Revised
A. Review of Cartesian coordinate system
B.
Review of relations and functions:
1. Domain
2. Range
3. Even functions
4. Odd functions
5. Functions
increasing/decreasing over intervals
C. Review
of graphs of functions
1. Reflections
about x-axis
2. Vertical translations
3. Horizontal translations
D. Algebra of functions
1. Addition/subtraction
2. Multiplication/division
3. Composition
E.
One-to-one functions
F.
Inverse functions
1. Definition
2. Finding inverses
3. Graphing inverses
4. Inverse trigonometric
functions (Review)
II. POLYNOMIAL and RATIONAL FUNCTIONS
B.
Solution of quadratic equations
1. Review of factoring
2. Method of completing the
square
3. Review of the quadratic
formula
C. Solution of quadratic inequalities
D. Solution of polynomial inequalities in which the polynomials
are in factored form
1. Solutions expressed in set
notation
2. Solutions expressed in
interval notation
E. Solution
of polynomial equations of degree greater than 2
1. Synthetic division
2. Remainder theorem
3. Factor theorem
4. Rational zeros
5. Descartes’ rule of signs
G.
Rational Functions
1. Domains
2. Zeros (odd/even)
3. Y-intercepts
4. Removable singularities
5. Asymptotes
a. Vertical (odd/even)
b. Horizontal
c. Oblique
6.
Graphs
*7. Introduction to the concept
of limits
III. EXPONENTIAL AND LOGARITHMIC FUNCTIONS
A. Definition and sketch of exponential functions (including base
e)
B. Definition and sketch of logarithmic functions (including base
e)
C.
Review of conversions between logarithmic and exponential forms
D.
Review of basic properties of logarithms
E.
Logarithmic equations
IV. LINEAR ALGEBRA
A. Solutions to systems of equations (Review)
1.
Linear systems
a.
Elimination by addition
b.
Substitution
2.
Nonlinear systems: Substitution
B. Matrices
1. Row and column vectors
2. 2 x 2 and 3 x 3 matrices
3. Matrix operations
4. Matrix inverses
5. Use of inverse matrices to solve linear systems
C. Determinants
1.
2 x 2 determinants
a.
Evaluation
b.
Cramer’s Rule
2. 3
x 3 determinants
a. Evaluation
*i) By diagonals
ii) By
minors
b. Cramer’s Rule
*D. Vectors
1.
Scalar (dot) product
2.
Vector (cross) product
V. POLAR COORDINATES
A. Conversions
to/from rectangular coordinates
VI. COMPLEX NUMBERS
A. Square roots of negative numbers
B. Powers of i
C.
Rectangular form of a complex number
D.
Operations in rectangular form
1. Addition and subtraction
2. Multiplication
and division
a) Monomial
by monomial
b) Monomial
by binomial
c) Binomial
by binomial
d) Product
of a number and its conjugate
E.
The complex number plane and vector interpretation
F.
Trigonometric and polar forms of a complex number
1. Changing to and from rectangular form
2. Operations in trigonometric and polar forms
a) Multiplication
b) Division
G. DeMoivre’s
Theorem: finding complex roots
VII. ANALYTIC GEOMETRY
1. Center, radius
2. Graph
3. Determination of the equation from given information
B. Parabola: standard and
general equation
1.
Focus, vertex
2.
Graph
3.
Determination of the equation from given information
C Ellipse: standard and general equation
1.
Foci, vertices
2.
Graph
3.
Determination of the equation from given information
D. Hyperbola:
standard and general equation
1.
Foci, vertices, asymptotes
2.
Graph
3.
Determination of the equation from given information
*VIII. BINOMIAL
THEOREM
*Optional topics
Note: As time permits the use of graphing calculators should be demonstrated, but in no way
should it replace the teaching and testing of graphing by mathematical analysis.