Precalculus A

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Use the structure of an expression to identify ways to rewrite it.A.SSE.A.2

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Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. A.SSE.B.3

Clarifications/Examples: Produce an equivalent form of a rational expression to reveal information about the behavior of the graph of the related function.   

Clarifications/Examples: Rewrite complex fractions as rational expressions 

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Use the properties of exponents to transform expressions for exponential functions. For example, the expression 𝟏𝟏. 𝟏𝟏𝟏𝟏𝒕𝒕 can be rewritten as to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.A.SSE.B.3.c

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Know and apply the Remainder Theorem: For a polynomial 𝒑𝒑(𝒙𝒙) and a number a, the remainder on division by 𝒙𝒙 − 𝒂𝒂 is 𝒑𝒑(𝒂𝒂), so 𝒑𝒑(𝒂𝒂) = 𝟎𝟎 if and only if (𝒙𝒙 − 𝒂𝒂) is a factor of 𝒑𝒑(𝒙𝒙). A.APR.B.2

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Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. A.APR.B.3.a

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Know and apply the Binomial Theorem for the expansion of (𝒙𝒙 + 𝒚𝒚)𝒏𝒏 in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal's Triangle.A.APR.C.5

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Rewrite simple rational expressions in different forms.A.APR.D.6

Clarifications/Examples: Rational expressions have no restrictions on degree of the numerator or denominator. 

Clarifications/Examples: Understand the connection between rewriting rational expressions and using long division when factoring polynomials.  

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Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication and division by a nonzero rational expression; add, subtract, multiply and divide rational expressions.A.APR.D.7

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Create equations and inequalities in one variable and use them to solve problems.A.CED.A.1.a

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Create polynomial equations given roots.A.CED.A.1b

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Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.A.CED.A.3

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Solve equations and inequalities in one variable.A.REI.B

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Solve systems of equations comprised of various combinations of all algebraic and transcendental functions in two variables.A.REI.C.7a

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Extend evaluating functions to include operations with composite functions, e.g. 𝑓𝑓(𝑥𝑥 + 2) − 𝑓𝑓(𝑥𝑥). F.IF.A.2a

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For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities; sketch graphs showing key features given a verbal description of the relationship. F.IF.B.4

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Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. F.IF.B.5

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Graph all functions including piecewise-defined functions, step functions and absolute value functionsF.IF.C.7f

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Determine the end behavior of the graph of a polynomial function using the degree and leading coefficient.F.IF.C.7g

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Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. F.IF.C.8

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Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables or by a verbal description). F.IF.C.9

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Write a function that describes a relationship between two quantities, including more complex functions.F.BF.A.1

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Compose functions. For example, if 𝑇𝑇(𝑦𝑦) is the temperature in the atmosphere as a function of height, and ℎ(𝑡𝑡) is the height of a weather balloon as a function of time, then is the temperature at the location of the weather balloon as a function of time.F.BF.A.1c

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Identify the effect on the graph of replacing 𝑓𝑓(𝑥𝑥) by 𝑓𝑓(𝑥𝑥) + 𝑘𝑘, 𝑘𝑘𝑘𝑘(𝑥𝑥), 𝑓𝑓(𝑘𝑘𝑘𝑘), and 𝑓𝑓(𝑥𝑥 + 𝑘𝑘) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.F.BF.B.3

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Find inverse functions.F.BF.B.4

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Verify by composition that one function is the inverse of another. F.BF.B.4b

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Read values of an inverse function from a graph or a table, given that the function has an inverse.F.BF.B.4c

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Produce an invertible function from a non-invertible function by restricting the domain.F.BF.B.4d

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Build inverse trigonometric functions. F.BF.B.4e

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Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.F.BF.B.5

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Use properties of logarithms, including both common and natural logarithms, to rewrite and solve exponential models.  F.LE.A.4a

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Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.F.TF.A.2

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Use special triangles to determine geometrically the values of sine, cosine, tangent for 𝜋𝜋 3 , 𝜋𝜋 4 , 𝑎𝑎𝑎𝑎𝑎𝑎 𝜋𝜋 6 and use the unit circle to express the values of sine, cosine, and tangent for 𝑥𝑥, 𝜋𝜋 + 𝑥𝑥, 𝑎𝑎𝑎𝑎𝑎𝑎 2𝜋𝜋 − 𝑥𝑥 in terms of their values for x, where x is any real number.F.TF.A.3

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Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.F.TF.A.4

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Choose trigonometric functions to model real world phenomena.F.TF.B.5

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Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.F.TF.B.6

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Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology and interpret them in context.F.TF.B.7

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Use trigonometric identities to rewrite expressions and as a tool when solving trigonometric equations.F.TF.C.9.a

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Prove the Laws of Sines and Cosines and use them to solve problems. G.SRT.D.10

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Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying, resultant forces).G.SRT.D.11

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Fit a function to data represented by a scatterplot; use functions fitted to data to solve problems in the context of the data.S.ID.B.6d

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Distinguish between situations that can be modeled with exponential functions and logistic functions.F.LE.A.1.d

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Interpret the parameters in a logistic function in terms of a context.F.LE.B.5a

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Build and interpret logistic functions to model real-world problems. F.LE.B.6

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Sketch and analyze the graphs of logistic functions.F.LE.B.6a

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Compare and contrast the exponential, logarithmic, and logistic models.F.LE.B.6b

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Apply understanding of logarithmic and logistic functions to solve real-world problems.F.LE.B.6c

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