Course Outline for Mathematics 31
College Algebra

Effective: Fall 2020
SLO Rev: 12/06/2016
Catalog Description:

MTH 31 - College Algebra

3.00 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.
Prerequisite: MTH 55, MTH 55B or an appropriate placement through the Mathematics Placement/Assessment 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 0.00 18.00 0.00 18.00
Total 3.00 72.00 108.00 180.00
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 functions and graphs
    1. Definition
    2. Operations
    3. Inverse functions
    4. Linear functions
    5. Quadratic functions
  2. Graphing factorable polynomial functions of degree three or higher
    1. Intercepts 
    2. Signed charts
  3. Graphing rational functions
    1. Intercepts
    2. Sign charts
    3. Vertical and horizontal asymptotes
  4. Solving equations
    1. Review linear
    2. Review quadratic and quadratic in form
    3. Polynomial
    4. Rational 
    5. Radical
    6. Exponential and logarithmic
  5. Solving inequalities
    1. Review linear
    2. Polynomial
    3. Rational
    4. Absolute value
  6. Exponential and logarithmic functions
    1. Definition
    2. Graphing, including translations of basic graph
    3. Applications
  7. Circles and parabolas
    1. Find equations
    2. Graphing, including translations
  8. Sequences and series
    1. Summation notation (sigma)
    2. Arithmetic
    3. Geometric
  9. Binomial theorem
  10. Systems of equations
Methods of Instruction:
  1. Audio-visual materials
  2. Collaborative small groups
  3. Lecture/Discussion
  4. Distance Education
Assignments and Methods of Evaluating Student Progress:
  1. 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.
  2. Homework : Read the definitions of rational function, asymptotes. Work out problems 1, 5, 9, 10, 11, 13, 15, 21, 23: submit detailed graphs of # 45, 65. The graphs should be on graph paper.
  3. Collaborative Assignment: using a small mirror and a yard stick, work with your group to find the height of a tree or a building.
  1. Quizzes
  2. Home Work
  3. Midterm Examination
  4. Collaboratives
  5. Final Examination
Upon the completion of this course, the student should be able to:
  1. Critically analyze mathematical problems using a 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 (2019). College Algebra (Aug 8, 2019). OpenStax.
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.
Prerequisite: MTH 55, MTH 55B or an appropriate placement through the Mathematics Placement/Assessment process.
Discipline:
Mathematics*