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Algebra II
Page history last edited by Julie Dansby 1 yr ago
A2.1.A Evaluate algebraic expressions when variables are assigned specific values. (ASN.1.D)
Expressions include those involving polynomials, radicals, absolute values, and rational exponents.
A2.1.B Explain how whole, integer, rational, real, and complex numbers are related, and identify the number system(s) within which a given algebraic equation can be solved. (ASN.1.E)
A2.1.C Use algebra and the properties of number systems to develop valid mathematical arguments, make and prove conjectures, and find counterexamples to refute false statements. (ASN.1.F)
A2.1.D Interpret and use integer and rational exponents, and apply the laws and properties of exponents to translate among equivalent forms of numeric and algebraic expressions. (ASN.1.H)
A2.1.E Add, subtract, multiply, divide, and simplify polynomials and rational algebraic expressions, and explain the procedures used. (ASN.1.J)
A2.2.A Write exponential equations of the form k = abx, and approximate solutions to answer questions that arise in situations modeled by
exponential functions. (FCN.3.B)
A2.2.B Analyze and translate among various representations of an exponential function of the form f(x) = ab^x, and from each representation, determine f(0),
the asymptote, and whether it is an increasing or decreasing function. (FCN.3.D)
A2.2.C Express 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. (FCN.3.E)
A2.2.D Approximate the solution to an exponential equation. (ASN.2.F)
A2.3.A Write and solve quadratic equations and inequalities to answer questions that arise in situations modeled by quadratic functions. (FCN.4.A)
A2.3.B Solve quadratic equations over real or complex numbers. (ASN.2.E)
A2.3.C Solve algebraic equations that involve the square root of a linear expression over the real numbers; identify extraneous solutions and explain how they arose. (ASN.2.G)
A2.3.D Sketch the graphs of functions of the form f(x) = a sqrt(x-c) +d and cubic polynomial functions of the form f(x) = a^3 + d. (FCN.4.D)
A2.3.E Graph a function of the form f(x) = a/x + b and specify the asymptotes and end behaviorof the graph. (FCN.4.E)
A2.3.F Solve equations of the form f(x) / g(x) = k, where f(x) and g(x) are polynomials of degree no greater than two. (ASN.2.H)
A2.4.A Demonstrate that a bivariate data set can be modeled with an exponential or quadratic curve of best fit, approximate the curve of best fit, and use the curve to interpolate and extrapolate in order to make and defend predictions. (DSP.1.D)
A2.4.B Identify common examples of data that are and are not reasonably modeled with normal distributions, and justify reasoning. (DSP.1.G)
A2.4.C Make valid inferences and draw conclusions based on data; determine whether arguments based on data confuse association with causation. (DSP.1.I)
A2.4.D Evaluate the reasonableness of and make judgments about statistical claims, reports, studies, and conclusions. (DSP.1.J)
A2.4.E Describe the nature and purpose of sample surveys, statistical experiments, and observational studies, relating each to the types of research questions they are best suited to address. (DSP.2.A)
A2.4.F Distinguish between random sampling in surveys and random assignment of subjects to treatments in statistical experiments. (DSP.2.B)
A2.4.G Distinguish between populations and samples, explain the rationale for using random selection in research design, and describe and evaluate methods for selecting a simple random sample. (DSP.2.C)
A2.4.H Select and justify an appropriate data collection method (e.g., survey, statistical experiment, or observation) for a given research question, and, conversely, identify specific research questions that could be addressed by a given data collection method. (DSP.2.D)
A2.4.I Use reliable sample data or simulate the collection of data in order to make conjectures, draw conclusions, and answer a research question for a statistical study. (DSP.2.E)
A2.4.J Determine possible sources of bias in survey and research questions, describe how bias can impact the validity of the results of an experiment or study, and analyze data representations to determine how such representations can be misleading. (DSP.2.F)
A2.4.K Critique various methods of statistical experimental design, data collection, and data presentation used to investigate important problems, including those reported in public studies. (DSP.2.G)
A2.4.L Formulate a question that can be answered by analyzing data, identify relevant data sources, create an appropriate data display, select appropriate statistical techniques to answer the question, report results, and draw and defend conclusions. (DSP.2.H)
A2.5.A Translate among representations of functions described by symbolic expressions "y = " and (“f(x) = "), tables, graphs, and verbal descriptions. (FCN.1.B)
A2.5.B Evaluate f(x) at a (i.e., f(a)), solve for x in the equation f(x) - b, and distinguish between the two. (FCN.1.C)
A2.5.C Identify the domain and range of a function determined by a symbolic expression in the form y = f(x), and describe further restrictions
on the domain that are appropriate for a given context. (FCN.1.D)
A2.5.D Describe the graph of a function defined by a symbolic expression, and use key characteristics of the graph of a function to infer properties of the related symbolic expression. (FCN.1.E)
A2.5.E Solve an application problem by selecting an appropriate function to model the problem, justifying the selection, identifying appropriate units related to the situation, describing restrictions on the domain, identifying the range, solving the problem, and verifying the reasonableness of the solution. (FCN.1.F)
A2.5.F Describe relationships among the graphs of f(x) and the transformations f(x - h), f(x) + k, cf(x), or combinations of these. (FCN.1.G)
A2.6.A Analyze a problem situation, determine the question(s) to be answered, synthesize given information, determine how to represent the problem mathematically, and identify implicit and explicit assumptions that have been made. (PRC.1.A)
A2.6.B Solve problems by formulating one or more strategies, applying the strategies, and verifying the solutions. (PRC.1.B)
A2.6.C Evaluate a solution for reasonableness and interpret the meaning of the solution in the context of the original problem. (PRC.1.C)
A2.6.D Generalize a solution strategy for a single problem to a class of related problems. (PRC.1.D)
A2.6.E Read and interpret diagrams, graphs, and text containing the symbols, language, and conventions of mathematics. (PRC.1.E)
A2.6.F Summarize and communicate mathematical ideas and reasoning with precision and efficiency in ways appropriate for the intended audience and purpose.(PRC.1.F)
A2.6.G Synthesize mathematical information from multiple sources to draw a conclusion, evaluate the conclusions of others, analyze a mathematical argument, and recognize flaws or gaps in reasoning. (PRC.1.G)
A2.6.I Use inductive reasoning to make conjectures, use deductive reasoning to prove a valid conjecture, and develop a counterexample to refute an invalid conjecture. (PRC.1.H)
A2.6.J Explain and demonstrate the importance of generalizations in mathematics and the role of generalizations in inductive and deductive reasoning. (PRC.1.I)
Algebra II
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