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Course ID: MATH R117 Curriculum Committee Approval Date: 10/24/2018 Catalog Start Date: Fall 2019 COURSE OUTLINE

OXNARD COLLEGE

I. Course Identification and Justification: A. Proposed course id: MATH R117 Banner title: Precalculus & Full title: Precalculus and Trigonometry

B. Reason(s) course is offered: This course is the prerequisite for at most four-year universities and fulfills lower division transfer admission requirements at most universities. This course was created to prepare students to succeed at Calculus. It is aligned with C-ID MATH 955.

C. C-ID: 1. C-ID Descriptor: 2. C-ID Status:

D. Co-listed as: Current: None

II. Catalog Information: A. Units: Current: 6.00

B. Course Hours: 1. In- Contact Hours: Lecture: 105 Activity: 0 Lab: 0 2. Total In-Class Contact Hours: 105 3. Total Outside-of-Class Hours: 210 4. Total Student Learning Hours: 315

C. Prerequisites, Corequisites, Advisories, and Limitations on Enrollment: 1. Prerequisites Current: MATH R015: Beginning and Intermediate Algebra or MATH R014 or MATH R014B or MATH R033 or Placement as determined by the college's multiple measures assessment process.

2. Corequisites Current: 3. Advisories: Current:

4. Limitations on Enrollment: Current:

D. Catalog description: Current: This course gives the calculus-bound student a solid foundation in precalculus algebra and analytic trigonometry, with emphasis on concepts and graphing. Topics include and inequalities, analytic of lines and conic sections, properties of functions, techniques of graphing, elementary functions (linear, quadratic, rational, exponential, logarithmic, and trigonometric) and inverse functions, trigonometric identities and equations, polar graphing, optimization applications, systems of equations, theory of equations, , binomial , , and series.

E. Fees: Current: $ None

F. Field trips: Current: Will be required: [ ] May be required: [ ] Will not be required: [X]

G. Repeatability: Current: A - Not designed as repeatable

H. Credit basis: Current: Letter Graded Only [ ] Pass/No Pass [ ] Student Option [X]

I. Credit by exam: Current: Petitions may be granted: [ ] Petitions will not be granted: [X]

III. Course Objectives: Upon successful completion of this course, the student should be able to: A. Graph functions and relations in rectangular coordinates and polar coordinates. B. Synthesize results from the graphs and/or equations of functions and relations. C. Apply transformations to the graphs of functions and relations. D. Recognize the relationship between functions and their inverses graphically and algebraically. E. Solve and apply equations including rational, linear, , exponential, absolute value, and logarithmic functions. F. Solve linear, nonlinear, and absolute value inequalities. G. Solve systems of equations and inequalities. H. Apply functions to model real world applications. I. Prove trigonometric identities. J. Identify special triangles and their related angle and side measures. K. Evaluate the trigonometric function at an angle whose measure is given in degrees and radians. L. Manipulate and simplify a trigonometric expression. M. Solve trigonometric equations. N. Graph the basic trigonometric functions and apply changes in period, phase and amplitude to generate new graphs. O. Evaluate and graph inverse trigonometric functions. P. Convert between polar and rectangular coordinates. Q. Calculate powers and roots of complex using DeMoivre's Theorem. R. Represent a vector in the form and ai + bj

IV. Student Learning Outcomes: A. Re-write and/or simplify algebraic and trigonometric expressions by using appropriate mathematical properties, identities, and substitutions. B. Solve polynomial, exponential, logarithmic, trigonometric, systems of and inequalities.

