Santa Barbara City College Course Outline

MATH 150C - Support Course for Calculus with Analytic Geometry I

MATH 150C
Support Course for Calculus with Analytic Geometry I
Disciplines
Mathematics (Masters Required)
2.000
0 - May not be repeated
A review of core prerequisite skills, competencies and advanced algebra concepts for calculus. Intended for students who are concurrently enrolled in Math 150 Calculus with Analytic Geometry I at Santa Barbara City College. Review topics include skills developed in college algebra and precalculus, with an emphasis on refining skills in algebraic manipulation, functions, trigonometry and geometry.
32.000-36.000 Total Hours
Total Hours
64.000-72.000 Total Hours
32.000-36.000 Total Hours
Prerequisite: MATH 138 or equivalent based on SBCC's Assessment Center placement via multiple measures
Prerequisite or Corequisite: None
Concurrent Corequisite: MATH 150
Course Advisories: None
Limitation on Enrollment: None
Course Objectives:
Use specific study habits, such as the use of reading and metacognitive strategies, to improve understanding and performance.
Apply geometric concepts to solve problems involving triangles, cylinders, and rectangular prisms.
Use refined skills in algebraic manipulation and simplification of polynomial, radical, and rational expressions.
Solve linear, quadratic, exponential, logarithmic, radical, and rational equations, as well as linear and non-linear systems.
Analyze and apply the general concepts of functions, the algebra of functions, composition, and inverse functions.
Identify properties of polynomial, power, rational, exponential and logarithmic functions and their graphs.
Use trigonometric functions appropriate for the study of calculus and for applications to the physical sciences.
Student Learning Outcomes
MATH150C SLO1 - Use a problem solving process to extract relevant information and execute relevant geometric, advanced algebraic, and trigonometric calculations/simplifications.
MATH150C SLO2 - Interpret results derived from geometric, advanced algebraic, and trigonometric calculations relevant to the solution of a problem.

  1. Functions and graphing

    1. Graphs, functions and relations

    2. Notation

    3. Translations and reflections

    4. Symmetry/Even and odd functions, algebraically and graphically

    5. Expansions and contractions

    6. Algebra of functions, function composition

    7. Inverse functions

    8. Piecewise-defined functions

    9. Graphs of rational functions

    10. Exponential functions and their graphs

    11. Logarithmic functions and their graphs

    12. Calculator usage with respect to graphs

2.  Trigonometry

a.Graphs of trig functions

b.Inverse trig functions and their graphs.

C. Review of unit circle

d .Trigonometric identities

e. Law of sines and law of cosines.

3. Algebra

    1. Finding equations of lines

    2. Review slope as rate of change

    3. Review of factoring polynomials

    4. Simplifying expressions (difference quotients, other rational expressions)

    5. Solving equations (linear, polynomial, rational, exponential, logarithmic, radical, trigonometric)

    6. Solving inequalities (linear, polynomial, rational, exponential)

    7. Properties of logarithms and exponents

    8. Review of modeling with distance = rate x time

4. Geometry

  1. Writing algebraic expressions for areas and volumes of common geometric shapes

  2. Writing algebraic expressions using similar triangles and right triangle trigonometry

5. Sequences and Series

  1. Sequence and summation notation

  2. Arithmetic and geometric sequences and series.

6. Logic and Proof

  1. Review of if-then statements, if-and-only-if statements.

  2. Converse, inverse, and contrapositive.

  3. Induction.

Statement: Course will cover a SUBSET of these topics in just-in-time remediation for the “parent” course.



Methods of Instruction
Directed Study
Discussion
Lecture
Student activities, groupwork, and computer-facilitated instruction (optional).
Solve the trigonometric equation given by
sin(x) + sin(x/2) = 0 for 0 ≤ x ≤ 2pi
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