Santa Barbara City College Course Outline

MATH 137C - Support for College Algebra

MATH 137C
Support for College Algebra
Disciplines
Mathematics (Masters Required)
2.000
0 - May not be repeated
A review of core prerequisite skills, competencies, and concepts for college algebra. Intended for students who are concurrently enrolled in Math 137 College Algebra at Santa Barbara City College. Review topics include skills developed in elementary algebra and intermediate algebra, with an emphasis on refining skills in algebraic manipulation and simplification of linear, quadratic, polynomial, radical, and rational expressions, functions and graphing.
32.000-36.000 Total Hours
Total Hours
64.000-72.000 Total Hours
32.000-36.000 Total Hours
Prerequisite: MATH 107 or equivalent based on SBCC's Assessment Center placement via multiple measures.
Prerequisite or Corequisite: None
Concurrent Corequisite: MATH 137
Course Advisories: None
Limitation on Enrollment: None
Course Objectives:
Develop study habits, such as the use of reading and metacognitive strategies to improve understanding and performance.
Demonstrate refined skills in algebraic manipulation and simplification of linear, quadratic, polynomial, radical, and rational expressions.
Solve linear, quadratic, and power equations, and linear inequalities.
Demonstrate familiarity with the general concepts of functions.
Factor polynomials using the basic factorization techniques.
Graph and use linear functions to analyze and model problems.
Simplify radical expressions and define nth root expressions as rational exponents.
Student Learning Outcomes
MATH137C SLO1 - Use a problem solving process to extract relevant information and execute relevant calculations/simplifications.
MATH137C SLO2 - Interpret results derived from algebraic calculations relevant to the solution of a problem.


The following topics should be covered with a focus on skills development and just-in-time remediation for college algebra and pre-calculus, and an emphasis on modeling and applications:

  1. Algebraic Expressions – simplify and evaluate
  2. Rational Exponents
  3. Polynomials – Monomial, Binomial, Trinomial

a.    Rigorous study of factoring including Substitution

b.    Solve Equations by factoring

c.    Quadratic Formula

d.    Graphing

  1. Rational Expressions and Equations

a.    Solve Equations

b.    Introduction to Graphing

  1. Inequalities – Linear, Absolute Value, Quadratic, Rational

a.    Solve

b.    Graphing

c.    Introduction to non-linear inequalities

  1. Radical Expressions and Equations – Square Root, Cube Root, nth root

a.    Rational Exponents

b.    Introduction to Complex Numbers

  1. Exponential and Logarithmic Equations

a.    Conversion between basic logarithmic and exponential equations

b.    Properties of logarithms

c.    Solving exponential and logarithmic equations

  1. Functions – Polynomial, Rational, Radical, Exponential, Logarithmic

a.    Function Notation

b.    Algebra of functions and composition of functions

c.    Domain and Range

d.    Graphing

e.    Inverse Functions

  1. Conic Sections – Parabolas and Circles
  2. Systems of Linear Equations
  3. Affective Domain experiences such as the use of reading and metacognitive strategies to improve understanding and performance.

     


    Methods of Instruction
    Directed Study
    Discussion
    Lecture
    Student activities, groupwork, and computer-facilitated instruction (optional).
     The accountant for College Sound Company has analyzed sales and discovered that if the selling price of one speaker is $225, then they will sell 260 units per month. However, if the selling price is $270 then they will sell 240 units per month. Assume that the equation relating the number of units sold, y and the price per unit, p, is linear. Find an equation for y in terms of  p.
    A. Writing Assignments: Students must work on assigned mathematical problems requiring the manipulation of abstract symbols. B. Appropriate Outside Assignments: Students will be expected to spend a sufficient amount of time outside of class to practice techniques taught during class time, read assigned materials, and complete homework assignments. C. Appropriate Assignments that Demonstrate Critical Thinking: Students must demonstrate mathematical skills such as equation solving and graphing which involve analyzing information, recognizing concepts in new contexts, and drawing analogies. Critical thinking will also be emphasized through numerous treatments of word problems.
    A grading system will be established by the instructor and implemented uniformly. Grades will be based on demonstrated proficiency in subject matter determined by multiple measurements for evaluation, one of which must be essay exams, skills demonstration or, where appropriate, the symbol system. 1)Independent exploration activities which measure students’ ability to analyze the connections between the numeric, algebraic, and verbal representations of various types of algebraic expressions, equations, graphs when applied to real-world problems and data analysis. 2)Quizzes and exams (including a comprehensive in-class final exam) which measure students’ ability to work independently using graphic, numeric, and algebraic techniques. 3)Homework in which students apply graphic, numeric and algebraic principles discussed in class to a series of practice problems to help them formulate questions and receive feedback from the instructor, tutors, or classmates. 4)(Optional) Computer laboratory assignments in which students apply algebraic principles and problem-solving techniques discussed in class to help students identify gaps in their skill attainment and concept mastery and to improve their symbolic manipulation abilities and problem-solving skills. Out-of-Class Assignments 1)Problem sets 2)Exploratory activities and/or projects 3)Reading and/or writing assignments
    • Projects/activities created by SBCC Math faculty.
    09/28/2018
    Board of Trustees: 12/13/2018
    CAC Approval: 11/19/2018