Course Outline for Mathematics 20
Pre-Calculus Mathematics

Effective: Fall 2022
SLO Rev: 10/26/2021
Catalog Description:

MTH 20 - Pre-Calculus Mathematics

5.00 Units

This course prepares students for enter the calculus sequence intended for majors in mathematics, engineering, and physical sciences. The course covers rational functions and relations with emphasis on logical development and graphing; solutions of polynomial equations and inequalities; the binomial theorem; strengthening of skills on exponential, logarithmic, and trigonometric functions, equations, and graphs; and applications.
Prerequisite: MTH 36 or MTH 36S MTH 37 or MTH 37S an appropriate skill level demonstrated through the Mathematics Assessment Process.
1701.00 - Mathematics, General
Letter Grade Only
Type Units Inside of Class Hours Outside of Class Hours Total Student Learning Hours
Lecture 5.00 90.00 180.00 270.00
Total 5.00 90.00 180.00 270.00
Measurable Objectives:
Upon completion of this course, the student should be able to:
  1. apply the methods of the Theory of Equations (Fundamental Theorem of Algebra and Rational Roots Theorem) to factor polynomials and to solve algebraic equations;
  2. solve equations involving logarithmic, exponentials and trigonometric functions;
  3. use sign graphs to solve polynomial and rational inequalities;
  4. solve inequalities and equations involving absolute values;
  5. create mathematical models using algebraic or transcendental functions;
  6. identify and use the trigonometric functions in problem solving;
  7. identify and use logarithmic and exponential functions in problem solving;
  8. rewrite expressions using trigonometric substitutions;
  9. develop and use exponential, logarithmic and trigonometric formulas;
  10. graph exponential and trigonometric functions and their inverses;
  11. graph algebraic functions and relations;
  12. prepare detailed graphs of conic sections;
  13. graph polar equations;
  14. graph using translations and reflections;
  15. use summation notation;
  16. use the Binomial Theorem to expand an expression;
  17. find the terms and partial sums of sequences, including arithmetic and geometric sequences;
  18. find the sum of the infinite geometric series;
  19. perform basic vector algebra in R^2 and R^3 and interpret the results geometrically.
Course Content:
  1. Functions, relations and their graphs
    1. Algebraic functions, including polynomial and rational
    2. Algebraic relations
    3. Conic Sections
    4. Transformation
      1. Translation
      2. Scaling
      3. Reflection
    5. Symmetry
    6. Algebra of functions
    7. Inverse functions
    8. Modeling and applications
  2. Inequalities
    1. Review linear
    2. Absolute value
    3. Non-linear
    4. Solutions
      1. By graphing
      2. By sign chart
    5. Graphs
  3. Sequences and Series
    1. Summation notation
    2. Summations algebra
    3. Arithmetic and geometric sequence
      1. Find the nth term
      2. Find the nth partial sum
    4. Arithmetic and geometric series
      1. Fint the sum of finite series
      2. Find the sum of infinite geometric series
  4. The Binomial Theorem
  5. Roots of polynomial equations
    1. Division of polynomials
    2. Fundamental theorem of algebra
    3. Remainder theorem
    4. Rational roots theorem
    5. Complex roots
  6. Exponents and logarithms
    1. Exponential and logarithmic functions and graphs
    2. Properties of exponents and logarithms
    3. Solving equations
    4. Modeling and applications
  7. Trigonometry
    1. Trigonometric functions and graphs
    2. Inverse trigonometric functions and their graphs
    3. Trigonometric formulas and identities
    4. Rewrite algebraic expression using trigonometric substitution
    5. Solving equations
    6. Modeling and applications
  8. Polar coordinates
    1. Convert equation between polar and rectangular form
    2. Graph polar equations
  9. Introduction to vectors in two and three dimensions
    1. Algebraic operation on vectors
    2. Geometric interpretation of algebric operations
Methods of Instruction:
  1. Lecture/Discussion
  2. Distance Education
  3. Group Activities
  4. Problem Solving
  5. Textbook reading assignments
Assignments and Methods of Evaluating Student Progress:
  1. Convert the rectangular equation 2x+3y=1 to polar form.
  2. The population of a certain city was 112,000 in 1994, and the observed relative growth rate is 4% per year. a) Find a function that models the population after t years. b) Find the projected population in the year 2000. c) In what year will the population reach 200,000?
  3. Solve sin 2x = cos x over the interval [2, 2pi).
  1. Exams/Tests
  2. Homework
  3. Quizzes
  4. 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. Zill, D., J. Dewar (2017). Precalculus with Calculus Previews (6th). Jones and Bartlett Learning.
  • Either scientific or graphing calculator
Abbreviated Class Schedule Description:
Rational functions and relations with emphasis on logical development and graphing. Solutions of polynomial equations and inequalities, the binomial theorem, strengthening of skills on exponential, logarithmic, and trigonometric functions, equations, graphs, and applications.
Prerequisite: MTH 36 or MTH 36S MTH 37 or MTH 37S an appropriate skill level demonstrated through the Mathematics Assessment Process.
Discipline:
Mathematics*