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Poyen School |
| Relations and Functions |
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Domain/range
The learner will be able to determine, with or without technology, the domain and range of a relation defined by a graph, a table of values, or a symbolic equation including those with restricted domains and whether a relation is a function.
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Operations with functions
The learner will be able to evaluate, add, subtract, multiply, divide, and compose functions and give appropriate domain and range restrictions.
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Inverse of a function
The learner will be able to determine the inverse of a function (Graph, with and without appropriate technology, functions and their inverses).
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Changing parameters: affect on graph
The learner will be able to analyze and report, with and without appropriate technology, the effect of changing coefficients, exponents, and other parameters on functions and their graphs (linear, quadratic, and higher degree polynomial).
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Piece-wise/step
The learner will be able to graph, with and without appropriate technology, functions defined as piece-wise and step.
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Periodic Phenomena
The learner will be able to recognize periodic phenomena (sine or cosine functions such as sound waves, length of daylight, circular motion).
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Period Functions and graphs
The learner will be able to investigate and identify key characteristics of period functions and their graphs (period, amplitude, maximum, and minimum).
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Frequency and Amplitude
The learner will be able to use basic properties of frequency and amplitude to solve problems.
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Real World Situations: functions
The learner will be able to apply the concepts of functions to real world situations.
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| Linear/Absolute Value:Equations/Inequal |
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Absolute value equations/inequalities
The learner will be able to solve, with and without appropriate technology, abosolute value equations and inequalities written in one or two variable, and graph solutions.
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Linear equations: two variables
The learner will be able to solve, with and without appropriate technology, systems of linear equations with two variables and graph the solution set.
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Matrices
The learner will be able to develop and apply, with and without appropriate technology, the basic operations and properties of matrices (associative, commutative, identity, and inverse).
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Linear Equations: three variables
The learner will be able to solve, with and without appropriate technology, systems of linear equations with three variables using algebraic methods, including matrices.
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Real World Situations: linear/absolute
The learner will be able to apply, with or without technology, the concepts of linear and absolute value equations and inequalities and systems of linear equations and inequalities to model real world situations including linear programming.
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| Quadratic Equations and Functions |
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Computations with radicals
The learner will be able to perform computations with radicals: 1. Simplify radicals with different indices 2. Add, subtract, multiply, and divide radicals. 3. Rationalize denominators 4. Solve equations that contain radicals or radical expressions.
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Complex numbers
The learner will be able to extend the number system to include the complex numbers 1. define the set of complex numbers 2. Add, subtract, multiply, and divide complex numbers 3. Rationalize denominators.
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Solve quadratic equations
The learner will be able to analyze and solve quadratic equations with and without appropriate technology by 1. factoring 2. graphing 3. extracting the square root 4. completing the square 5. using the quadratic formula.
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Derive quadratic formula
The learner will be able to derive the quadratic formula and use it to solve equations.
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Quadratic Relations
The learner will be able to develop and analyze, with and without appropriate technology, quadratic relations 1. graph a parabolic relationship when given its equation 2. write an equation when given its roots (zeros or solutions) or graph 3. determine the nature of the solutions graphically and by evaluating the discriminant 4. determine the maximum or minimum values and the axis of symmetry both graphically and algebraically.
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Real Word Situations: quadratic eq/funct
The learner will be able to apply the concepts of quadratic equations and functions to model real world situations by using appropriate technology when needed.
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| Polynomial and Rational Functions |
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Factors of polynomials
The learner will be able to determine the factors of polynomials by : 1. Using factoring techniques including grouping and the sum or difference of two cubes. 2. Using long division 3. Using synthetic division.
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Graph of polynomial functions
The learner will be able to analyze and sketch, with and without appropriate technology, the graph of a given polynomial function, determining the characteristics of domain and range, maximum and minimum points, end behavior, zeros, multiplicity of zeros, y-intercept, and symmetry.
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Write equation of polynomial
The learner will be able to write the equation of a polynomial function given its roots.
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Identify polynomial equation
The learner will be able to identify the equation of a polynomial function given its graph or table.
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Power functions
The learner will be able to identify the characteristics of graphs of power functions of the for f(x) = ax to the nth power, for negative integral values of n, including domain, range, end behavior, and behavior at x=0, and compare these characteristics to the graphs of related positive integral power functions.
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Rational expressions
The learner will be able to simplify, add, subtract, multiply, and divide with rational expressions.
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Radical expressions/rational exponents
The learner will be able to establish the relationship between radical expressions and expressions containing rational exponents.
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Simplify rational exponents
The learner will be able to simplify variable expressions containing rational exponents using the laws of exponents.
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| Exponential and Logarithmic Functions |
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Recognize graphs of exponential function
The learner will be able to recognize the graphs of exponential functions distinguishing between growth and decay.
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Exponential functions/characteristics
The learner will be able to graph exponential functions and identify key characteristics: domain, range, intercepts, asymptotes, and end behavior.
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Changes in Parameters of exponential
The learner will be able to identify the effect that changes in the parameters of the base have on the graph of the exponential function.
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Recognize/Solve problems
The learner will be able to recognize and solve problems that can be modeled using exponential functions.
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Relationship bn exponential/logarithmic
The learner will be able to establish the relationship between exponential and logarithmic functions.
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Logarithms
The learner will be able to evaluate simple logarithms using the definition (Ex-see ELF.5.AII.6 for example).
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Properties of logarithms
The learner will be able to use properties of logarithms to manipulate logarithmic expresions.
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| Data Analysis and Probability |
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Regression Line
The learner will be able to find regression line for scatter plot, using appropriate technology, and interpret the correlation coefficient.
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Correlation Coefficient
The learner will be able to interpret and use the correlation coefficient to assess the strength of the linear relationship between two variables.
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Quadratic Curve
The learner will be able to find the quadratic curve of best fit using appropriate technology.
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Regression Equations
The learner will be able to identify strengths and weaknesses of using regression equations to approximate data.
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Measures of spread
The learner will be able to compute and explain measures of spread (range, percentiles, variance, standard deviation.
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Gaussian normal distribution
The learner will be able to describe the characteristics of a Gaussian normal distribution.
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