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# Mathematics Content Expectations

 Form A: Math Alignment Table Alignment to Math High School Content Expectations Math High School Content Expectations Prealgebra Math 050 to Summer 2006 Prealgebra Math 050 to Fall 2006 Introductory Algebra Math 107 Summer and Fall 2006 Math 112 ACCUPLACER Tests A1.1 Construction, Interpretation, and Manipulation of Expressions (linear, quadratic, polynomial, rational, power, exponential, logarithmic, and trigonometric)  ELAGLG.pro CLM.pro A1.1.1 Give a verbal description of an expression that is presented in symbolic form, write an algebraic expression from a verbal description, and evaluate expressions given values of the variables.    ARIT.pro ELAGLG.pro CLM.pro A1.1.2 Know the definitions and properties of exponents and roots, transition fluently between them, and apply them in algebraic expressions.    ARIT.pro ELAGLG.pro CLM.pro A1.1.3 Factor algebraic expressions using, for example, greatest common factor, grouping, and the special product identities (e.g., differences of squares and cubes). ELAGLG.pro CLM.pro A1.1.4 Add, subtract, multiply, and simplify polynomials and rational expressions (e.g., multiply (x – 1) (1 – x2 + 3); simplify 9x - x3x + 3)  ELAGLG.pro CLM.pro A1.1.5 Divide a polynomial by a monomial.  ELAGLG.pro CLM.pro A1.1.6 Transform exponential and logarithmic expressions into equivalent forms using the properties of exponents and logarithms including the inverse relationship between exponents and logarithms. A1.2 Solutions of Equations and Inequalities (linear, quadratic, polynomial, rational, power, exponential, logarithmic, and trigonometric) CLM.pro A1.2.1 Write equations and inequalities with one or two variables to represent mathematical or applied situations, and solve.   ELAGLG.pro CLM.pro A1.2.2 Associate a given equation with a function whose zeros are the solutions of the equation.  CLM.pro A1.2.3 Solve (and justify steps in the solutions) linear and quadratic equations and inequalities, including systems of up to three linear equations with three unknowns; apply the quadratic formula appropriately.  CLM.pro A1.2.4 Solve absolute value equations and inequalities, (e.g. solve l x - 3 l ≤ 6), and justify steps in the solution. CLM.pro A1.2.5 Solve polynomial equations and equations involving rational expressions (e.g. solve -2x(x2 + 4x+3) = 0; solve x - 1x + 6 = 3), and justify steps in the solution. CLM.pro A1.2.6 Solve power equations (e.g., (x + 1)3 = 8) and equations including radical expressions (e.g., 3x - 7 = 7), justify steps in the solution, and explain how extraneous solutions may arise. A1.2.7 Solve exponential and logarithmic equations (e.g., 3(2x ) = 24), 2 ln (x + 1) = 4), and justify steps in the solution. A1.2.8 Solve an equation involving several variables (with numerical or letter coefficients) for a designated variable, and justify steps in the solution.  ELAGLG.pro CLM.pro A1.2.9 Know common formulas (e.g., slope, distance between two points, quadratic formula, compound interest, distance = velocity • time), and apply appropriately in contextual situations. CLM.pro A1.2.10 Use special values of the inverse trigonometric functions to solve trigonometric equations over specific intervals (e.g., 2sin x – I = 0 for 0 ≤ x ≤ 2). STANDARD A2: FUNCTION Students understand functions, their representations, and their attributes. They perform transformations, combine and compose functions, and find inverses. Students classify functions and know the characteristics of each family. They work with functions with real coefficients fluently. (mainly linear) A2.1 Definitions, Representations, and Attributes of Functions A2.1.1 Recognize whether a relationship (given in contextual, symbolic, tabular, or graphical form) is a function; and identify its domain and range.  ELAGLG.pro CLM.pro A2.1.2 Read, interpret, and use function notation, and evaluate a function at a value in its domain.  ELAGLG.pro A2.1.3 Represent functions in symbols, graphs, tables, diagrams, or words, and translate among representations.  ELAGLG.pro A2.1.4 Recognize that functions may be defined by different expressions over different intervals of their domains; such functions are piecewise-defined (e.g., absolute value and greatest integer functions). A2.1.5 Recognize that functions may be defined recursively, and compute values of and graph simple recursively defined functions e.g., f (0) = 5, and f (n ) = f (n -1) + 2. CLM.pro A2.1.6 Identify the zeros of a function and the intervals where the values of a function are positive or negative, and describe the behavior of a function, as x approaches positive or negative infinity, given the symbolic and graphical representations. CLM.pro A2.1.7 Identify and interpret the key features of a function from its graph or its formula(s), (e.g. slope, intercept(s), asymptote(s), maximum and minimum value(s), symmetry, average rate of change over an interval, and periodicity). A2.2 Operations and Transformations A2.2.1 Combine functions by addition, subtraction, multiplication, and division. CLM.pro A2.2.2 Apply given transformations (e.g., vertical or horizontal shifts, stretching or shrinking, or reflections about the x - and y -axes) to basic functions, and represent symbolically. CLM.pro A2.2.3 Recognize whether a function (given in tabular or graphical form) has an inverse and recognize simple inverse pairs e.g., f (x ) = x3and g(x ) = x/3. 