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Poyen School |
| Polynomial and Rational Functions |
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Graph polynomial and rational functions
The learner will be able to investigate and sketch, with and without appropriate technology, the graphs of polynomial and rational functions using the characteristics of domain and range, upper and lower bounds, maximum and minimum points, asymptotes and end behavior, zeroes multiplicity of zeroes, y - intercepts, and symmetry.
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Solve polynomial equations
The learner will be able to solve, with and without appropriate technology, polynomial equations utilizing techniquest such as Descartes' Rule of Signs, upper and lower bounds, Intermediate Value Theorem and Rational Root Theorem.
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Fund. characteristics:Rational Functions
The learner will be able to describe, with and without appropriate technology, the fundamental characteristics of rational functions: zeroes, discontinuities (including vertical asymptotes), end behavior (including horizontal asymptotes).
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Apply Concepts: polynomial & rationa
The learner will be able to apply the concepts of polynomial and rational functions to model real world situations using appropriate technology when needed.
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| Exponential and Logarithmic Functions |
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Inverse relationship: exponential &
The learner will be able to establish the inverse relationship between exponential and logarithmic functions.
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Laws of log/change of base
The learner will be able to develop and apply the laws of logarithms and the change of base formula to simplify and evaluate expressions.
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Solve exponential & log equations
The learner will be able to solve graphically, algebraically, and numerically, with and without appropriate technology, equations and real world problems involving exponential and logarithmic expressions.
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Domain/range/intercepts/asymptotes
The learner will be able to find, with and without appropriate technology, the domain, range, intercepts, and asymptotes of logarithmic and exponential functions.
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Graph log & exponential functions
The learner will be able to draw and analyze, with and without appropriate technology, graphs of logarithmic and exponential functions.
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| Conics |
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Conic sections
The learner will be able to identify, graph, write, and analyzie equations of conic sections, using properties such as symmetry, intercepts, foci, asympototes, and eccentricity, and when appropriate, use technology.
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Systems of equations & inequalities
The learner will be able to solve, with and without appropriate technology, systems of equations and inequalities involving conics and other types of equations.
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Real world problems: conics
The learner will be able to solve, with and without appropriate technology, real world problems involving conic sections.
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| Sequences and Series |
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Sequence: recursive
The learner will be able to develop, with and without appropriate technology, a representation of sequences recursively.
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Arithmetic/geometric:sequences & ser
The learner will be able to define and discriminate between arithmetic and geometric sequences and series and use appropriate technology when needed.
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Sum: finite & infinite sequences/ser
The learner will be able to solve, with and without appropriate technology, problems involving the sum (including Sigma notation) of finite and infinite sequences and series.
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Find the nth term of sequence
The learner will be able to determine the nth term of a sequence give a rule or specific terms and use appropriate technology when needed.
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Solve real world problems
The learner will be able to use, with and without appropriate technology, sequences and series to solve real world problems.
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| Trigometric Functions |
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Define 6 trig functions
The learner will be able to define the six trigometric functions as: 1. Circular functions 2. Ratios of sides of right triangles 3. Functions of an angle in standard position when given a point on the terminal side of the angle.
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Interchange degrees and radians
The learner will be able to use degrees and radians interchangeably to represent angle measures.
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Reference angle/Conterminal angle
The learner will be able to sketch and angle in standard position and determine the reference angle and coterminal angles.
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Solve for trig functions
The learner will be able to find the values of the trigometric functions given the value of one trigometric function and an additional piece of qualifying information or given the coordinates of a point on the terminal side of an angle.
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Exact values trig functions
The learner will be able to develop and become fluent in the recall of the exact values of the trigometric funtions for special angles.
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Apply trig functions
The learner will be able to solve, with and without appropriate technology, real world problems involving applications of trigometric functions.
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Graph 6 trig functions
The learner will be able to graph the six trigometric functions, identify domain, range, intercepts, period, amplitude, and asymptotes as applicable and use symmetry to determine whether the function is even or odd through appropriate technology when needed.
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Transformations of trig functions
The learner will be able to determine, with and without appropriate technology, the amplitude, period, phase shift, and vertical shift, and sketch the graph of transformations of the trigometric functions.
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Inverse of trig functions
The learner will be able to identify and garph, wtih and without appropriate technology, the inverse of trigometric functions including the restrictions on the domain.
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| Oblique Triangles |
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Oblique triangles
The learner will be able to develop and use the Law of Sines and the Law of Cosines to solve oblique triangles and use appropriate technology when needed.
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Apply Law of Sines/Cosines
The learner will be able to solve real world problems applying the Law of Sines and the Law of Cosines and appropriate technology when needed.
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Area of oblique triangle
The learner will be able to determine the area of an oblique triangle by using an appropriate formula and appropriate technology when needed.
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Use vectors
The learner will be able to use vectors to solve problems and describe addition of vectors and multiplication of a vector by a scalar, both symbolically and geometrically.
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Vectors to model situations
The learner will be able to use vectors to model situations defined by magnitude and direction and analyze and solve real world problems by using appropriate technology when needed.
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| Trig Equations and Identities |
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Trig identities
The learner will be able to develop the Pythagorean Identities and use to verify other identities and simplify expressions.
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Trig formulas
The learner will be able to develop and use trigometric formulas including sum and difference formulas and multiple angle formulas.
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Solve trig equations
The learner will be able to solve trigometric equations algebraically and graphically and use appropriate technology when needed.
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| Polar coordinates |
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Polar/rectangular coordinates: convert
The learner will be able to convert polar coordinates to rectangular coordinates and rectangular coordinates to polar coordinates.
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Represent equations
The learner will be able to represent equations given in rectangular coordinates in terms of polar coordinates.
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Graph polar equations
The learner will be able to graph polar equations and use appropriate technology when needed.
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Apply polar coordinates
The learner will be able to apply polar coordinates to real world situations and use appropriate technology when needed.
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