Course Outline for Mathematics 31S
College Algebra with Support

Effective: Fall 2019
SLO Rev: 09/08/2018
Catalog Description:

MTH 31S - College Algebra with Support

4.00 Units

Preparation for Calculus for Business and Social Science students. Functions and graphs: polynomials, rational functions, exponential and logarithmic functions, circles, parabolas, binomial theorem, sequences and series. Solving rational, radical, quadratic in form, exponential and logarithmic equations. This course is equivalent to MTH 31 with additional lab hours for students who did not place directly into MTH 31 or for students who place directly into MTH 31 but desire additional instruction.
Prerequisite: MTH 55 or MTH 55B or an appropriate placement through the Mathematics Placement process.
1701.00 - Mathematics, General
Letter Grade Only
Type Units Inside of Class Hours Outside of Class Hours Total Student Learning Hours
Lecture 3.00 54.00 108.00 162.00
Laboratory 1.00 54.00 0.00 54.00
Total 4.00 108.00 108.00 216.00
Measurable Objectives:
Upon completion of this course, the student should be able to:
  1. graph given algebraic functions and relations;
  2. sketch the graphs of circles and parabola;
  3. find the equation of circles and parabolas;
  4. sketch the graphs of logarithmic and exponential functions involving translations of basic graphs;
  5. solve exponential and logarithmic equations;
  6. apply the concepts of logarithmic and exponential functions to other fields;
  7. find specified terms and sums of arithmetic and geometric progressions;
  8. expand a power of a binomial and find a specified term in a binomial expansion:
  9. solve nonlinear inequalities.
Course Content:
  1. Review of simplifying and evaluating algebraic expressions
    1. Polynomial expression
    2. Rational expression
    3. Radical expression
    4. Exponential expression
    5. Logarithms expression
    6. Factoring techniques
  2. Review of functions and graphs
    1. Definition
    2. Operations
    3. Inverse functions
    4. Linear functions
    5. Quadratic functions
    6. Domain and range
  3. Graphing factorable polynomial functions of degree three or higher
    1. Intercepts 
    2. Signed charts
  4. Graphing rational functions
    1. Intercepts
    2. Sign charts
    3. Vertical and horizontal asymptotes
  5. Solving equations
    1. Review linear
    2. Review quadratic and quadratic in form
    3. Polynomial
    4. Rational 
    5. Radical
    6. Exponential and logarithmic
  6. Solving inequalities
    1. Review linear
    2. Polynomial
    3. Rational
    4. Absolute value
  7. Exponential and logarithmic functions
    1. Definition
    2. Graphing, including translations of basic graph
    3. Applications
  8. Circles and parabolas
    1. Find equations
    2. Graphing, including translations
  9. Sequences and series
    1. Summation notation (sigma)
    2. Arithmetic
    3. Geometric
  10. Binomial theorem
  11. Systems of equations
  12. Study Skills
    1. Grit and Growth Mindset
    2. How Learning Math is Different
    3. Resources On and Off Campus
    4. Time Management
    5. How to Be an Effective Listener and Take Notes
    6. How to Approach Homework
    7. How to Study for an Exam
    8. Overcoming Math and Test Anxiety
Methods of Instruction:
  1. Lecture/Discussion
  2. Group Activities
  3. Class and group discussions
  4. Review
Assignments and Methods of Evaluating Student Progress:
  1. Homework: In Section 3.7, read the definitions of rational function and asymptotes. Work out problems #1, 5, 9, 10, 11, 13, 15, 21, 23, and submit detailed graphs of #45, 65. The graphs should be on graph paper.
  2. Collaborative assignments: Using a small mirror and a yard stick, work with your group to find the height of a tree or a building.
  3. Homework: Read Section 8.1. Learn all the definitions. Work out problems #1 – 27 every other odd, 29 – 33 odds, 35 – 45 all, and 47 – 57 odds.
  1. Midterm Examination
  2. Final Examination
  3. Quizzes
  4. Homework
  5. Class Work
Upon the completion of this course, the student should be able to:
  1. Analyze mathematical problems critically using logical methodology.
  2. Communicate mathematical ideas, understand definitions, and interpret concepts.
  3. Increase confidence in understanding mathematical concepts, communicating ideas and thinking analytically.
Textbooks (Typical):
  1. OpenStax College Algebra (2018). College Algebra (Jul 31, 2018 ). OpenStax CNX.
  • Online homework system may be required.
Abbreviated Class Schedule Description:
Preparation for Calculus for Business and Social Science students. Functions and graphs: polynomials, rational functions, exponential and logarithmic functions, circles, parabolas, binomial theorem, sequences and series. Solving rational, radical, quadratic in form, exponential and logarithmic equations. This course is equivalent to MTH 31 with additional lab hours for students who did not place directly into MTH 31 or for students who place directly into MTH 31 but desire additional instruction.
Prerequisite: MTH 55 or MTH 55B or an appropriate placement through the Mathematics Placement process.
Discipline:
Mathematics*