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Common Core: Math
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 Students revisit the fundamental theorem of algebra as they explore complex roots of polynomial functions. They use polynomial identities, the binomial theorem, and Pascal’s Triangle to find roots...

 This module revisits trigonometry that was introduced in Geometry and Algebra II, uniting and further expanding the ideas of right triangle trigonometry and the unit circle. New tools are introduced...

 In Topic B, students explore composition of functions in depth and notice that a composition of a polynomial function with the function f(x) = 1/x gives functions that can be written as ratios of...

 Student Outcomes Students reduce rational expressions to lowest terms. Students determine the domain of rational functions.

 Student Outcomes Students describe the end behavior of rational functions.

 Student Outcomes Students identify vertical and horizontal asymptotes of rational functions.

 Student Outcomes Students graph rational functions showing intercepts, asymptotes, and end behavior.

 Student Outcomes Students graph transformations of functions in the form f(x) = 1/xn.

 Student Outcome Students compose functions and describe the domain and range of the compositions.

 Student Outcomes Students write equations that represent functional relationships and use the equations to compose functions. Students analyze the domains and ranges of functions and function...

 In Topic C students study inverse functions, being careful to understand when inverse functions do and do not exist, working to restrict the domain of a function to produce an invertible function. ...

 Student Outcomes Students read the inverse values of a function from a table and graph. They create the inverse of a function by solving an equation of the form f(x) = y. They understand the...

 Student Outcomes Students continue to read the inverse values of a function from a table and graph. They create the inverse of a function by solving an equation of the form f(x) = y. Students verify...

 Student Outcomes In order to demonstrate understanding of the inverse relationship between exponents and logarithms, students construct the inverse of exponential and logarithmic functions from a...

 Student Outcomes Students understand the inverse relationship between logarithms and exponents and apply their understanding to solve realworld problems.

 Topic A helps students recall how to use special triangles positioned within the unit circle to determine geometrically the values of sine, cosine, and tangent at special angles. The unit circle is...

 Student Outcomes Students determine the values of the sine, cosine, and tangent functions for rotations of π/3, π/4, and π/6 radians. Students use the unit circle to express the values of the sine,...

 Student Outcomes Students explore the symmetry and periodicity of trigonometric functions. Students derive relationships between trigonometric functions using their understanding of the unit circle.

 Student Outcomes Students prove the subtraction formula for cosine and use their understanding of the properties of the trigonometric functions to derive the remaining addition and subtraction...

 Student Outcomes Students use the addition formulas to derive the doubleangle formulas for sine, cosine, and tangent and evaluate trigonometric expressions for specific values of θ. Students use the...

 Student Outcomes Students model waveforms using sinusoidal functions and understand how standing waves relate to the sounds generated by musical instruments. Students use trigonometric identities to...

 The graphs of the trigonometric functions are revisited in Topic C. Students visualize these graphs with the aid of the appropriate software and briefly recall how changing various parameters of a...

 Student Outcomes Students graph the sine, cosine, and tangent functions and analyze characteristics of their graphs.

 Student Outcomes Students understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed. Students use...