Washington Math Standards - Algebra

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A1.1. Core Content: Solving Problems (Algebra)
A1.1.A Select and justify functions and equations to model and solve problems. (Algebraic Sentences 2 , Algebraic Sentences )
A1.1.B Solve problems that can be represented by linear functions, equations, and inequalities. (Train Problems , Mixture Word Problems , Work Word Problems )
A1.1.C Solve problems that can be represented by a system of two linear equations or inequalities. (Age Problems , Mixture Word Problems )
A1.1.D Solve problems that can be represented by quadratic functions and equations. (Integer Word Problems )
A1.1.E Solve problems that can be represented by exponential functions and equations. (Compound Interest , Continuous Compound Interest )

A1.2. Core Content: Numbers, expressions, and operations (Numbers, Operations, Algebra)
A1.2.A Know the relationship between real numbers and the number line, and compare and order real numbers with and without the number line.
A1.2.B Recognize the multiple uses of variables, determine all possible values of variables that satisfy prescribed conditions, and evaluate algebraic expressions that involve variables. (Single Variable Equations , Single Variable Equations 2 , Single Variable Equations 3 , Domain and Range , Variable Substitution , Absolute Value Equations , Simplifying Algebraic Expressions , Simplifying Algebraic Expressions 2 , System of Equations Substitution , System of Equations Addition , Foil Method , Binomial Fraction Simplification , Polynomial Fraction Simplification , Two Variable Equations , Variable Substitution 2 )
A1.2.C Interpret and use integer exponents and square and cube roots, and apply the laws and properties of exponents to simplify and evaluate exponential expressions. (Simplifying Algebraic Expressions 2 , Exponents Of Fractional Bases , Negative Exponents Of Fractional Bases , Multiplying and Dividing Exponent Expressions , Exponent Rules For Fractions , Roots Of Exponential Expressions , Simplifying Radical Expressions , Adding and Subtracting Radical Expressions , Multiplying and Dividing Radical Expressions )
A1.2.D Determine whether approximations or exact values of real numbers are appropriate, depending on the context, and justify the selection.
A1.2.E Use algebraic properties to factor and combine like terms in polynomials. (Trinomial Factoring , Binomial Fraction Simplification , Polynomial Fraction Simplification )
A1.2.F Add, subtract, multiply, and divide polynomials. (Simplifying Algebraic Expressions , Foil Method )

A1.3. Core Content: Characteristics and behaviors of functions (Algebra)
A1.3.A Determine whether a relationship is a function and identify the domain, range, roots, and independent and dependent variables. (Domain and Range , Independent and Dependent Variables )
A1.3.B Represent a function with a symbolic expression, as a graph, in a table, and using words, and make connections among these representations. (Graphs to Linear Equations , Graphs to Linear Equations 2 , Graphs to Linear Inequalities )
A1.3.C Evaluate f(x) at a (i.e., f(a)) and solve for x in the equation f(x) = b. (Linear Equations )

A1.4. Core Content: Linear functions, equations, and inequalities (Algebra)
A1.4.A Write and solve linear equations and inequalities in one variable. (Single Variable Equations , Single Variable Equations 2 , Single Variable Equations 3 , Single Variable Inequalities , Absolute Value Equations )
A1.4.B Write and graph an equation for a line given the slope and the yintercept, the slope and a point on the line, or two points on the line, and translate between forms of linear equations. (Applied Linear Equations 1 , Graphs to Linear Equations 2 )
A1.4.C Identify and interpret the slope and intercepts of a linear function, including equations for parallel and perpendicular lines. (Determining Slope , Applied Linear Equations 2 )
A1.4.D Write and solve systems of two linear equations and inequalities in two variables. (System of Equations Substitution , System of Equations Addition )
A1.4.E Describe how changes in the parameters of linear functions and functions containing an absolute value of a linear expression affect their graphs and the relationships they represent.

A1.5. Core Content: Quadratic functions and equations (Algebra)
A1.5.A Represent a quadratic function with a symbolic expression, as a graph, in a table, and with a description, and make connections among the representations. (Nonlinear Functions )
A1.5.B Sketch the graph of a quadratic function, describe the effects that changes in the parameters have on the graph, and interpret the xintercepts as solutions to a quadratic equation. (Quadratic X-Intercepts , Quadratic Zero Equations , Quadratic Formula )
A1.5.C Solve quadratic equations that can be factored as (ax + b)(cx + d) where a, b, c, and d are integers. (Quadratic Zero Equations )
A1.5.D Solve quadratic equations that have real roots by completing the square and by using the quadratic formula. (Quadratic Zero Equations , Quadratic Formula )

A1.6. Core Content: Data and distributions (Data/Statistics/Probability)
A1.6.A Use and evaluate the accuracy of summary statistics to describe and compare data sets.
A1.6.B Make valid inferences and draw conclusions based on data.
A1.6.C Describe how linear transformations affect the center and spread of univariate data.
A1.6.D Find the equation of a linear function that best fits bivariate data that are linearly related, interpret the slope and y-intercept of the line, and use the equation to make predictions.
A1.6.E Describe the correlation of data in scatterplots in terms of strong or weak and positive or negative.

A1.7. Additional Key Content (Algebra)
A1.7.A Sketch the graph for an exponential function of the form y = abⁿ where n is an integer, describe the effects that changes in the parameters a and b have on the graph, and answer questions that arise in situations modeled by exponential functions. (Nonlinear Functions )
A1.7.B Find and approximate solutions to exponential equations. (Compound Interest , Continuous Compound Interest )
A1.7.C Express arithmetic and geometric sequences in both explicit and recursive forms, translate between the two forms, explain how rate of change is represented in each form, and use the forms to find specific terms in the sequence.
A1.7.D Solve an equation involving several variables by expressing one variable in terms of the others. (Two Variable Equations )

A1.8. Core Processes: Reasoning, problem solving, and communication
A1.8.A Analyze a problem situation and represent it mathematically.
A1.8.B Select and apply strategies to solve problems.
A1.8.C Evaluate a solution for reasonableness, verify its accuracy, and interpret the solution in the context of the original problem.
A1.8.D Generalize a solution strategy for a single problem to a class of related problems, and apply a strategy for a class of related problems to solve specific problems.
A1.8.E Read and interpret diagrams, graphs, and text containing the symbols, language, and conventions of mathematics.
A1.8.F Summarize mathematical ideas with precision and efficiency for a given audience and purpose.
A1.8.G Synthesize information to draw conclusions, and evaluate the arguments and conclusions of others.
A1.8.H Use inductive reasoning about algebra and the properties of numbers to make conjectures, and use deductive reasoning to prove or disprove conjectures.

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