SRJC Course Outlines

10/31/2020 12:52:48 AMMATH 27 Course Outline as of Fall 2013

Changed Course
CATALOG INFORMATION

Discipline and Nbr:  MATH 27Title:  PRECALC ALG AND TRIG  
Full Title:  Precalculus Algebra and Trigonometry
Last Reviewed:10/22/2018

UnitsCourse Hours per Week Nbr of WeeksCourse Hours Total
Maximum5.00Lecture Scheduled5.0017.5 max.Lecture Scheduled87.50
Minimum5.00Lab Scheduled08 min.Lab Scheduled0
 Contact DHR0 Contact DHR0
 Contact Total5.00 Contact Total87.50
 
 Non-contact DHR0 Non-contact DHR Total0

 Total Out of Class Hours:  175.00Total Student Learning Hours: 262.50 

Title 5 Category:  AA Degree Applicable
Grading:  Grade Only
Repeatability:  00 - Two Repeats if Grade was D, F, NC, or NP
Also Listed As: 
Formerly:  MATH 57

Catalog Description:
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College algebra and trigonometry topics, including analytic geometry, functions and their graphs, trigonometric functions of angles, trigonometric identities, trigonometric solution of triangles, polar coordinates, parametric equations, complex numbers, vectors, sequences and series.

Prerequisites/Corequisites:
Course Completion of MATH 154 or Course Completion of MATH 155 or higher


Recommended Preparation:

Limits on Enrollment:

Schedule of Classes Information
Description: Untitled document
College algebra and trigonometry topics, including analytic geometry, functions and their graphs, trigonometric functions of angles, trigonometric identities, trigonometric solution of triangles, polar coordinates, parametric equations, complex numbers, vectors, sequences and series.
(Grade Only)

Prerequisites:Course Completion of MATH 154 or Course Completion of MATH 155 or higher
Recommended:
Limits on Enrollment:
Transfer Credit:CSU;UC.
Repeatability:00 - Two Repeats if Grade was D, F, NC, or NP

ARTICULATION, MAJOR, and CERTIFICATION INFORMATION

Associate Degree:Effective:Fall 1981
Inactive: 
 Area:B
MC
Communication and Analytical Thinking
Math Competency
 
CSU GE:Transfer Area Effective:Inactive:
 B4Math/Quantitative ReasoningFall 1996
 B4Math/Quantitative ReasoningFall 1981Spring 1984
 
IGETC:Transfer Area Effective:Inactive:
 2AMathematical Concepts & Quantitative ReasoningFall 1998
 
CSU Transfer:TransferableEffective:Fall 1981Inactive:
 
UC Transfer:TransferableEffective:Fall 1998Inactive:
 
C-ID:

Certificate/Major Applicable: Both Certificate and Major Applicable



COURSE CONTENT

Outcomes and Objectives:
Upon completion of the course, students will be able to:
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Upon completion of the course, students will be able to:
 1.   Perform advanced operations with functions (using symbolic,
       graphical, and numerical representations) and apply knowledge to
       application and modeling problems.
 2.   Define and graph inverse functions.
 3.   Define the trigonometric fuctions, using both right triangle and unit
       circle approaches, and develop applications of radian measure.
 4.   Define and apply characteristics of functions (including intercepts,
         turning points, extreme values, intervals of positive/negative/
        increasing/decreasing value, transformations, symmetry) in graphing
         polynomial, rational, absolute value, radical, exponential, logarithmic,
         trigonometric, and inverse trigonometric functions.
 5.    Graph asymptotes and recognize a hole in the graph.
 6.    Develop and verify trigonometric identities.
 7.    Solve equations symbolically and graphically --involving polynomial, rational,
        absolute value, radical, exponential, logarithmic, and trigonometric functions --
        over the real numbers; and, as appropriate, the complex numbers.
 8.    Solve application and modeling problems using the trigonometric functions,
        identities, and the Laws of Sines and Cosines.
 9.    Represent complex numbers in, and perform operations using,
         trigonometric form.
 10.  Graph circles, piecewise-defined functions, and parametric equations.

