Mathematics Curriculum Framework
November 2000

Learning Standards

Patterns, Relations, and Algebra
for Grades 11-12

cross symbolUnderstand patterns, relations, and functions
solid circle symbolRepresent and analyze mathematical situations and structures using algebraic symbols
solid triangle symbolUse mathematical models to represent and understand quantitative relationships
solid square symbolAnalyze change in various contexts

Learning Standards

Students engage in problem solving, communicating, reasoning, connecting, and representing as they:
12.P.1Describe, complete, extend, analyze, generalize, and create a wide variety of patterns, including iterative and recursive patterns such as Pascal's Triangle.
12.P.2Identify arithmetic and geometric sequences and finite arithmetic and geometric series. Use the properties of such sequences and series to solve problems, including finding the general term and sum recursively and explicitly.
12.P.3Demonstrate an understanding of the binomial theorem and use it in the solution of problems.
12.P.4Demonstrate an understanding of the trigonometric, exponential, and logarithmic functions.
12.P.5Perform operations on functions, including composition. Find inverses of functions.
12.P.6Given algebraic, numeric and/or graphical representations, recognize functions as polynomial, rational, logarithmic, exponential, or trigonometric.
12.P.7Find solutions to quadratic equations (with real coefficients and real or complex roots) and apply to the solu-tions of problems.
12.P.8Solve a variety of equations and inequalities using algebraic, graphical, and numerical methods, including the quadratic formula; use technology where appropriate. Include polynomial, exponential, logarithmic, and trigonometric functions; expressions involving absolute values; trigonometric relations; and simple rational expressions.
12.P.9Use matrices to solve systems of linear equations. Apply to the solution of everyday problems.
12.P.10Use symbolic, numeric, and graphical methods to solve systems of equations and/or inequalities involving algebraic, exponential, and logarithmic expressions. Also use technology where appropriate. Describe the relationships among the methods.
12.P.11Solve everyday problems that can be modeled using polynomial, rational, exponential, logarithmic, trigonometric, and step functions, absolute values, and square roots. Apply appropriate graphical, tabular, or symbolic methods to the solution. Include growth and decay; joint (e.g., I = Prt, y = k(w1 + w2)) and combined (F = G(m1m2)/d2) variation, and periodic processes.
12.P.12Relate the slope of a tangent line at a specific point on a curve to the instantaneous rate of change. Identify maximum and minimum values of functions in simple situations. Apply these concepts to the solution of problems.
12.P.13Describe 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, logarithmic, and trigonometric functions.

Exploratory Concepts and Skills
for Grades 11-12 and Single-Subject Courses

  • Prove theorems using mathematical induction.
  • Investigate parametrically defined curves and recursively defined functions, including applications to dynamic systems.

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