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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
A2.3 Families of Functions (linear, quadratic,
polynomial, rational, power, exponential,
logarithmic, and trigonometric)
         
A2.3.1 Identify a function as a member of a family of
functions based on its symbolic, or graphical
representation; recognize that different families of
functions have different asymptotic behavior at
infinity, and describe these behaviors.
         
A2.3.2 Describe the tabular pattern associated with
functions having constant rate of change (linear); or
variable rates of change.
         
A2.3.3 Write the general symbolic forms that
characterize each family of functions. e.g., f (x ) =
A0ax ; f (x ) = AsinBx.
         
A2.4 Lines and Linear Functions          
A2.4.1 Write the symbolic forms of linear functions
(standard [i.e., Ax + By = C, where B ≠ 0 ], pointslope,
and slope-intercept) given appropriate
information, and convert between forms.
         
A2.4.2 Graph lines (including those of the form x =
h and y = k ) given appropriate information.
        CLM.pro
A2.4.3 Relate the coefficients in a linear function to
the slope and x - and y -intercepts of its graph.
        CLM.pro
A2.4.4 Find an equation of the line parallel or
perpendicular to given line, through a given point;
understand and use the facts that non-vertical
parallel lines have equal slopes, and that non-vertical
perpendicular lines have slopes that multiply to give -
1.
        CLM.pro
A2.5 Exponential and Logarithmic Functions          
A2.5.1 Write the symbolic form and sketch the graph
of an exponential function given appropriate
information. (e.g., given an initial value of 4 and a
rate
of growth of 1.5, write f (x ) = 4 (1.5)x ).
        CLM.pro
A2.5.2 Interpret the symbolic forms and recognize
the graphs of exponential and logarithmic functions
(e.g., f (x ) = 10 x , f (x ) = log x , f (x ) = ex , f (x ) = ln
x ); recognize the logarithmic function as the inverse
of the exponential function.
         
A2.5.3 Apply properties of exponential and
logarithmic functions (e.g., ax+y = axa y ; log(ab )=
log a + log b ).
         
A2.5.4 Understand and use the fact that the base of
an exponential function determines whether the
function increases or decreases and understand how
the base affects the rate of growth or decay.
         
A2.5.5 Relate exponential and logarithmic functions
to real phenomena, including half-life and doubling
time.
         
A2.6 Quadratic Functions          
A2.6.1 Write the symbolic form and sketch the graph
of a quadratic function given appropriate information
(e.g., vertex, intercepts, etc.).
   
from equation
   
A2.6.2 Identify the elements of a parabola (vertex,
axis of symmetry, direction of opening) given its
symbolic form or its graph, and relate these elements
to the coefficient(s) of the symbolic form of the
function.
        CLM.pro
A2.6.3 Convert quadratic functions from standard to
vertex form by completing the square .
         
A2.6.4 Relate the number of real solutions of a
quadratic
equation to the graph of the associated
quadratic function.
         
A2.6.5 Express quadratic functions in vertex form to
identify their maxima or minima, and in factored form
to identify their zeros.
         
A2.6.5 Express quadratic functions in vertex form to
identify their maxima or minima, and in factored form
to identify their zeros.
         
A2.7 Power Functions (including roots, cubics,
quartics, etc.)
         
A2.7.1 Write the symbolic form and sketch the graph
of power functions.
        CLM.pro
A2.7.2 Express direct and inverse relationships as
functions (e.g., y = kxn and y = kx-n , n > 0) and
recognize their characteristics (e.g., in y = x3 , note
that doubling x results in multiplying y by a factor of
8).
        CLM.pro
A2.7.3 Analyze the graphs of power functions,
noting reflectional or rotational symmetry.
         
A2.8 Polynomial Functions          
A2.8.1 Write the symbolic form and sketch the graph
of simple polynomial functions.
         
A2.8.2 Understand the effects of degree, leading
coefficient, and number of real zeros on the graphs
of polynomial functions of degree greater than 2.
         
A2.8.3 Determine the maximum possible number of
zeros of a polynomial function, and understand the
relationship between the x -intercepts of the graph
and the factored form of the function.
         
A2.9 Rational Functions          
A2.9.1 Write the symbolic form and sketch the graph
of simple rational functions.
         
A2.9.2 Analyze graphs of simple rational functions
(e.g., ) and understand the relationship between the
zeros of the numerator and denominator and the
function’s intercepts, asymptotes, and domain.
         
A2.10 Trigonometric Functions          
A2.10.1 Use the unit circle to define sine and cosine;
approximate values of sine and cosine (e.g., sin 3 ,
or cos 0.5 ); use sine and cosine to define the
remaining trigonometric functions; explain why the
trigonometric functions are periodic.
        CLM.pro
A2.10.2 Use the relationship between degree and
radian measures to solve problems.
        CLM.pro
A2.10.3 Use the unit circle to determine the exact
values of sine and cosine, for integer multiples of ⁄6
and ⁄4.
         
A2.10.4 Graph the sine and cosine functions;
analyze graphs by noting domain, range, period,
amplitude, and location of maxima and minima.
         
A2.10.5 Graph transformations of basic
trigonometric functions (involving changes in period,
amplitude, and midline) and understand the
relationship between constants in the formula and
the transformed
graph.
         
STANDARD A3: MATHEMATICAL MODELING
Students construct or select a function to model a
real-world situation in order to solve applied
problems. They draw on their knowledge of families
of functions to do so.
     
A3.1 Models of Real-world Situations Using
Families of Functions.

Example: An initial population of 300 people grows at
2% per year. What will the population be in 10 years?
        ARIT.pro
A3.1.1 Identify the family of function best suited for
modeling a given real-world situation (e.g., quadratic
functions for motion of an object under the force of
gravity; exponential functions for compound interest;
trigonometric functions for periodic phenomena. In
the example above, recognize that the appropriate
general function is exponential (P = P0at )
         
A3.1.2 Adapt the general symbolic form of a function
to one that fits the specifications of a given situation
by using the information to replace arbitrary
constants with numbers. In the example above,
substitute the given values P0 = 300 and a = 1.02 to
obtain P = 300(1.02)t .
         
A3.1.3 Using the adapted general symbolic form,
draw reasonable conclusions about the situation
being modeled. In the example above, the exact
solution is 365.698, but for this problem an
appropriate approximation is 365.
         
        CLM.pro

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