V. Course Content: Topics to be covered include, but are not limited to: A. Coordinates, graphs, and inequalities 1. Rectangular Coordinates a. Finding the equation of a circle b. Given the equation, finding the center and radius c. Finding the midpoint and length of a segment 2. Graphs and functions a. Identifying and sketching the 6 basic graphs of mathematics b. Finding the x- and y- intercepts of graphs 3. Equations of lines a. Finding the equation of a line having a specified geometric relationship with a b. Finding the slope of a line through two arbitrary points on curve 4. Symmetry and graphs a. Determining analytically if a graph possesses symmetry b. Graphing a of points symmetric with respect to a given axis or line 5. Linear inequalities and absolute value inequalities a. Solving compound linear inequalities b. Solving absolute value inequalities 6. Quadratic and rational equations and inequalities a. Solving quadratic equations and inequalities b. Solving rational inequalities B. Functions 1. Definition of a function a. Stating the definition of a function and determining if a relation is a function b. Calculating using functional notation and computing quotients of the forms c. Algebraically finding the domain and range of a function 2. a. Calculating the average rate of change of a function b. Graphing functions with restricted domains or piecewise functions c. Calculating the instantaneous rate of change of a function by making up a table of values C. (optional) 1. Graphing using translation and reflection techniques 2. Combining functions a. Combining two functions using arithmetic operations b. Combining functions using composition c. Decomposing a function into two or more functions 3. Iteration (Optional) a. Performing iterations on a function b. Finding the fixed point of a function 4. Inverse functions a. Determining if two functions are inverses of each other b. Finding the equation of the c. Graphing the inverse function d. Applying the one-to-one concept to determine if a function has an inverse D. Polynomial and rational functions 1. Linear functions a. Formulating linear models to applications such as total cost, marginal cost, and depreciation b. Finding the equation of the regression line (optional) c. Computing iterations on a linear function (optional) 2. Graphs of quadratic functions a. Finding the vertex b. Finding the line of symmetry 3. Applied functions: applying function models to set up equations that optimize values for maximum/minimum problems 4. Graphing polynomial functions that are in factored form 5. Graphing rational functions that are in factored form E. Exponential and logarithmic functions 1. Introduction to exponential functions and their graphs a. Graphing functions of the form y = ax b. Solving simple exponential equations without using 2. The exponential function y = ex a. Graphing functions of the form y = ex + B + C b. Finding the domain, range, intercepts, and asymptote 3. Logarithmic functions and their properties a. Graphing logarithmic functions including y = a + ln(x - c) b. Rewriting a logarithmic expression using the change-of-base formula c. Solving exponential equations using logarithms d. Solving logarithmic equations using exponentials e. Finding the inverse of an exponential function f. Finding the inverse of a logarithmic function g. Simplifying logarithmic expressions using properties of logarithms F. The trigonometric functions 1. Radian measure a. Converting between degree and radian measure b. Solving problems involving angular speed, and arc length, and linear speed 2. Defining the trigonometric functions using unit circle and right triangle approaches 3. Simplifying expressions and calculating the trigonometric values of general angles using the reference angle concept G. Graphs of trigonometric functions 1. Trigonometric functions of real numbers a. Simplifying algebraic expressions using trigonometric substitutions b. Calculating sin0, cos0, given any trigonometric functions of 0 by using the Pythagorean identities 2. Graphing curves of the form y = Asin(Bx + C) + D and y = Acos(Bx + C) + D 3. Graphing the tangent and reciprocal functions H. Analytical trigonometry 1. Calculating trigonometric functions of opposite angles, double angles, half­ angles, and sums of angles 2. Solving trigonometric equations using radian and degree measure 3. Inverse trigonometric functions a. Graphing inverse trigonometric functions of y = arcsin x, y = arccos x, and y = arctan x b. Solving equations involving inverse trigonometric functions c. Calculating inverse trigonometric values such as arcsin (1/2) d. Calculating composition of trigonometric function with inverse trigonometric functions I. Additional topics in trigonometry 1. Right-triangle applications a. Resolving right triangles b. Solving application problems involving angle of elevation/depression c. Finding the area of a triangle using trigonometric formula 2. Resolving oblique triangles and solving applications using Law of Sines and Law of Cosines 3. Vectors in the , a geometric approach a. Calculating the sum of two vectors algebraically and illustrating the sum b. Calculating the horizontal and vertical components of a vector 4. Graphing equations given in parametric form 5. Polar coordinates a. Converting between rectangular and polar coordinates b. Converting equations between rectangular and polar form 6. Graphing polar curves J. Solving systems of equations using Gaussian Elimination, determinants and matrices 1. Solving nonlinear system of equations 2. Solving systems of inequalities (Optional) K. Analytic geometry of conic sections 1. Finding the equation, sketch the conic section, and label the appropriate attributes of foci,directrix, eccentricity, vertex, and/or center for: parabola, hyperbola, , and circle 2. Sketching the graph of a conic section written in polar form 3. Rotation of axes (Optional) L. Roots of polynomial equations 1. Solving polynomial equations using synthetic division, remainder theorem, factor theorem, and Fundamental Theorem of Algebra 2. Applying Descartes’ Rules of Signs to equation solving (Optional) 3. Finding the partial fraction decomposition of rational expressions M. Additional topics in algebra 1. Using the Principle of Mathematical Induction to prove statements 2. Expanding a binomial using the Binomial Theorem 3. Finding common difference, common ratio, partial sum, general term, and infinite sum as required for arithmetic and geometric sequences and series 4. Finding roots of equations using DeMoivre’s Theorem

