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 Algebra II Module 1: Polynomial, Rational, and Radical Relationships Students connect polynomial arithmetic to computations with whole numbers and integers. Students learn that the arithmetic of...

 Module 2 builds on students’ previous work with units and with functions from Algebra I, and with trigonometric ratios and circles from high school Geometry. The heart of the module is the study of...

 Student Outcomes Students prove the Pythagorean identity sin2(x) + cos2(x) = 1. Students extend trigonometric identities to the real line, with attention to domain and range. Students use the...

 Student Outcomes Students prove simple identities involving the sine function, cosine function, and secant function. Students recognize features of proofs of identities.

 Student Outcomes Students see derivations and proofs of the addition and subtraction formulas for sine and cosine. Students prove some simple trigonometric identities.

 Exponential and Logarithmic Functions In this module, students synthesize and generalize what they have learned about a variety of function families. They extend the domain of exponential functions...

 At the beginning of Topic B, students apply the properties of exponents to solve exponential equations numerically (FBF.1a) as a way to motivate the need for logarithms, which are first introduced...

 Student Outcomes Students approximate the value of quantities that involve positive irrational exponents. Students extend the domain of the function f(x) =bx for positive real numbers b to all real...

 Student Outcomes Students write an exponential function that represents the amount of water in a tank after t seconds if the height of the water doubles every 10 seconds. Students discover Euler’s...

 Student Outcomes Students solve simple exponential equations numerically.

 Student Outcomes Students calculate a simple logarithm using the definition.

 Student Outcomes Students construct a table of logarithms base 10 and observe patterns that indicate properties of logarithms.

 Student Outcomes Students construct a table of logarithms base 10 and observe patterns that indicate properties of logarithms.

 Student Outcomes Students justify properties of logarithms using the definition and properties already developed.

 Student Outcomes Students understand how to change logarithms from one base to another. Students calculate logarithms with any base using a calculator that computes only logarithms base 10 and base e...

 Student Outcomes Students solve simple logarithmic equations using the definition of logarithm and logarithmic properties.

 Student Outcomes Students use logarithm tables to calculate products and quotients of multidigit numbers without technology. Students understand that logarithms were developed to speed up arithmetic...

 Student Outcomes Students interpret addition and multiplication of two irrational numbers in the context of logarithms and find betterandbetter decimal approximations of the sum and product,...

 In Topic C, students graph logarithmic functions, identifying key features (FIF.4, FIF.7) and discover how the logarithmic properties are evidenced in the graphs of corresponding logarithmic...

 Student Outcomes Students graph the functions f(x) = log(x), g(x) = log2(x), and h(x) = ln(x) by hand and identify key features of the graphs of logarithmic functions.

 Student Outcomes Students compare the graph of an exponential function to the graph of its corresponding logarithmic function. Students note the geometric relationship between the graph of an...

 Student Outcomes Students will understand that the logarithm function base b and the exponential function base b are inverse functions.

 Student Outcomes Students study transformations of the graphs of logarithmic functions. Students use the properties of logarithms and exponents to produce equivalent forms of exponential and...

 Student Outcomes Students understand that the change of base property allows us to write every logarithm function as a vertical scaling of a natural logarithm function. Students graph the natural...