Developmental

• Math 372
• Math 372L
• Math 376
• Math 376L
• Math 380
• Math 380L
• Math 101
• Math 120
• Math 120L

College Transfer

• Math 4
• Math 5
• Math 15
• Math 25
• Math 30
• Math 45
• Math 50A
• Math 50B
• Math 50C
• Math 52
• Math 55

Course Proposals (Drafts)

Course Outlines

• Course Outline Home Page

Math 30 --- College Algebra

Click here to download Curriculum Committee document

Catalog Description

A course covering first-degree and absolute value equations and inequalities;composite and inverse functions;polynomial, rational, exponential, and logarithmic functions; systems of equations and inequalities; matrices; sequences and series; mathematical induction; binomial expansion theorem; and complex numbers.

Special notes or advisories: Graphing calculator required, TI-83 or 84 recommended.

Prerequisites

Math 120 (or equivalent) with a grade of "C" or better or appropriate score on the math placement exam.

Describe representative skills without which the student would be highly unlikely to succeed: Ability to solve linear, quadratic, absolute value, polynomial,rational, radical, exponential and logarithmic equations analytically, graphically, numerically and verbally in real world settings. Ability to use technology in the study of these functions.

Recommended Preparation

Course Learning Outcomes

What should the student be able to do as a result of taking this course? State some of the objectives in terms of specific, measurable student accomplishments.

1. Accurately communicate mathematical ideas using correct mathematical notation, graphs, and vocabulary.
2. Demonstrate appropriate use of the graphing calculator to explore mathematical concepts and to verify their symbolic conclusions.
3. Solve problems and applications demonstrating the skills required for college-level math and science.
4. Demonstrate the characteristics of an effective learner, such as note-taking, critical reading, communication through writing, verbal discussions, etc.
5. Explain the concept of a function, identify the characteristics of different classes of functions, and use functions to solve the problems of mathematics.
6. Perform symbolic manipulations and use technology that will support success in the outcomes.

