| MATH 141 List of Topics
[DRAFT February 21, 2005]
Items that are not covered in
Math 118 (or are significantly expanded) are in blue.
I. Introductory Review
A. Properties of real numbers
B. Using calculator to simplify expressions and evaluate equations
C. Properties of functions and function notation
D. Graphing linear equations and functions
E. Find equation of linear function given two points
F. Interpreting the slope of a function or graph of a function
G. Modelingtranslating English phrases to math expressions
and vice versa
H. Solving linear equations and solving linear formulas for a specified
variable
I. Solving linear inequalities (in one variable) and functions algebraically
and graphically
J. Interval notation
II. Functions
A. Interpret functionsdistinguish input and output variables and the rule
B. Interpret
intercepts of a function or the graph of a function in context
C. Expand understanding of domain and range
D. Solve for input values given output values
E. Algebra of functionssum, difference, product, quotient
F. Composition of
functions
1. find and simplify algebraically and graphically
2. write formulas
by composing functions
G. Function
inverse
1. importance of one-to-one and graphical relationships
2. finding inverses of linear and cubic functions
3. derivation of exponential and log functions
4. finding inverse relations (sideways parabola) [YES OR NO?]
H. Find difference quotient for polynomial and rational functions
III. Graphing
A. Graph a linear function
B. Graph a linear equation using slope and intercept, both intercepts, or
two points
C. Read, interpolate and extrapolate graphical
data
D. Recognize relationship of slope of parallel and perpendicular lines
E. Interpreting slope and intercepts of a graph (in context of units and
causality)
F. Graph linear
inequalities in two variables and their intersection and union
G. Recognize "shape" of linear, absolute value, quadratic, cubic, root,
exponential, and
logarithmic functions and graphs
H. Graph functions
(see previous) that have been transformedshifted, stretched
(vertically), or reflected
I. Write the equation of a given functionfrom a description or a graph
J. Graph the inverse of a function
K. Graph polynomial functions and find domain, range, and local maximum or
minimum
values
L. Graph
piece-wise defined functions and write the piece-wise function of a given
graph
M. Graph rational functions with holes, and horizontal and vertical
asymptotes
N. Graph relations (circles and sideways parabola
IV. Graphing Calculator
Skills
A. Using graph to solve application problems
B. Using intersection of graphs to solve equation in one variable
polynomial, rational,
radical, exponential or logarithmic equations
C. Using intersection of graphs to solve system
of two linear equations
D. Finding maximum and minimum values
E. Finding zeros (roots) and y-intercept
F.
Doing matrix operations (algebra, row
operations, solving systems of linear equations)
G. Using quadratic formula and synthetic division programs to find
irrational roots of
polynomial functions
H. Data analysisgenerating scatter plots and regression equations and
graphs and
evaluating the appropriateness of the regression equationlinear, quadratic,
cubic,
power, and logarithmic regressions
I. Solve inequalities graphically polynomial, rational, and systems of
linear inequalities
V. Modeling (and solving)
A. Applications of linear functions and equations
B. Interpret slope and
intercepts in context of problemunits and causality of problem
C. Applications of
linear inequalities
D. Modeling with angle geometryinterior angles, transverse, and
supplementary
E. Systems of
linear equations (up to three variable linear equations)
F. Quadratic relationships (area and projectiles)
G. Finding maximum
and minimum with quadratic applications
H. Applications of rational relationships -- formulas and equating rates or
time
I. Applications
involving direct variation, joint variation and indirect variation
J. Systems of linear inequalities (finding feasible space)
K. Applications involving roots
1. Pythagorean theorem (triangles)
2. Distance formula
3. Solving formulas for a variable
L. Polynomial
functions and inequalities -- cost functions, etc.
M. Applications of exponential functions -- compound interest
N. Applications of logarithmic functions and formulas
VI. Linear Equations and
Formulas
A. Find slope-intercept form of any linear equationdiscern slope and
intercept
B. Recognize standard form, slope-intercept form, and
point-slope form (?)
