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) |
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| 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. |
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| A1.1.2 Know the definitions and properties of exponents and roots, transition fluently between them, and apply them in algebraic expressions. |
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| 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). |
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| A1.1.4 Add, subtract, multiply, and simplify polynomials and rational expressions (e.g., multiply (x – 1) (1 – x2 + 3); simplify 9x - x3x + 3) |
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| A1.1.5 Divide a polynomial by a monomial. | |
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| 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. |
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| A1.2 Solutions of Equations and Inequalities (linear, quadratic, polynomial, rational, power, exponential, logarithmic, and trigonometric) |
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| A1.2.1 Write equations and inequalities with one
or two variables to represent mathematical or applied situations, and solve. |
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| A1.2.2 Associate a given equation with a function whose zeros are the solutions of the equation. |
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| 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. |
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| A1.2.4 Solve absolute value equations and inequalities, (e.g. solve l x - 3 l ≤ 6), and justify steps in the solution. |
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| 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. |
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| 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. |
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| A1.2.7 Solve exponential and logarithmic
equations (e.g., 3(2x ) = 24), 2 ln (x + 1) = 4), and justify steps in the solution. |
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| A1.2.8 Solve an equation involving several
variables (with numerical or letter coefficients) for a designated variable, and justify steps in the solution. |
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| 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. |
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| 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). |
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| 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. |
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| A2.1 Definitions, Representations, and
Attributes of Functions |
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| A2.1.1 Recognize whether a relationship (given in contextual, symbolic, tabular, or graphical form) is a function; and identify its domain and range. |
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| A2.1.2 Read, interpret, and use function
notation, and evaluate a function at a value in its domain. |
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| A2.1.3 Represent functions in symbols, graphs, tables, diagrams, or words, and translate among representations. |
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| 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). |
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| 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. |
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| 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. |
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| 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). |
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| A2.2 Operations and Transformations | |||||
| A2.2.1 Combine functions by addition,
subtraction, multiplication, and division. |
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| 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. |
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| 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. |
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