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Algebra I

These standards require students to use algebra as a tool for representing and solving a variety of practical problems. Tables and
graphs will be used to interpret algebraic expressions, equations, and inequalities and to analyze behaviors of functions.

# Expressions and Operations

A.1         The student will represent verbal quantitative situations algebraically and evaluate these expressions for given replacement
values of the variables.

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# Equations and Inequalities

A.4         The student will solve multistep linear and quadratic equations in two variables, including

a)   solving literal equations (formulas) for a given variable;

b)   justifying steps used in simplifying expressions and solving equations, using field properties and axioms of equality that are valid
for the set of real numbers and its subsets;

c)   solving quadratic equations algebraically and graphically;

d)   solving multistep linear equations algebraically and graphically;

e)   solving systems of two linear equations in two variables algebraically and graphically; and

f)   solving real-world problems involving equations and systems of equations.

Graphing calculators will be used both as a primary tool in solving problems and to verify algebraic solutions.

Performance Assessments:

A.5         The student will solve multistep linear inequalities in two variables, including

a)   solving multistep linear inequalities algebraically and graphically;

b)   justifying steps used in solving inequalities, using axioms of inequality and properties of order that are valid
for the set of real numbers and its subsets;

c)   solving real-world problems involving inequalities; and

d)   solving systems of inequalities.

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A.6         The student will graph linear equations and linear inequalities in two variables, including

a)   determining the slope of a line when given an equation of the line, the graph of the line, or two points on the line. Slope will be
described as rate of change and will be positive, negative, zero, or undefined; and

b)   writing the equation of a line when given the graph of the line, two points on the line, or the slope and a point on the line.

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# Functions

A.7         The student will investigate and analyze function (linear and quadratic) families and their characteristics both
algebraically and graphically, including

a)   determining whether a relation is a function;

b)   domain and range;

c)   zeros of a function;

d)   x- and y-intercepts;

e)   finding the values of a function for elements in its domain; and

f)   making connections between and among multiple representations of functions including concrete, verbal, numeric, graphic,
and algebraic.

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# Statistics

A.9         The student, given a set of data, will interpret variation in real-world contexts and calculate and interpret mean
absolute deviation, standard deviation, and z-scores.

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A.10       The student will compare and contrast multiple univariate data sets, using box-and-whisker plots.

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A.11       The student will collect and analyze data, determine the equation of the curve of best fit in order to make predictions,
and solve real-world problems, using mathematical models. Mathematical models will include linear and quadratic
functions.

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Algebra II

These standards include a transformational approach to graphing functions. Transformational graphing uses translation, reflection,
dilation, and rotation to generate a “family of graphs” from a given graph and builds a strong connection between algebraic and
graphic representations of functions. Students will vary the coefficients and constants of an equation, observe the changes in
the graph of the equation, and make generalizations that can be applied to many graphs.

# Expressions and Operations

AII.2       The student will investigate and apply the properties of arithmetic and geometric sequences and series to solve real-world problems,
including writing the first n terms, finding the nth term, and evaluating summation formulas. Notation will include Σ and an.

Performance Assessments:

# Equations and Inequalities

AII.4       The student will solve, algebraically and graphically,

a)   absolute value equations and inequalities;

b)   quadratic equations over the set of complex numbers;

c)   equations containing rational algebraic expressions; and

Graphing calculators will be used for solving and for confirming the algebraic solutions.

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and graphically. Graphing calculators will be used as a tool to visualize graphs and predict the number of solutions.

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# Functions

AII.6       The student will recognize the general shape of function (absolute value, square root, cube root, rational, polynomial,
exponential, and logarithmic) families and will convert between graphic and symbolic forms of functions.
A transformational approach to graphing will be employed. Graphing calculators will be used as a tool to investigate
the shapes and behaviors of these functions.