C. Recognize parallel or perpendicular equations
D. Find equation of line parallel (or perpendicular) to given line through a
point
E. Find slopes and equations of described horizontal, vertical lines and
proportional lines
F. Use "increasing, decreasing and constant" to describe lines and determine
which is
steepest
VII. Linear Inequalities
A. Solve, graph and interpret linear inequalities in one variable
B. Solve, graph and interpret linear inequalities in two variable
C. Solve, graph
and interpret systems of linear inequalities in two variables -- both union
and intersection
D. Use "and," "or," "inclusive," and "exclusive" terminology appropriately
VIII. Absolute Value Equations
A. Solve equations with one absolute value algebraically and
graphically
B.
Solve absolute value inequalities
algebraically and graphically
IX. Systems of Equations
A. Solve two variable linear systems by graphing, substitution and
elimination
B. Determine whether lines intersect, are parallel, or coincide
C.
Solve three variable linear systems using
row operations and matrices
D. Identify inconsistent and dependent systems of equations
X. Exponents
A. Review definition of zero, negative and rational exponents
B. Evaluating expressions containing integer and rational exponents
C.
Simplifying expressions containing
integer and rational exponents
XI. Polynomial Expressions and Equations
A. Add, subtract, multiply polynomial expressions
B.
Use long division and synthetic division
to divide two polynomials
C. Factor Polynomial Expressions
1. Recognize and factor out greatest
common factor
2. Recognize and factor by grouping
3. Factor trinomials
4. Recognize and factor special productsperfect squares, difference
of squares,
and sum or difference of cubes
5. Extensions of Factoring (to non-polynomials expressions with
integer, rational, and
variable exponents)
D.
Recognize the connection between zeros of
a polynomial equation and the factors
E. Use zero factor property to solve simple cubic equations
F. Solve quadratic equations in one variable (real solutions only) ..
1. using zero factor property (by
factoring)
2. using square root property
3. by completing the square
4. using the quadratic formula
5. by graphing
G. Recognize relationship of discriminant to
# of real zeros and x-intercepts
H. Use formula -b/(2a) to find the vertex of a parabola
I.
Calculate difference quotient for polynomial
functions
J. Find intercepts of quadratic equation algebraically
K.
Extensions of solution methods (to solving
equations that are quadratic in form using
substitution)
L. Properties of 3rd degree and higher polynomial equations, functions and
expressions
1. relationship of factored equation, zeros,
multiplicity of zeros, and graph
2. relate domain and range, local extrema
and end behavior to degree of polynomial
3.
use sign chart to find solution set for
polynomial inequalities
XII. Roots and Radical Expressions and
Equations
A. Review simplifying radical expressions -- with and without rational
exponents
B. Review how to add, subtract, and multiply radical expressions
C. Review dividing rational expressions (rationalize denominators with
and without
conjugate)
D. Review translation from radical to rational exponents
E.
Find domain of radical functions --
including ones with polynomial as radicand
F. Solve radical equations with up to two radicals graphically and
algebraically
G. Re-write radical function to determine horizontal and/or vertical
shift, stretch, and
compression
H. Solve radical formulas for a designated variable
XII. Rational Expressions and Equations
A. Simplify rational expressions
B. Divide rational expressions (simplify complex fractions)
C.
Find domain and range of rational
functions
D. Find inverse of one-to-one rational functions
E. Re-write functions to determine any shift, stretch or compression
F. Use language of variation (direct, indirect, joint)
G. Find difference quotient with rational function
XIV. Exponential Expressions and Equations
A. Introduce exponential expressions, equations and functions
B. Evaluate exponential functions for given input
C. Solve exponential equations algebraically and graphically
D. Derive equation from a table of values
E. Identify the domain and range and restrictions on base
F. Find the inverse of an exponential function
G. Solve exponential equations that are quadratic in form (using
substitution)
XV. Logarithmic Expressions and Equations
A. Introduce logarithmic expressions, equations and functions
B. Switch between exponential and logarithmic forms of an equation
C. Use properties of logarithms
D. Identify the domain and range and restrictions on base
E. Find the inverse of a logarithmic function
F. Solve logarithmic equations algebraically
XVI.
Complex Numbers (we are still discussing whether the existence of
complex numbers should be introduced in this course)
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