Course Content

• Themes: What themes, if any, are threaded throughout the learning experiences in this course?
  • Functions.
  • Critical thinking.
  • Problem solving.
  • Symbol manipulation.
  • Use of technology.
  • Graphing and Data Analysis.
  • Communication.
• Concepts: What concepts do students need to understand to demonstrate course outcomes?
  • A multiple-step problem solving process.
  • The presentation of mathematical solutions in a logical, coherent structure, including the use of writing skills, grammar, and punctuation.
  • The use of the graphing calculator as a problem solving tool.
  • The connection between graphs and properties of functions.
  • Apply concepts to real world problems.
  • Knowledge of functions to include definitions, graphs, properties, and their application to the problem solving process.
  • The recognition that proper symbolic manipulation is an important tool in multiple problem solving situations.
• Issues: What primary issues or problems, if any, must students understand to achieve course outcomes.
  • The role of the student in becoming a successful learner.
  • The importance of writing mathematics using correct notation and grammar.
  • The limitations of technology.
  • The connection between mathematics, science, and the "real world."
  • The necessity to read unfamiliar mathematics using their text and other resources.
• Skills: What skills must students master to demonstrate course outcomes?
  1. Use a calculator to: graph a function, find an appropriate viewing window, trace, find intersections, zeros, extrema, increasing/decreasing intervals, continuity and inverses; enter data and find appropriate mathematical models; approximate solutions to equations and inequalities; generate sequences and series, and their graphs; solve systems of equations.
  2. Be able to identify the properties of linear, quadratic, polynomial, rational, radical, exponential, logarithmic, absolute value functions, piece-wise functions, arithmetic sequences, geometric sequences, and series.
  3. Analysis of Graphs of Functions:
  4. • Determine intervals of continuity.
     • Identify intervals of domain for which a function is increasing/decreasing/constant.
     • Analyze functions for symmetry with respect to the y-axis and the origin.
     • Identify graphs of equations that have symmetry with respect to the x-axis.
     • Analytically determine whether a function is even, odd, or neither.
     • Identify the equation or graph of a function that has been translated by a vertical or horizontal shift.
     • Identify the equation or graph of a function that has been vertically stretched or compressed.
     • Identify equations or graphs of a function that has been reflected across an axis.
  5. Linear functions:
  6. • Identify slope from the graph and the formula.
     • Calculate slope from data and the formula.
     • Explain slope as a rate of change.
     • Understand intercepts and their importance.
     • Identify parallel and perpendicular lines and the relationship between the slopes.
     • Distinguish between the linear forms: slope-intercept, point-slope, standard.
     • Graph lines.
     • Find linear models using regression capabilities of the calculator.
     • Solve linear equations and inequalities.
  7. Systems of equations:
  8. • Solve a system of two linear equations in two unknowns using graphing, substitution, and elimination.
     • Solve a system of three first degree equations in three unknowns using the echelon method.
     • Solve a linear system using matrix row transformations, reduced row echelon, and the graphing calculator.
     • Solve non-linear systems.
     • Apply methods of solving systems to value, mixture, rate, etc.
  9. Absolute Value Functions:
  10. • Apply the properties of absolute value.
      • Solve equations and inequalities.
      • Apply absolute value to real world situations.
  11. Quadratic Functions:
  12. • Use the method of completing the square to find the vertex form.
      • Identify the vertex and the axis of symmetry symbolically and graphically.
      • Identify the domain and range.
      • Locate intercepts.
      • Identify intervals when function is increasing/decreasing/constant.
      • Find zeros symbolically through the zero product property or the quadratic formula.
      • Identify extreme points and extreme values.
      • Interpret the discriminant.
      • Solve quadratic inequalities using a sign graph.
      • Apply principles of quadratic functions to model real world situations.
      • Enter data and use calculator to perform quadratic regression.
  13. Polynomial Functions:
  14. • Identify symmetry of even and odd functions.
      • Determine the end behavior of odd and even functions.
      • Identify zeros.
      • Identify local and absolute extrema.
      • Determine intervals for which polynomial is increasing/decreasing/constant.
      • Solve polynomial equations.
      • Plot data and identify an appropriate model.
      • Use calculator to perform cubic and quartic regression.
      • Apply the intermediate value theorem.
      • Divide polynomials by long division.
      • Divide a polynomial by linear factor using synthetic division.
      • Identify factors of polynomials by application of the Remainder Theorem.
      • Apply Descartes' Rule of Signs.
      • Find complex zeros using Conjugate Zeros Theorem.
      • Apply the Fundamental Theorem of Algebra to determine factors of a polynomial.
      • Define a polynomial function satisfying given conditions.
      • Determine possible rational zeros by the Rational Zeros Theorem.
      • Determine the number of complex roots by the Complex nth Roots Theorem.
      • Use polynomial functions to describe real world applications.
  15. Rational Functions:
  16. • Simplify rational functions and identify vertical asymptotes, discontinuities, and zeros.
      • Identify horizontal and oblique asymptotes.
      • Graph using a calculator.
      • Understand the technological limits of the calculator.
      • Explore end behavior.
      • Identify domain and range.
      • Solve rational equations.
      • Analyze applications of rational functions.
      • Develop equations describing direct, inverse, or joint variation.
      • Identify the constant of variation.
  17. Power and root functions:
  18. • Identify domain and range.
      • Use a rational exponent for root functions.
      • Solve equations representing applications.
  19. Inverse Functions:
  20. • Identify one-to-one functions analytically.
      • Identify one-to-one functions using the horizontal line test.
      • Compare the graphs of a function and its inverse.
      • Find the inverse of a function.
      • Apply composition of functions to prove functions are inverses.
  21. Exponential Functions:
  22. • Identify the domain and range.
      • Compare graphs of exponential growth and decay.
      • Determine the value of e.
      • Locate intercepts and asymptotes.
      • Use translations to graph exponential functions.
      • Solve problems involving compound interest calculated n times per year.
      • Solve problems involving continuous compound interest.
  23. Logarithmic Functions:
  24. • Define the logarithmic function as the inverse of the exponential function.
      • Identify the domain and range.
      • Relate the domain and range of the exponential and logarithmic functions.
      • Find intercepts and asymptotes.
      • Compare common and natural logarithms.
      • Evaluate logarithms.
      • Evaluate logarithms using change of base rule.
      • Simplify logarithmic expressions using the properties of logarithms.
      • Solve exponential and logarithmic equations.
      • Solve logarithmic models of real life situations.
  25. Sequences and Series:
  26. • Identify domain.
      • Write statements about sequences and series using correct notation.
      • Determine whether a series is convergent or divergent.
      • Apply formulae for nth term and sum of first n terms of arithmetic and geometric sequences and series.
      • Simplify expressions using the properties and rules of summation.
      • Apply concepts to real world problems.
  27. The Binomial Theorem:
  28. • Expand a binomial using Pascal's Triangle.
      • Expand a binomial using the binomial theorem.
      • Find a specific term in the expansion of a binomial.

Represenative Learning Activities

What will the students be doing (i.e., Listening to lectures, participating in discussions and/or group activities, attending a field trip, etc.)? Relate the activities directly to the Course Learning Outcomes.

• Listening to lectures.
• Participating in group activities or assignments.
• Participating in in-class assignments or discussions.
• Completing daily homework assignments.
• Completing online activities on the computer.

Assessment Tasks

How will the student show evidence of achieving the Course Learning Outcomes? Indicate which assessments (if any) are required for all sections.

• Representative assessment tasks:
• • In-class exams.
  • Writing assignments to develop communication of mathematical concepts.
  • Quizzes.
  • Group projects or other in-class activities.
  • Portfolios.
  • Individual projects or presentations.
• Required assessments for all sections – to include but not limited to:
  • At lease two proctored, closed-book examinations, plus a comprehensive final examination.

Examples of Appropriate Texts or Other Readings

• Author: Hornsby, Lial, Rockwood; Title: A graphical Approach to College Algebra, Third Edition; Date 2003
• Author: Sullivan; Title: Algebra and Trigonometry, Seventh Edition; Date 2002