Performance Assessments:

AII.7       The student will investigate and analyze functions algebraically and graphically. Key concepts include

a)   domain and range, including limited and discontinuous domains and ranges;

b)   zeros;

c)   x- and y-intercepts;

d)   intervals in which a function is increasing or decreasing;

e)   asymptotes;

f)   end behavior;

g)   inverse of a function; and

h)   composition of multiple functions.

Graphing calculators will be used as a tool to assist in investigation of functions.

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AII.8       The student will investigate and describe the relationships among solutions of an equation, zeros of a function, x-intercepts
of a graph, and factors of a polynomial expression.

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# Statistics

AII.9       The student will collect and analyze data, determine the equation of the curve of best fit, make predictions, and solve
real-world problems, using mathematical models. Mathematical models will include polynomial, exponential, and
logarithmic functions.

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AII.10      The student will identify, create, and solve real-world problems involving inverse variation, joint variation,
and a combination of direct and inverse variations.

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AII.11      The student will identify properties of a normal distribution and apply those properties to determine probabilities
associated with areas under the standard normal curve.

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Algebra, Functions, and Data Analysis

Through the investigation of mathematical models and interpretation/analysis of data from real life situations, students will
strengthen conceptual understandings in mathematics and further develop connections between algebra and statistics. Students
should use the language and symbols of mathematics in representations and communication throughout the course.

These standards include a transformational approach to graphing functions and writing equations when given the graph of the equation.
Transformational graphing builds a strong connection between algebraic and graphic representations of functions.

# Algebra and Functions

AFDA.1       The student will investigate and analyze function (linear, quadratic, exponential, and logarithmic) families
and their characteristics. Key concepts include

a)   continuity;

b)   local and absolute maxima and minima;

c)   domain and range;

d)   zeros;

e)   intercepts;

f)   intervals in which the function is increasing/decreasing;

g)   end behaviors; and

h)   asymptotes.

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AFDA.2       The student will use knowledge of transformations to write an equation given the graph of a function

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AFDA.3       The student will collect data and generate an equation for the curve (linear, quadratic, exponential, and logarithmic)
of best fit to model real-world problems or applications. Students will use the best fit equation to interpolate function
values, make decisions, and justify conclusions with algebraic and/or graphical models.

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AFDA.4       The student will transfer between and analyze multiple representations of functions, including algebraic formulas, graphs,
tables, and words. Students will select and use appropriate representations for analysis, interpretation, and prediction.

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AFDA.5       The student will determine optimal values in problem situations by identifying constraints and using linear
programming techniques.

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# Data Analysis

AFDA.6       The student will calculate probabilities. Key concepts include

a)   conditional probability;

b)   dependent and independent events;

d)   counting techniques (permutations and combinations); and

e)   Law of Large Numbers.

Performance Assessments:

AFDA.7       The student will analyze the normal distribution. Key concepts include

a)   characteristics of normally distributed data;

b)   percentiles;

c)   normalizing data, using z-scores; and

d)   area under the standard normal curve and probability.

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AFDA.8       The student will design and conduct an experiment/survey. Key concepts include

a)   sample size;

b)   sampling technique;

c)   controlling sources of bias and experimental error;

d)   data collection; and

e)   data analysis and reporting.

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Mathematical Analysis

Mathematical Analysis develops students’ understanding of algebraic and transcendental functions, parametric and polar equations,
sequences and series, and vectors.

MA.1         The student will investigate and identify the characteristics of polynomial and rational functions and use these to sketch
the graphs of the functions. This will include determining zeros, upper and lower bounds, y-intercepts, symmetry, asymptotes,
intervals for which the function is increasing or decreasing, and maximum or minimum points. Graphing utilities will be used
to investigate and verify these characteristics.

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MA.3         The student will investigate and describe the continuity of functions, using graphs and algebraic methods.

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MA.7         The student will find the limit of an algebraic function, if it exists, as the variable approaches either a finite number or infinity.
A graphing utility will be used to verify intuitive reasoning, algebraic methods, and numerical substitution.

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