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National Standards for Grade 12 - Mathematics (page 4)

— National Assessment Governing Board
Updated on Mar 14, 2011

Algebra

In high school, students should become comfortable in manipulating and interpreting more complex expressions. The rules of algebra should come to be appreciated as a basis for reasoning. Non-linear functions, especially quadratic functions, and also power and exponential functions, are introduced to solve real-world problems. Students should become accomplished at translating verbal descriptions of problem situations into symbolic form. Expressions involving several variables, systems of linear equations, and the solutions to inequalities are encountered by grade 12.

GRADE 12

1) Patterns, relations, and functions

a) Recognize, describe, or extend arithmetic, geometric progressions, or patterns using words or symbols.

b) Express the function in general terms (either recursively or explicitly), given a table, verbal description, or some terms of a sequence.

c) Identify or analyze distinguishing properties of linear, quadratic, inverse (y = k/x) or exponential functions from tables, graphs, or equations."

d) Determine the domain and range of functions given various contexts.

e) Recognize and analyze the general forms of linear, quadratic, inverse, or exponential functions (e.g., in y = ax + b, recognize the roles of a and b).

f) Express linear and exponential functions in recursive and ex­plicit form given a table or verbal description.

2) Algebraic representations

a) Translate between different rep­resentations of algebraic expressions using symbols, graphs, tables, diagrams, or written ­descriptions.

b) Analyze or interpret relationships expressed in symbols, graphs, tables, diagrams, or written descriptions.

c) Graph or interpret points that are represented by one or more ordered pairs of numbers on a rectangular coordinate system.

d) Perform or interpret transformations on the graphs of linear and quadratic functions.

e) Use algebraic properties to develop a valid mathematical argument.

f) Use an algebraic model of a situation to make inferences or predictions.

g) Given a real-world situation, determine if a linear, quadratic, inverse, or exponential function fits the situation (e.g., half-life bacterial growth).

h) Solve problems involving exponential growth and decay.

3) Variables, expressions, and operations

a) Write algebraic expressions, equations, or inequalities to represent a situation.

b) Perform basic operations, using appropriate tools, on algebraic expressions (including grouping and order of multiple operations involving basic operations, ex­ponents, roots, simplifying, and ­expanding).

c) Write equivalent forms of algebraic expressions, equations, or inequalities to represent and explain mathematical relationships.

4) Equations and inequalities

a) Solve linear, rational, or quad­ratic equations or inequalities.

b) Analyze situations or solve problems using linear or quadratic equations or inequalities sym­bolically or graphically.

c) Recognize the relationship between the solution of a system of linear equations and its graph.

d) Solve problems involving more advanced formulas [e.g., the volumes and surface areas of three dimensional solids; or such formulas as: A = P(1 + r)t, A = Pert]."

e) Given a familiar formula, solve for one of the variables.

f) Solve or interpret systems of equations or inequalities.

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