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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
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

           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

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


          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

          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

          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)