequences and Series
o Construct recursive functions (algebraic and tabular) [PC.F.6.1 and PC.F.6.2]
· Unit 10: Conics
o Identify conic sections (ellipse and hyperbola) from its algebraic representation in standard form, graph conic sections and identify key features. [PC.F.4.8, PC.F.4.9, PC.F.4.10]
· Unit 11: Limits
o Determine limits graphically
o Determine limits analytically