Topics and Scope
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I.       Equations and Inequalities
         A. Graphical and algebraic solutions to radical and quadratic-form
               equations, and to absolute value equations and inequalities
         B. Solutions to systems of nonlinear equations
II.     Topics From Analytic Geometry
         A. Midpoint and distance formulas
         B. Circles
III.    Analysis of Functions and Their Graphs
         A. Definition
          B. Notation
         C. Domain
         D. Range
         E.  Operations, including difference quotients and composition of functions
         F.  Catalog of functions
         G.  Symmetry
         H.  Even and odd functions
         I.   Shifts
         J.   Scaling
         K.  Reflections of graphs, along with modeling
IV.    Polynomial and Rational Functions
         A. Linear, quadratic, polynomial functions of higher
              degree and their graphs
         B. Long division of polynomials
         C. Graphs of rational functions
         D. Asymptotes and holes
         E. Introduction to limit concepts and notation
         F.  Solutions of polynomial and rational equations and inequalities,
               using real numbers and complex numbers as appropriate
V.     Inverse, Exponential and Logarithmic Functions
         A. Definitions
         B. Properties
         C. Graphs
         D. Equations
         E. Applications
VI.    Trigonometric Functions
         A. Radian and degree measures of angles
              1.  Arc length
              2.  Area of a sector
              3.  Linear and angular velocity
         B. Right triangle and unit circle definitions
         C. Characteristics of trigonometric functions
VII.   Identities and Conditional Equations
         A. Fundamental identities
         B. Sum and difference identities
         C. Related identities and their derivations
         D. Conditional trigonometric equations and applications
VIII. Graphical Representation of Trigonometric Functions
         A. Amplitude
         B. Period
         C. Phase (horizontal) shifts
IX.    Inverse Trigonometric Functions
         A. Definitions
         B. Properties of inverse trigonometric functions
         C. Inverse trigonometric functions and their graphs
X.     Solutions of Triangles
         A. Right triangles
         B. Oblique triangles
         C. Laws of Sines and Cosines
         D. Applications
XI.    Complex Numbers, Polar Coordinates, and Parametric Equations
         A.  Definitions
         B.  Operations
         C.  Graphical representation of complex numbers
         D.  DeMoivre's Theorem
         E.  Polar coordinates
         F.  Parametric equations
XII.  Two Dimensional Vectors
         A.  Geometric and analytic definitions
         B.  Algebra of vectors
         C.  Trigonometric form of vectors
         D.  Dot product
         E.  Applications
XIII. Sequences and Series
         A.  Finite and infinite geometric sequences and series
         B.  Summation of powers of integers

Assignments:
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1.  Daily reading outside of class (20-50 pages per week).
2.  Problem set assignments from required text(s) or supplementary
     materials chosen by the instructor (1-6 per week).
3.  Quizzes (0-4 per week).
4.  Exams (3-8 per term).
5.  Projects (for example, computer explorations or modeling activities,
     0-10 per term).

Methods of Evaluation/Basis of Grade.
Writing: Assessment tools that demonstrate writing skill and/or require students to select, organize and explain ideas in writing.Writing
0 - 0%
None
This is a degree applicable course but assessment tools based on writing are not included because problem solving assessments are more appropriate for this course.
Problem solving: Assessment tools, other than exams, that demonstrate competence in computational or non-computational problem solving skills.Problem Solving
5 - 20%
Homework problems
Skill Demonstrations: All skill-based and physical demonstrations used for assessment purposes including skill performance exams.Skill Demonstrations
0 - 0%
None
Exams: All forms of formal testing, other than skill performance exams.Exams
70 - 95%
Multiple choice and free response exams; quizzes
Other: Includes any assessment tools that do not logically fit into the above categories.Other Category
0 - 10%
Projects


Representative Textbooks and Materials:
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Precalculus:  Enhanced with Graphing Utilities (6th ed), Sullivan, Prentice Hall; 2013

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