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MATH 118  -- List of Topics [DRAFT  20-Feb-05]

Items not in existing Math 115 (or have been significantly expanded ) are in blue

I.  Introductory Review

A. Numbers -- natural, whole, integer, rational, irrational and real numbers

          1. Definitions

         2. Exact and approximate values [EXPAND]

B. Simplifying algebraic expressions -- order of operations [EXPAND]

C. Equivalent equations and inverse operations [NEW]

D. Cartesian coordinate system -- graphing points, knowing Quadrants

E. Reading graphs [NEW]

F Basic geometric relationships -- perimeter, area, and sum of angles

G. Modeling -- translating English phrases to math expressions and vice versa [NEW]

II.  Functions

          A. Function notation

1. Identify input variable, output variable and rule [NEW]

2. Differentiating f(x) and f(10)

3. Relation to ordered pairs

          B. Graphing linear functions

          C. Is a relation also a function -- vertical line test

          D. Is a function a one-to-one function -- horizontal line test (pre-view)

          E. Domain and range

          F. Algebra of functions -- sum, difference, product, quotient

          G. Composition of functions -- find and simplify algebraically

          H. Function inverse

1. Recognize graphical relationship -- points and curves (preview)

2. Recognize need for one-to-one function (preview)

3. Calculate inverse of a one-to-one linear function

III.  Graphing

          A. Graphing points and labeling with ordered pairs

          B. Graph a linear function

          C. Graph a linear equation using slope and intercept, both intercepts, or two points

          D. Identify and graph horizontal and vertical lines

          E. Recognize relationship of slope of parallel and perpendicular lines

          F. Reading and interpreting information from graphs [NEW]

          G. Interpreting slope of a graph (in context of units and causality) [NEW]

          H. Recognize "shape" of linear, absolute value, quadratic, cubic, and root functions

          I. Graph parabolas and relate vertex to maximum or minimum value

          J. Transformations of graphs -- parabolas

1. horizontal shifts

2. vertical shifts

3. reflections about x-axis

IV.  Graphing Calculator Skills

         A. Calculating values (using parentheses appropriately)

         B. Using table and graph to find values of functions

         C. Using table and graph to solve application problems

         D. Using intersection of graphs to solve equation in one variable

         E. Using intersection of graphs to solve system of two linear equations

         F. Finding maximum and minimum values

         G. Finding zeros (roots)

V.   Modeling

         A. Modeling with area -- How many cans of paint

         B. Modeling with perimeter -- stress "length is 3 less than width"

         C. Modeling with angle geometry -- interior angles, transverse, and supplementary

         D. Modeling with linear functions and equations

1. Translate two points to rule (use TWOPOINT program

2. Translate table to rule

3. Translate English to rule -- given slope and intercept
           a. Break-even
           b. Comparing cost function

4. Translate English to rule -- given two points

5. Interpret slope in context of problem -- units and causality of problem

          E. Modeling linear inequalities

          F. Modeling with systems of equations (two variable linear problems)

1. current/wind problems

2. mixing problems

3. value problems (sum of price times quantity for each type of item)

4. perimeter problem

          G. Modeling quadratic relationships (area and projectile)

          H. Modeling rational relationships

    1. "in the same time" [I wasn't sure what Barb meant by WORK]

    2. "working together"

           J. Modeling proportions [NEW]

           K. Modeling with roots

    1. Pythagorean theorem (triangles)

    2. Distance formula

VI.  Linear Equations and Formulas

           A. Solve linear equations algebraically

           B. Solve linear formulas for a given variable

           C. Solve linear equations graphically

           D. Find slope-intercept form of any linear equation -- discern slope and intercept

           E. Recognize standard form, slope-intercept form, and point-slope form (?)

           F. Recognize parallel or perpendicular equations

           G. Find equation of line parallel (or perpendicular) to given line through a point

           H. Find slopes and equations of described horizontal and vertical lines

VII.  Absolute Value Equations

           A. Solve absolute value equations algebraically

           B. (?) Check graphically (?) [Preview dont test?] {[NOT ON MATRIX]

VIII.  Systems of Equations

           A. Solve system by graphing (2 variable, 2 equation)

           B. Solve system by substitution (2 variable, 2 equation)

           C. Solve system by elimination (2 variable, 2 equation)

           D. Determine whether lines intersect are parallel or coincide

IX.   Inequalities -- linear inequalities in one variable

           A. solve algebraically

           B. graph solution on number line

           C. give solution in interval notation

X.   Exponents

           A. Definition/derivation of zero, negative and rational exponents

           B. Properties of exponents

           C. Evaluating expressions containing integer and rational exponents

           D. Simplifying expressions containing integer and rational exponents

           E. Scientific notation

    1. Converting to standard notation and vice versa

    2. Doing operations on numbers given in scientific notation (in word problems)

XI.  Polynomial Expressions and Equations

           A. Add, subtract, multiply polynomial expressions

           B. Divide quadratic by binomial algebraically and check using multiplication

           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 products -- perfect 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. Find intercepts of quadratic equation algebraically

            J. Extensions of solution methods (to solving equations that are quadratic in form using

            K. Recognize whether an equation is quadratic (or quadratic in form)

XII.  Roots and Radical Expressions and Equations

            A. Simplify radical expressions -- product and quotient properties

            B. Add, subtract, and multiply radical expressions

            C. Divide rational expressions (rationalize denominators with and without conjugate)

            D. Translate from radical to rational exponents

            E. Find domain of radical functions

            F. Simplify radical expressions and expressions with rational exponents

            G. Solve radical equations with one radical term algebraically and graphically

            H. Solve radical formulas for a designated variable

            I. Calculate using radical formulas

XIII.  Rational Expressions and Equations

            A. Simplify rational expressions (factor and reduce)

            B. Add, subtract and multiply rational expressions

            C. Divide rational expressions (simplify complex fractions)

            D. Solve equations containing rational expressions

            E. Solve a proportion mathematically (NEW)