SRJC Course Outlines

4/16/2024 8:08:20 AMMATH 27 Course Outline as of Summer 2019

Changed Course

Discipline and Nbr:  MATH 27Title:  PRECALC ALG AND TRIG  
Full Title:  Precalculus Algebra and Trigonometry
Last Reviewed:3/14/2022

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 equations, expressions, functions, inverse functions, and graphs. Also includes polar coordinates, parametric equations, complex numbers, vectors, sequences and series.

Completion of MATH 156 OR MATH 154 OR MATH 155 or AB705 placement into Math Tier 3 or higher

Recommended Preparation:

Limits on Enrollment:

Schedule of Classes Information
Description: Untitled document
College algebra and trigonometry topics, including equations, expressions, functions, inverse functions, and graphs. Also includes polar coordinates, parametric equations, complex numbers, vectors, sequences and series.
(Grade Only)

Prerequisites:Completion of MATH 156 OR MATH 154 OR MATH 155 or AB705 placement into Math Tier 3 or higher
Limits on Enrollment:
Transfer Credit:CSU;UC.
Repeatability:00 - Two Repeats if Grade was D, F, NC, or NP


Associate Degree:Effective:Fall 1981
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:

Certificate/Major Applicable: Major Applicable Course


Student Learning Outcomes:
At the conclusion of this course, the student should be able to:
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1.  Perform advanced operations with functions (polynomial, rational, absolute value, radical,
    exponential, and logarithmic), understand the characteristics and graphs of these
    functions, and apply knowledge to modeling problems.
2.  Solve selected algebraic equations symbolically over the complex numbers, and solve
    polynomial, rational, absolute value, radical, exponential, and logarithmic equations
    graphically and symbolically over the real numbers.
3.  Define and graph the six trigonometric functions and their inverses, solve equations involving
    trigonometric functions symbolically and graphically, and verify trigonometric identities.
4.  Use trigonometric functions, identities, and Laws of Sines and Cosines to solve applications
5.  Define, graph, and demonstrate appropriate applications of vectors, complex numbers, polar
    coordinates, parametric equations, and inverse functions.

Objectives: Untitled document
During this course, students will:
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 and apply the trigonometric functions, using right triangle and unit circle approaches,
      and using degree and radian measures.
4.   Identify and interpret characteristics of functions (including intercepts, turning points, extreme
      values, intervals of positive/negative/increasing/decreasing value, transformations,
      symmetry, asymptotes, and holes).
5.   Graph polynomial, rational, absolute value, radical, exponential, logarithmic, trigonometric,
      and inverse trigonometric functions.
6.   Verify and apply 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 trigonometric form and perform operations.
10. Graph piecewise-defined functions and parametric equations.
11. Use vectors to model applications in mathematics and science.

Topics and Scope
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I. Equations and Inequalities
    A. Graphical and algebraic solutions to radical and quadratic form equations
    B. Graphical and algebraic solutions to absolute value equations and inequalities
II. 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 (even and odd functions)
    H. Transformations of graphs (shifts, scaling, reflections)
    I. Modeling
III. Polynomial and Rational Functions
    A. Linear, quadratic, and 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
IV. Inverse, Exponential, and Logarithmic Functions
    A. Definitions
    B. Properties
    C. Graphs
    D. Equations
    E. Applications
V. 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
VI. Identities and Conditional Equations
    A. Fundamental identities
    B. Sum and difference identities
    C. Related identities and their derivations
    D. Conditional trigonometric equations and applications
VII. Graphical Representation of Trigonometric Functions
    A. Amplitude
    B. Reflections
    C. Period
    D. Phase (horizontal) shift
    E. Vertical shifts
VIII. Inverse Trigonometric Functions
    A. Definitions
    B. Properties
    C. Graphs
IX. Solutions of Triangles
    A. Right triangles
    B. Oblique triangles
    C. Laws of Sines and Cosines
    D. Applications
X. 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
XI. Two Dimensional Vectors
    A. Geometric and analytic definitions
    B. Algebra of vectors
    C. Trigonometric form of vectors
    D. Dot product
    E. Applications
XII. Sequences and Series
    A. Introduction to finite and infinite sequence and series (sigma) notation
    B. Finite and infinite geometric sequences and series
    C. Summation of powers of integers
    D. Binomial Expansion
         1. Factorial notation
         2. Pascal's Triangle and/or binomial coefficients

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1. Reading outside of class (0-60 pages per week)
2. Problem sets (1-8 per week)
3. Quizzes (0-4 per week)
4. Projects (0-10)
5. Exams (3-8)
6. Final exam

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%
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%
Problems sets
Skill Demonstrations: All skill-based and physical demonstrations used for assessment purposes including skill performance exams.Skill Demonstrations
0 - 0%
Exams: All forms of formal testing, other than skill performance exams.Exams
70 - 95%
Exams and quizzes
Other: Includes any assessment tools that do not logically fit into the above categories.Other Category
0 - 10%

Representative Textbooks and Materials:
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Precalculus: Enhanced with Graphing Utilities. 7th ed. Sullivan, Michael and Sullivan III, Michael. Pearson. 2016
Precalculus. 3rd corrected ed. Stitz, Carl and Zeager, Jeffrey. Open Source Text. 2013 (classic)

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