                        ALGEBRA, A SKILL-ORIENTED APPROACH


CATALOG


All exercises (except those in [intro]), can be adjusted by the user for levels
of difficulty.  Answers are provided in forms suitable to the classroom
situation, i.e., fractions only (where applicable) with positive, rationalized
denominators; no decimals.

[intro]   Introduction to algebra.  This program provides the following
          exercises:

          1.  Axioms and postulates.
          2.  The real number system.
          3.  Order of operations.
          4.  Algebraic expressions.     
          5.  A test covering all the areas outlined above. It is recommended
              this be an "open-book" test; i.e., student notebooks permitted.

[isn]     Signed number arithmetic, integers.  This program pro- vides the
          following exercises, (75 line-items, each).

          1.  Addition, subtraction and mixed, addition and subtraction.
          2.  Multiplication, division and mixed, multiplication and division.
          3.  Sequenced operations, 15 items each in addition, subtraction
              multiplication and division.  The last15 items are mixed addition
              and subtraction.
          4.  Random mix, all operations.

[eqs1]    Linear equations, one variable.  Exercises are provided in the five
          options indicated below:

          1.  Ax + B = C or C = Ax + B
          2.  Ax + B = Cx + D
          3.  A(Bx + C) = Dx + E or Dx + E = A(Bx + C)
          4.  A(Bx + C) + D = E + F(G + Hx)
          5.  A two-page test with 24 items, sequenced in the same order listed
              above, and graduated in levels of difficulty.

[xplot]   Linear equations in two variables, plotting.  These are simple
          exercises containing nine items each, comprising an introduction to
          linear equations in two variables.  All equations are in the
          slope-intercept form:

                y = mx + b

[lineqs]  Linear equations, two variables.  Options are as listed below:

          1.  Finding equations given the slopes or y-intercepts and one
              ordered pair of integers with--

                a.  Slopes or y-intercepts given directly.
                b.  Slopes or y-intercepts given indirectly.

          2.  Finding slopes or full equations given two ordered pairs of
              integers.
          3.  A two page test with all the options listed above.

[simeqs]  Simultaneous equations, two variables.  All equations are given in
          standard form, e.g., Ax + By = C.  *Options are as listed below:

           1.  Plotting two equations, finding "ntersection".
           2.  Finding intersections (solutions) by substitution.
           3.  Finding intersections by addition and subtraction.
           4.  Finding intersections by method of matrices.
           5.  Sequenced mix of all exercises listed above.
           6.  A two-page test with all the options listed above.

*One further option is offered that generates equations in two, three or four
variables.  Non-independent sets are sometimes generated.  The user must
command small "coefficients" to increase this possibility.  The program then
checks for linear dependence and identifies sets with non-independent
equations: no "solutions." Occasionally, these equations are used (at the
board) to illustrate the power of the "matrix" method.  Discretion is advised.


[trifact]  Quadratic equations, employing all variations except equations with             complex solutions.  Options follow:

           1.  Multiplying binomials and monomials.
           2.  Factoring trinomials and binomials, (all factorable over the
               set of integers).
           3.  Solving factorable quadratic equations.
           4.  A two-page test with all the options as listed above.

           All exercises are offered with the additional options of positive or
           mixed (positive and negative) quadratic terms, factorable
           constants, or non-standard equations (where applicable).


[f.eqs]  Fractional equations.  Five options offered as list below.  The last
         type results in quadratic equations.

                  Ax + B         Dx + E            C             F
             1.  --------   =   --------   or   --------   =  --------
                    C               F            Ax + B        Dx + E

                    A
             2.  --------   +   D   =   E
                  Bx + C

                    A
             3.  --------   +   Dx   =   E
                  Bx + C

                    A          C          E         A          C
             4.    ----   +   ----   =   ---   or  ----   +   ----   =   E
                    Bx         Dx         F         Bx         Dx

                     A
             5.   --------   +   D   =   Ex   +   F
                   Bx + C

             6.  A two-page test with all the options listed above.


[eqs1.d] Decimal equations.  In the options listed below, all capital letters
         are decimal constants.

             1.  Ax + B  =  C  or C  =  Ax + B
             2.  Ax + B  =  Cx +  D
             3.  A(Bx + C)  =  Dx + E  or Dx + E  =  A(Bx + C)
             4.  A two page test with all the options listed above.


                         End of "Standard" Course


It should be recalled that this course is not designed for "at or above"
grade-level students.  The remaining exercises can be extremely difficult (and
therefore discouraging).  This is particularly true of the "rationals."  They
should be used with discretion.


[rfex]  Rational fractions, exponentials.  In all exercises exponents may be
        chosen positive, negative or both.

           1.  Multiplication, division or mixed, multiplication and division.
           2.  Addition, subtraction or mixed, addition and subtraction.
           3.  Line multiply, including "powers to powers."
           4.  Simplify.
           5.  Mixed exercises, all types, one page.
           6.  A two page test with all the options listed above.

[rff]   Rational fractions, factorables.  Options follow:

           1.  Addition, subtraction or mixed, addition and subtraction.
           2.  Multiplication, division or mixed, multiplication and division.
           3.  Simplify.
           4.  Sequential mix, all types, one page.
           5.  A two page test with all the options listed above.

[quad]  Quadratic equations, standard forms, with real or comlex solutions,
        user's choice.  In the public schools, this subject area is often
        deferred to advanced algebra.

