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Mathematics Curriculum Framework - November 2000

Learning Standards for Algebra II

Note: The parentheses at the end of a learning standard contain the code number for the corresponding standard in the two-year grade spans.

Number Sense and Operations

• Understand numbers, ways of representing numbers, relationships among numbers, and number systems
• Understand meanings of operations and how they relate to one another
• Compute fluently and make reasonable estimates
 Students engage in problem solving, communicating, reasoning, connecting, and representing as they: AII.N.1 Define complex numbers (e.g., a + bi) and operations on them, in particular, addition, subtraction, multiplication, and division. Relate the system of complex numbers to the systems of real and rational numbers. (12.N.1) AII.N.2 Simplify numerical expressions with powers and roots, including fractional and negative exponents. (12.N.2)

Patterns, Relations, and Algebra

• Understand patterns, relations, and functions
• Represent and analyze mathematical situations and structures using algebraic symbols
• Use mathematical models to represent and understand quantitative relationships
• Analyze change in various contexts
 Students engage in problem solving, communicating, reasoning, connecting, and representing as they: AII.P.1 Describe, complete, extend, analyze, generalize, and create a wide variety of patterns, including iterative and recursive patterns such as Pascal's Triangle. (12.P.1) AII.P.2 Identify arithmetic and geometric sequences and finite arithmetic and geometric series. Use the properties of such sequences and series to solve problems, including finding the formula for the general term and the sum, recursively and explicitly. (12.P.2) AII.P.3 Demonstrate an understanding of the binomial theorem and use it in the solution of problems. (12.P.3) AII.P.4 Demonstrate an understanding of the exponential and logarithmic functions. AII.P.5 Perform operations on functions, including com-position. Find inverses of functions. (12.P.5) AII.P.6 Given algebraic, numeric and/or graphical representations, recognize functions as polynomial, rational, logarithmic, or exponential. (12.P.6) AII.P.7 Find solutions to quadratic equations (with real coefficients and real or complex roots) and apply to the solu-tions of problems. (12.P.7) AII.P.8 Solve a variety of equations and inequalities using algebraic, graphical, and numerical methods, including the quadratic formula; use technology where appropriate. Include polynomial, exponential, and logarithmic functions; expressions involving the absolute values; and simple rational expressions. (12.P.8) AII.P.9 Use matrices to solve systems of linear equations. Apply to the solution of everyday problems. (12.P.9) AII.P.10 Use symbolic, numeric, and graphical methods to solve systems of equations and/or inequalities involving algebraic, exponential, and logarithmic expressions. Also use technology where appropriate. De-scribe the relationships among the methods. (12.P.10) AII.P.11 Solve everyday problems that can be modeled using polynomial, rational, exponential, logarithmic, and step functions, absolute values and square roots. Apply appropriate graphical, tabular, or symbolic methods to the solution. Include growth and decay; logistic growth; joint (e.g., I = Prt, y = k(w1 + w2)), and combined (F = G(m1m2)/d2) variation. (12.P.11) AII.P.12 Identify maximum and minimum values of func-tions in simple situations. Apply to the solution of problems. (12.P.12) AII.P.13 Describe the translations and scale changes of a given function f(x) resulting from substitu-tions for the various parameters a, b, c, and d in y = af (b(x + c/b)) + d. In particular, describe the effect of such changes on polynomial, rational, exponential, and logarithmic functions. (12.P.13)

Geometry

• Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships
• Specify locations and describe spatial relationships using coordinate geometry and other representational systems
• Apply transformations and use symmetry to analyze mathematical situations
• Use visualization, spatial reasoning, and geometric modeling to solve problems
 Students engage in problem solving, communicating, reasoning, connecting, and representing as they: AII.G.1 Define the sine, cosine, and tangent of an acute angle. Apply to the solution of problems. (12.G.1) AII.G.2 Derive and apply basic trigono-metric identities (e.g., sin2θ + cos2θ = 1, tan2θ + 1 = sec2θ) and the laws of sines and cosines. (12.G.2) AII.G.3 Relate geometric and algebraic representations of lines, simple curves, and conic sections. (12.G.4)

Data Analysis, Statistics, and Probability

• Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them
• Select and use appropriate statistical methods to analyze data
• Develop and evaluate inferences and predictions that are based on data
• Understand and apply basic concepts of probability
 Students engage in problem solving, communicating, reasoning, connecting, and representing as they: AII.D.1 Select an appropriate graphical representation for a set of data and use appropriate statistics (e.g., quartile or percentile distribution) to communicate information about the data. (12.D.2) AII.D.2 Use combinatorics (e.g., "fundamental counting principle," permutations, and combinations) to solve problems, in particular, to compute probabilities of compound events. Use technology as appropriate. (12.D.6)

Learning Standards for Geometry

Learning Standards for Precalculus

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