Fundamental Mathematics IV
(Too many days.)
1. (4 days) Introduction to Polynomial Expressions and Functions
(a) Definition
(b) Evaluation
(c) Domain/range
(d) Addition and subtraction (Be sure to give examples having fractional
coeficients.)
(e) Multiplication
(f) (Long) Division (?)
2. (8 days) Factors, zeros, x-intercepts
(a) Why factor?
i. Analogs with integers
ii. Solving equations
iii. Connection between x-ints, factors, and solutions of equations (Have
students gure it
out.)
(b) How to factor
i. Greatest common factor
ii. Simple trinomials
A. Perfect squares
B. misc
iii. Special binomials
(c) Applications: Back to connection between x-ints, factors, and solutions of
equations
i. Problem-solving with quadratic equations
ii. Problem-solving with quadratic inequalities (Come at it from graphical point
of view.)
iii. Problem-solving with systems of equations (?)
3. (6 days) Introduction to Rational Expressions and Functions
(a) Definition
(b) Evaluation
(c) Domain/range
i. Zeros (and factors of numerator)
ii. Vertical asymptotes (and factors of denominator)
iii. Horizontal asymptotes
(d) Simplification
(e) Addition and subtraction
(f) Multiplication and division
4. (3 days) Problem Solving with Rational Equations
(a) Rates
(b) Proportions (?)
5. (1 day) Testing.