1/15/2025 4:09:32 AM	MATH 27 Course Outline as of Fall 2018	Changed Course
CATALOG INFORMATION
Discipline and Nbr:  MATH 27	Title:  PRECALC ALG AND TRIG
Full Title:  Precalculus Algebra and Trigonometry
Last Reviewed:3/14/2022

Units		Course Hours per Week			Nbr of Weeks	Course Hours Total
Maximum	5.00	Lecture Scheduled	5.00		17.5 max.	Lecture Scheduled	87.50
Minimum	5.00	Lab Scheduled	0		8 min.	Lab Scheduled	0
		Contact DHR	0			Contact DHR	0
		Contact Total	5.00			Contact Total	87.50
		Non-contact DHR	0			Non-contact DHR Total	0

Total Out of Class Hours:  175.00

Total 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:

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:
Completion of MATH 154 or MATH 155 or higher; or Qualifying Placement from Math Assessment. See Student Success & Assessment Services for more information about the assessment process.

Recommended Preparation:

Limits on Enrollment:

Schedule of Classes Information
Description:

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:Completion of MATH 154 or MATH 155 or higher; or Qualifying Placement from Math Assessment. See Student Success & Assessment Services for more information about the assessment process.
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:
	B4	Math/Quantitative Reasoning		Fall 1996
	B4	Math/Quantitative Reasoning		Fall 1981	Spring 1984
IGETC:	Transfer Area			Effective:	Inactive:
	2A	Mathematical Concepts & Quantitative Reasoning		Fall 1998
CSU Transfer:	Transferable	Effective:	Fall 1981	Inactive:
UC Transfer:	Transferable	Effective:	Fall 1998	Inactive:
C-ID:

Certificate/Major Applicable: Both Certificate and Major Applicable

COURSE CONTENT

Outcomes and Objectives:
At the conclusion of this course, the student should be able to:

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 both right triangle and unit circle

    approaches, and using both degree and radian measure.

4. Identify and interpret characteristics of functions (including intercepts, turning points, extreme

    values, intervals of positive/negative/increasing/decreasing value, transformations, symmetry,

    asymptotes, holes) in graphing polynomial, rational, absolute value, radical, exponential,

    logarithmic, trigonometric, and inverse trigonometric functions.

5. Verify and apply trigonometric identities.

6. 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.

7. Solve application and modeling problems using the trigonometric functions, identities, and the

    Laws of Sines and Cosines.

8. Represent complex numbers in, and perform operations using, trigonometric form.

9. Graph circles, piecewise-defined functions, and parametric equations.

10. Use vectors to model applications in mathematics and science.

Topics and Scope

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

    L. 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. Reflections

     C. Period

    D. Phase (horizontal) shift

    E. Vertical 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:

1. Daily reading outside of class (30-60 pages per week)

2. Homework assignments (1-4 per week)

3. Quizzes (0-4 per week)

4. Exams (3-8)

5. Projects (0-10)

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%
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 assignments
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%
Quizzes, exams, and final exam
Other: Includes any assessment tools that do not logically fit into the above categories.		Other Category 0 - 10%
Projects

Representative Textbooks and Materials:

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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