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Arkansas: Algebra I Mathematics Standards Math Standards

58 standards · 6 domains

EXPONENTIAL FUNCTIONS & EQUATIONS

A1.EFE.1 Represent and solve real-world problems, using exponential equations in one variable.
A1.EFE.2 Represent real-world problems (growth, decay, and compound interest), using exponential equations.
A1.EFE.3 Construct exponential equations from geometric sequences with and without context.
A1.EFE.4 Determine the domain and range of exponential functions in mathematical problems.
A1.EFE.5 Determine reasonable domain and range values of exponential functions representing real-world situations, both continuous and discrete; interpret the solution as reasonable or unreasonable in context.
A1.EFE.6 Interpret the key features of an exponential function that models a relationship between two quantities in a given context.
A1.EFE.7 Flexibly use different representations of an exponential function, including graphs, tables, and equations.
A1.EFE.8 Interpret the quantities in an exponential equation in the context of a real-world problem, including growth, decay, and compound interest.
A1.EFE.9 Graph exponential functions that model real-world problems (growth, decay, and compound interest), showing key attributes.
A1.EFE.10 Write exponential functions that provide a reasonable fit to data and use them to make predictions with technology.

EXPRESSIONS

A1.EX.1 Add, subtract, and multiply polynomials; compare the system of polynomials to the system of integers when performing operations.
A1.EX.2 Simplify and perform operations with radical expressions without variables; rationalizing denominators should not include conjugates.
A1.EX.3 Simplify algebraic expressions using the laws of exponents.
A1.EX.4 Interpret the parts of expressions such as terms, factors, and coefficients in terms of a real-world context.

FUNCTIONS

A1.FN.1 Explain that a function assigns each element in the domain to exactly one element in the range.
A1.FN.2 Use function notation to represent functions, understanding that if 𝑓 is a function and 𝑥 is an element of its domain, then 𝑓(𝑥) represents the output of 𝑓 corresponding to the input 𝑥.
A1.FN.3 Graph functions given in function notation, understanding that the graph contains the points (𝑥,𝑓(𝑥)).
A1.FN.4 Evaluate functions expressed in function notation for one or more elements in their domains (inputs); use function notation to describe a contextual situation.
A1.FN.5 Differentiate between real-world scenarios that can be modeled by exponential or linear functions by determining whether the relationship has a common difference or a common ratio.
A1.FN.6 Compare the growth pattern of exponential to linear or quadratic functions using graphs and tables and recognize how exponential growth exceeds other functions.

LINEAR FUNCTIONS, EQUATIONS, & INEQUALITIES

A1.LFE.1 Represent and solve real-world problems, using linear expressions, equations, and inequalities in one variable.
A1.LFE.2 Construct linear functions from arithmetic sequences with and without context.
A1.LFE.3 Solve linear formulas for a specified variable.
A1.LFE.4 Solve linear equations, linear inequalities, and absolute value equations in one variable, including those with rational number coefficients, and variables on both sides of the equal or inequality sign; solve them fluently, explaining the process used.
A1.LFE.5 Determine the domain and range of linear functions in mathematical problems.
A1.LFE.6 Determine reasonable domain and range values of linear functions representing real-world situations, both continuous and discrete; interpret the solution as reasonable or unreasonable in context.
A1.LFE.7 Interpret the key features of a linear and absolute value functions that models a relationship between two quantities in a given context.
A1.LFE.8 Flexibly use different representations of a linear function, including graphs, tables, and equations.
A1.LFE.9 Calculate and interpret the rate of change of a linear function represented in a table, graph, or as an equation in context of real-world and mathematical problems.
A1.LFE.10 Translate among equivalent forms of equations for linear functions, including standard, point-slope, and slope-intercept forms; recognize that each form reveals key features in a given context.
A1.LFE.11 Solve systems of linear equations by substitution, elimination, and graphing with and without a real-world context; understand that the solutions will be the same regardless of the method for solving.
A1.LFE.12 Solve a system of equations consisting of a linear equation and a quadratic equation in two variables graphically with the assistance of technology.
A1.LFE.13 Explain why a solution to the equation 𝑓(𝑥)=𝑔(𝑥) is the x-coordinate where the y-coordinate of 𝑓(𝑥) and 𝑔(𝑥) are the same using graphs, tables, or approximations. Include cases where 𝑓(x) and/or 𝑔(𝑥) are linear, quadratic, absolute value, and exponential.
A1.LFE.14 Solve linear inequalities and systems of linear inequalities in two variables by graphing.
A1.LFE.15 Write linear equations that model the relationship between two quantities and produce a graph of the equation.
A1.LFE.16 Graph linear functions expressed as an equation and show intercepts of the graph without technology.
A1.LFE.17 Graph absolute value functions expressed as an equation with and without technology, showing intercepts and end behavior.
A1.LFE.18 Graph and generalize the effect of transformations on linear and absolute value functions. Transformations include: stretches, compressions, vertical, and horizontal
A1.LFE.19 Given the graph of a linear function, explain the effects of the transformation from the parent function, 𝑦=𝑥.
A1.LFE.20 Write linear functions that provide a reasonable fit to data and use them to make predictions, with and without technology; interpret the slope and y-intercept in context.
A1.LFE.21 Calculate, using technology, the correlation coefficient between two quantitative variables and interpret this quantity as a measure of the strength of the linear association.
A1.LFE.22 Compare and contrast correlation and causation in real-world problems.

QUADRATIC FUNCTIONS & EQUATIONS

A1.QFE.1 Represent and solve real-world problems using quadratic expressions and equations in one variable.
A1.QFE.2 Write quadratic equations with real number solutions that model the relationship between two quantities and produce a graph of the equation.
A1.QFE.3 Solve quadratic equations with real number solutions, containing one variable, including those with variables on both sides of the equal sign. Equations should be solved by:
A1.QFE.4 Determine the domain and range of quadratic functions in mathematical problems.
A1.QFE.5 Determine reasonable domain and range values of quadratic functions representing real-world situations, both continuous and discrete; interpret the solution as reasonable or unreasonable in context.
A1.QFE.6 Interpret the key features of a quadratic function that models a relationship between two quantities in a given context.
A1.QFE.7 Flexibly use different representations of a quadratic function, including graphs, tables, and equations.
A1.QFE.8 Explain how each form of a quadratic expression (standard, factored, and vertex form) identifies different key attributes, using the different forms to interpret quantities in context.
A1.QFE.9 Use factoring and completing the square to create equivalent forms of quadratic functions to reveal key attributes.
A1.QFE.10 Graph quadratic functions given as an equation or in function notation, labeling key attributes, without technology.
A1.QFE.11 Graph and describe the effect of transformations on quadratic functions. Transformations include: stretches, compressions, vertical, and horizontal
A1.QFE.12 Given the graph of a quadratic function, explain the effects of the transformation from the parent function, 𝑦=𝑥^2.
A1.QFE.13 Write quadratic functions that provide a reasonable fit to data and use them to make predictions with technology.

STATISTICS & PROBABILITY

A1.SP.1 Use box plots and histograms to determine the statistics appropriate to the shape of the data distribution; compare the center and spread of two or more data sets.
A1.SP.2 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points.
A1.SP.3 Summarize data from two categorical variables in a frequency table; interpret relative frequencies in the context of the data, recognizing data trends and associations.