Advanced Algebra: Concepts and Connections (Georgia's K-12 Mathematics Standards)

Mathematical Modeling (MM)

• AA.MM.1 Apply mathematics to real situations and build models of real-life phenomena.
  • AA.MM.1.1 Explain real problems by using a mathematical model.
  • AA.MM.1.2 Create models that explain situations in science, social science, the arts and humanities.
  • AA.MM.1.3 Use abstract and quantitative reasoning to make decisions in mathematical situations.
  • AA.MM.1.4 Use a range of representations and structures to solve real-life problems.

Data & Statistical Reasoning (DSR)

• AA.DSR.2 Gather, judge, analyze and interpret real data and communicate statistical findings.
  • AA.DSR.2.1 Tell surveys, experiments and observational studies apart, explain randomization, and primary vs secondary data.
  • AA.DSR.2.2 Consider ethics, privacy, bias and confounding variables in data collection and prepare large data sets.
  • AA.DSR.2.3 Tell population, sample and sampling distributions apart and use samples to estimate population values.
  • AA.DSR.2.4 Calculate and explain z-scores for relative standing and rescaling values.
  • AA.DSR.2.5 Estimate percentages in normal distributions with the Empirical Rule, z-scores or technology.
  • AA.DSR.2.6 Simulate samples to show how a statistic varies from one sample to another.
  • AA.DSR.2.7 Use margin of error to build and compare confidence intervals and judge how reliable they are.
  • AA.DSR.2.8 Evaluate reports for study design, analysis methods and the statistics used.

Functional & Graphical Reasoning (FGR)

• AA.FGR.3 Study exponential and logarithmic patterns and use them to model real situations.
  • AA.FGR.3.1 Find inverses of exponential and logarithmic functions, restricting domains where needed, and check them.
  • AA.FGR.3.2 Analyze, graph and compare exponential and logarithmic functions.
  • AA.FGR.3.3 Use the definition and properties of logarithms and their inverse link to exponents in context.
  • AA.FGR.3.4 Write exponential equations and solve them with logarithms in context.
  • AA.FGR.3.5 Write and interpret one-variable logarithmic equations to solve problems.
  • AA.FGR.3.6 Write and solve exponential equations numerically, algebraically and graphically.
  • AA.FGR.3.7 Write and solve logarithmic equations with two or more variables.
• AA.FGR.4 Study radical functions and use radical expressions to model real situations.
  • AA.FGR.4.1 Change radicals to rational exponents by extending the properties of integer exponents.
  • AA.FGR.4.2 Solve one-variable radical equations and explain how extraneous solutions arise.
  • AA.FGR.4.3 Analyze and graph radical functions.
  • AA.FGR.4.4 Write and solve radical equations with one unknown for real situations.
  • AA.FGR.4.5 Write and solve radical equations with several variables that describe relationships.
• AA.FGR.5 Extend solving quadratics to non-real numbers and model with polynomial functions.
  • AA.FGR.5.1 Graph and analyze quadratics in context, including regression on data sets.
  • AA.FGR.5.2 Define the imaginary unit i, the form of complex numbers and complex conjugates.
  • AA.FGR.5.3 Add, subtract and multiply complex numbers using algebraic properties.
  • AA.FGR.5.4 Factor quadratics by reading the structure of the expression.
  • AA.FGR.5.5 Write and solve quadratic equations and inequalities and explain solutions in context.
  • AA.FGR.5.6 Solve systems of a quadratic and a linear equation to find where they meet.
  • AA.FGR.5.7 Write and analyze quadratic models of relationships between quantities.
  • AA.FGR.5.8 Use a polynomial's degree and leading coefficient to find its number of zeros and end behavior.
  • AA.FGR.5.9 Find zeros of polynomials with technology or factored form, then graph and analyze key features.
  • AA.FGR.5.10 Factor polynomials, including sums and differences of cubes and higher-degree quadratic forms.
  • AA.FGR.5.11 Use all the zeros of a polynomial to write its factors and multiply them into standard form.
• AA.FGR.8 Analyze the behavior of rational functions to model problems.
  • AA.FGR.8.1 Rewrite simple rational expressions in equivalent forms.
  • AA.FGR.8.2 Add, subtract, multiply and divide rational expressions and simplify fully, including in context.
  • AA.FGR.8.3 Graph rational functions and find their key features.
  • AA.FGR.8.4 Solve simple one-variable rational equations and explain how extraneous solutions arise.

Patterning & Algebraic Reasoning (PAR)

• AA.PAR.6 Represent data with matrices, calculate with them and solve linear systems and programming problems.
  • AA.PAR.6.1 Use matrices to represent data and calculate, noting which real-number properties do not carry over.
  • AA.PAR.6.2 Rewrite systems of linear equations in matrix form.
  • AA.PAR.6.3 Solve systems of linear equations using inverse matrices.
  • AA.PAR.6.4 Model constraints with linear programming and decide whether points are feasible.

Geometric & Spatial Reasoning (GSR)

• AA.GSR.7 Build a first understanding of the unit circle and use it to solve trigonometric equations.
  • AA.GSR.7.1 Define the basic trigonometric ratios with x, y and r on a unit circle centered at the origin.
  • AA.GSR.7.2 Use unit circle angles and coordinates to solve real trigonometric problems.