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.
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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.
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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.