Santa Barbara City College Course Outline

MATH 107 - Intermediate Algebra

MATH 107
Intermediate Algebra
Disciplines
Mathematics (Masters Required)
5.000
0 - May not be repeated
Second course in algebra, including algebraic manipulation of polynomials, rational expressions, exponents, radicals, linear equations, ratio and proportion, inequalities, word problems, quadratic equations, systems of linear and quadratic equations. An introduction to functions and nonlinear equations. Exponential and logarithmic functions and their applications.
80.000-90.000 Total Hours
Total Hours
160.000-180.000 Total Hours
80.000-90.000 Total Hours
Prerequisite: MATH 095 or or equivalent based on SBCC's Assessment Center placement via multiple measures. MATH 007C or
Prerequisite or Corequisite: None
Concurrent Corequisite: None
Course Advisories: None
Limitation on Enrollment: None
Course Objectives:
Demonstrate refined skills in algebraic manipulation and equation solving through extensions of techniques taught in Elementary Algebra by solving equations and inequalities, solving systems of equations, and manipulating and simplifying algebraic expressions.
Apply the above skills while analyzing and finding solutions to word problems.
Demonstrate the ability to graph functions and relations involving two variables.
Demonstrate the ability to graph exponential and logarithmic functions and explain them in the context of the problem
Use and interpret standard mathematical terminology and notation, verbally and in writing.
Student Learning Outcomes
MATH107 SLO1 - Model and solve word problems involving linear, quadratic, exponential, and logarithmic functions.
MATH107 SLO2 - Broaden elementary algebra computational skills to include fractional exponents and the corresponding radical expressions, inverse variation, complex fractions.
MATH107 SLO3 - Graph and interpret the specific properties of linear, quadratic, exponential, logarithmic, or rational functions within the context of the problem.
MATH107 SLO4 - Solve equations with exponentials, logarithms, and square roots.
MATH107 SLO5 - Communicate mathematical information verbally, symbolically, visually, and/or numerically, using appropriate terminology related to intermediate algebra.

  1. Linear Equations and Inequalities

    1. Expressions vs. Equations/Inequalities

    2. Solving equations and inequalities (including literal equations)

    3. Graphing lines using slope-intercept form and general/standard form

    4. Finding equations of lines

    5. Modeling with linear equations and inequalities

  2. Systems of Linear Equations

    1. Solving 2x2 linear systems, algebraically and graphically

    2. Modeling with 2x2 linear systems

  3. Operations with polynomials

    1. Definition of polynomials and other terminology including coefficient, degree and term

    2. Addition, subtraction, and multiplication of polynomials

  4. Factoring

    1. Greatest Common Factor

    2. Trinomials

    3. Grouping

    4. Special cases

  5. Exponents

    1. Properties of Exponents

    2. Negative exponents

    3. Scientific Notation

  6. Functions and Their Graphs

    1. Definition and notation

    2. Domain and range

    3. Evaluation and graphing

    4. Brief introduction to inverse functions

      1. Inverse function notation

      2. Finding inverse given graphs and tables

      3. Finding inverse of linear functions algebraically

  7. Exponential and Logarithmic Functions

    1. Exponential functions of the form f(x)=abx–definitions and graphs

    2. Logarithmic functions of the form f(x)=logb(x)–definitions and graphs

    3. Base e and base 10 exponentials and logarithms

    4. Power and change-of-base properties of logarithms

    5. Solving exponential and logarithmic equations that do not require product or quotient properties of logarithms

    6. Modeling using exponential and logarithmic equations

  8. Quadratic Equations and Functions

    1. Solving quadratic equations by factoring, quadratic formula and the square root method

    2. Graphing parabolas in general/standard and vertex form

    3. Modeling using quadratic functions

  9. Rational Expressions and Equations

    1. Domain of rational functions

    2. Simplifying, multiplying, dividing, adding, and subtracting rational expressions

    3. Complex fractions

    4. Solving rational equations

    5. Using rational equations to solve word problems

  10. Radicals

    1. Simplifying radicals

    2. n-th roots as rational exponents

    3. Solving radical equations

    4. Solving power equations

  11. Optional

    1. Absolute Value equations and functions

Methods of Instruction
Directed Study
Discussion
Distance Education
Individualized Instruction
Lecture
Mediated Learning
Lecture is the primary activity to be used, along with student problem-solving. Students are expected to work outside of class on assigned exercises as well as on supplementary reading from the text.
Ms. Feldman invested $10,000 for 1 year, part at 7% and part at 6.25%.

If she earned a total interest of $656.50, how much was invested at each rate?

A. Appropriate Readings: Students are required to read assigned chapters in text. Outside readings are generally not required. B. Writing Assignments: Students must work on assigned mathematical problems requiring the manipulation of abstract symbols. C. 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 frequent homework assignments. D. 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 student's grade will be based on multiple measures of performance in the solving of algebra problems. Such measures will include at least three exams and a comprehensive final examination requiring demonstrations of problem-solving skills. In addition, instructors may make use of quizzes, written homework assignments, or other appropriate means to judge a student's dexterity with algebra skills and familiarity with mathematical vocabulary. Instructors are required to provide students, in writing, with a course syllabus, in accordance with district policy, which will include the specific procedures by which students will be evaluated. These procedures must be consistent with the objectives and course content stated above.
    Intermediate AlgebraMiller, ONeill, Hyde, McGraw Hill, 2017Intermediate Algebra: Concepts and GraphsMcKeague, xyz Textbooks, 2014
  • Graphing Calculator. TI-83 or TI-84 (preferred) or equivalent.
  • For online version: Reliable MAC or PC, reliable internet connection. Software: MyMathLab, Pearson Education, or similar product.
06/14/2018
Board of Trustees: 10/25/2018
CAC Approval: 10/01/2018