FDLTCC Math

Placement Exams

     FDLTCC uses Accuplacer developed by The College Board.  A calculator is not
necessary nor permitted for these placement exams.  There are three math tests:

1. arithmetic
2. elementary algebra
3. college level mathematics

     Placement in college algebra is accomplished by a passing score of 85 or
greater on the Accuplacer elementary algebra test.

Accuplacer student guide
About Accuplacer

Recommended High School Curriculum

     Algebra 1, Algebra 2, and Geometry.

     Integrated math curriculums usually cover standard topics in algebra and
geometry, yet some supplements may be necessary.  
     Mathematical techniques and concepts from algebra and geometry remain essential 
for mathematics-intensive careers in natural sciences, engineering, business, medicine, 
and technology.  More broadly, almost all colleges require a non-remedial mathematics 
course for graduation, and most of these suitable math courses require the equivalent 
of high school algebra 1, algebra 2, and geometry.

Skills needed before College Algebra

1.  arithmetic and order of operations with rational and real numbers
2.  evaluating and simplifying algebraic expressions
3.  solving linear equations and inequalities
4.  solving absolute value equations and inequalities
5.  linear equations: graphs, slope, slope-intercept form, point-slope form
6.  polynomial arithmetic: addition, subtraction, multiplication, division
7.  factoring polynomials
8.  methods of solving 2x2 and 3x3 linear systems: substitution, elimination
9.  matrices and determinants: arithmetic including inverses (2x2)
10. rational expressions: simplify, arithemtic, rational equations
11. radicals: simplify, arithmetic, radical equations, complex numbers
12. quadratic equations and inequalties: factor, complete square, quadratic formula
13. exponents and logarithms: rules of exponents and logarithms
14. sequences and series: arithmetic, geometric, counting, binomial theorem

NOTE:
     These skills are necessary, but a course covering the skills alone would
be rather dry.  Few standard algebra textbooks omit interesting examples
when they are appropriate, and they should be used and obtained for spice as well
as general knowledge of mathematical applications, say, in physics.  
     Students should become good at translating word problems into equations and diagrams
in addition to the necessary techniques, and they should be able to answer the question in 
suitable words.  One helpful fact to emphasize is that every equation is a sentence in
the ordinary sense, i.e. subject-verb-object with "=" as the verb even if it is fussy to
demand periods after every such equation (sentence).
     On the other hand, it is difficult to find relevant and helpful "real world"
applications for every important skill at the time of instruction, e.g.
polynomial arithmetic, yet such skills remain essential for mathematics-intensive 
career training and work.
     For example, It is probably impossible to understand, much less design, the
core arithmetic components of a calculator or any other computing device without
strong skills in polynomial arithmetic.  (Decimal numbers are nothing else but polynomials.  
I.e. 2036 = 2x^3 + 0x^2 + 3x^1 + 6 when x = 10.)

Memorization and College-Prep Mathematics

     There is less to memorize in mathematics than most subjects, but some facts
and formulas (along with some techniques) are essential. 
1. Pythagorean theorem.  Knowledge of 1 simple proof (of many possible proofs)is also nice to know.
2. Slope of a line formula, e.g. change of y over change in x:  The cornerstone of rates as 
well as differential calculus.
3. Pt-slope formula.  Another cornerstone of differential calculus as well as myriad
practical topics using algebra.
4. Quadratic formula.  They should be able to complete the square and derive it, but this formula
is practical to have handy.
5. Basic triangle trigonometry definitions.  This is typically not covered in college algebra, but
it is good for students to see these early and more than once before calculus and practical career 
programs, say, in civil engineering technology or electrical technology.  Familiarity with triangle
trigonometry will make general trig functions easy later.
6. Basic geometry formulas.  E.g. the area of a circle, rectangle, and triangle.
7. Units and dimensional analysis.  E.g. metric system, definitions (1 in = 2.54 cm) and 
common conversions.

Artifact Skills which can easily be ommitted yet linger in textbooks
1. Descartes rule of signs.  Synthetic division is an easy topic so long as the focus is on
important results (remainder theorem, factor theorem,..) rather than computational speed.  Descartes
rule of signs shows up in discussion of the rational root theorem, interesting, but students
should not be spending much time actually applying the rational root theorem.
2. Factoring tronomials by trial and error or with great speed.  
Students should see and use methods which always work to factor trinomials over the integers, but 
they should not have to forever handle lots of tedious trinomials later, say, in working with rational
functions.
3. Computational speed with large matrices.  They should, however, know how to handle basic matrix
computation by hand so that they understand how one would handle large matrices of any size or
complexity.
4. log-trig tables.  Yuck!  Hard to believe these are still around since calculators became cheap,
but I've seen them hanging in there.  These obfuscate the subject these days.