| ROCHESTER
COMMUNITY & TECHNICAL COLLEGE
COMMON COURSE OUTLINE: Math 1115 - College Algebra
A. Catalog Description
1. Math 1115
2. College Algebra
3. 3 credits
4. 3 hours per week or as scheduled
5. Offered Fall, Spring, and Summer
6. Prerequisites
a. Appropriate ASAP score or Successful completion of Intermediate Algebra
(B or better recommended) or equivalent.
b. Reading level: A Reading ASAP score of at least 27.
c. Writing level: A Writing ASAP score of at least 22
7. CT: Critical Thinking
MA: Mathematical/Logical Reasoning
8. The first college level algebra course. Topics include but are not
limited to: Polynomial, Rational, Radical, Exponential, and Logarithmic
Functions and their Inverses, Solving and Graphing Higher Order Equations
and Inequalities, Optimization Applications, Methods of Solving Systems
of Equations, and Conic Sections.
B. Effective Date: 3/99
C. Prerequisites
Equations: Linear, Quadratic (real and complex solutions), Rational,
and Radical
Linear and Non-linear Inequalities
Graphs of Linear Equations
Equations of Lines
Exponents- Integer and Rational
Operations on Algebraic Expressions: Polynomial, Rational, and Radical
Systems of Linear Equations in 2 variables
Basic Function Notation
Graphing Skills
Intermediate Level Applications
D. Major content Areas
Solving higher order equations and inequalities
Conic sections
Characteristics of Graphs (symmetry, translations, intercepts, Min-Max,
increasing, decreasing, turning points, asymptotes, and behavior
Techniques of Graphing
Optimization Applications
Functions-polynomial, rational, radical, exponential, logarithmic, and
their
inverses
Characteristics of Polynomial Functions
Methods of solving systems of equations
Algebra of Functions
Algebra of Complex Numbers
E. Minnesota Transfer Curriculum Competencies
1. Mathematical/Logical Reasoning
a. illustrate historical and contemporary applications of mathematical/logical
reasoning
b. clearly express mathematical/logical ideas in writing
c. explain what constitutes a valid mathematical/logical argument (proof)
d. recognize higher order problem-solving and/or modeling strategies
2. Critical Thinking
a. gather factual information and apply it to a given problem in a manner
that is relevant, clear, comprehensive, and conscious of possible bias
in the information selected
b. imagine and seek out a variety of possible goals, assumptions, interpretations,
or perspectives which can give alternative meanings or solutions to
given situations or problems
c. analyze the logical connections among the facts, goals, and implicit
assumptions relevant to a problem or claim; generate and evaluate implications
that follow from them
d. recognize and articulate the value assumptions which underlie and
affect decisions, interpretations, analyses, and evaluations made by
ourselves and others
3. Other Competencies
Mastery (these are skills that should appear and be tested on during
the semester and/or on the final exam)
Solving higher order equations and inequalities
The student is expected to be able to solve:
polynomials with rational roots (know techniques of division, long and
synthetic, the rational root theorem, DesCartes Rule of sign, upper/lower
bounds theorem, conjugate pair theorem, and factoring).
non-linear inequalities by the use of the boundary point (sign graph)
method
rational and fractional equations
radical (rational exponents) equations
exponential and logarithmic equations
Algebra of expressions the student is expected to be able to simplify
forms
including polynomial, rational and fractional (including complex fractions),
radical, complex, absolute value
Techniques of graphing the student is expected to know:
polynomials (intercepts, turnaround points)
rational functions (intercepts, vertical asymptotes, horizontal and
oblique asymptotes)
radical (rational exponents) functions (including partial parabolas
and partial circles)
absolute value functions
piecewise defined functions
exponential and logarithmic functions (general shapes)
conics
lines as a review only (includes all forms such as point-slope, slope-intercept,
and standard form as well as the formulas and use of slope, parallel
and perpendicular, midpoint of a line segment, and distance)
parabolas (vertex, focus, directrix, axis of symmetry, direction of
opening), min/max theory and optimization techniques
circles (center, radius)
ellipses (center, major/minor axes, foci)
hyperbolas (center, asymptotes, foci, vertices)
Translations, shifts, stretches, and compressions as applied to functions
Use of the graphics calculator is generally introduced and included.
Functions and Inverse functions
The student is expected to know functional notation, to understand the
difference between functions and relations and find the domain and range
of a function or relation, how to find inverse functions mathematically,
sketch inverses, and know relationships of domains and range for functions
and their inverses.
Methods of solving systems of equations (linear and non-linear)
Included for linear systems of either two or three linear equations
are techniques of substitution, elimination (or addition), and matrix
methods (Gauss-Jordan elimination). An introduced technique is the matrix
method of Cramers Rule and the method of determinants. Included for
non-linear systems are substitution and elimination.
Algebra of functions
The student is expected to know addition, subtraction, multiplication,
division, and composition of functions and their notation as well as
their sketches.
Algebra of complex numbers
The student should know complex numbers and be able to relate complex
numbers to the radicals with respect to addition, subtraction, multiplication,
and division and also how to solve equations involving complex solutions.
Proportionality the student is expected to know how to read, set up
and solve proportionality problems including direct, inverse, square,
and joint
4. Optional Topics
Introductory Probability Topics
Linear Programming
F. Methods used for Evaluation
1. Tests over covered Topics
and/or 2. Quizzes
and/or 3. Homework
and/or 4. Group Assignments
and/or 5. Comprehensive Final Exam
(The comprehensive final should include but not be limited to evaluating
the skills listed under Mastery in part E above)
G. A graphing calculator is required.
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