VI. Lab Content: None VII. Methods of Instruction: Methods may include, but are not limited to: A. Instructor guided discussion and instruction to assist in formulating models to solve optimization problems, analyze functions, simplify trigonometric expressions, and resolve triangles using identities. B. Examples demonstrated and worked out by the instructor illustrating solving equations, graph sketching, and simplifying trigonometric expressions. C. Instructor led computerized and/or graphing calculator demonstrations to assist in analyzing functions, to assist in sketching graphs of equations, to assist in analyzing conic sections, and to assist in generating numerical data to calculate and support algebraic statements.

VIII. Methods of Evaluation and Assignments: A. Methods of evaluation for degree-applicable courses: Essays [X] Problem-Solving Assignments (Examples: Math-like problems, diagnosis & repair) [X] Physical Skills Demonstrations (Examples: Performing arts, equipment ) [ ]

For any course, if "Essays" above is not checked, explain why.

B. Typical graded assignments (methods of evaluation): 1. Homework exercises involving demonstration of computational skills and demonstration of analytical problem solving skills. (Homework exercises typically involve several course objectives mentioned. For instance, the homework problem asking the student to sketch the graph of involves analyzing a function, solving a trigonometric equation, sketching the graph, and possibly simplifying a trigonometric expression - 4 objectives.) Graded credit/no credit based on completion 2. Writing exercises that probe the students’ understanding of lecture concepts and homework problems. These exercises typically involve the calculation and proof of numerical or algebraic statements and compare the result of the task to establish or reject a conjecture. If the student rejects the conjecture, he/she must state why and sometimes rephrase the conjecture to make it true. Graded on accuracy. 3. Individualized and customized special assignments that enlarge upon the homework assignments. In these assignments, all students are assigned the same problem with different numerical coefficients. These will usually involve several objectives. Example: Find the minimum distance from a point to a given line, analytically, graphically, and numerically. The student has to perform several of the course objectives to work this problem: Solve a , formulate a mathematical model that generates the distance from the point to the line, sketch the graph of the quadratic function, and generate a numerical table of values listing the volume. Graded on completion and accuracy of the assignment. 4. Midterm exams. Each midterm exam typically emphasizes several objectives. Exams that are devoted primarily to algebra test each student’s ability to analyze functions, solve equations, sketch graphs and simplify expressions. Other exams test the student’s ability to analyze and graph conic section or resolve triangles by using identities, as well as solve equations and simplify expressions. Graded on accuracy. 5. Final Exam. The final examination will test the students on all objectives. Graded on accuracy. C. Typical outside of classroom assignments: 1. Reading a. Critical reading and thinking in application homework problems. For example: "A rectangular package can have a maximum combined length and girth (perimeter of a cross section) of 108 inches. Find the dimensions of the package of maximum volume." 2. Writing a. Three or four sentence responses, for example: Use your own words to explain how to determine if two functions are inverses of each other. 3. Other a. Analytical problem computation or sketch sample, for example: "Determine the amplitude, period, and phase shift for the given function. Graph the function over an of two complete periods."

IX. Textbooks and Instructional Materials: A. Textbooks/Resources: 1. Abramson, Jay (2014). Precalculus Openstax.com. B. Other instructional materials: 1. Graphing calculator 2. Overhead graphing calculator, Texas Instruments (TI-83, TI-84, TI-85, or equivalent)

X. Minimum Qualifications and Additional Certifications: A. Minimum qualifications: 1. Mathematics (Masters Required) B. Additional certifications: 1. Description of certification requirement: 2. Name of statute, regulation, or licensing/certification organization requiring this certification:

XI. Approval Dates Curriculum Committee Approval Date: 10/24/2018 Board of Trustees Approval Date: 11/13/2018 State Approval Date: Catalog Start Date: Fall 2019

XII. Distance Learning Appendix A. Methods of Instruction Methods may include, but are not limited to:

B. Information Transfer Methods may include, but are not limited to: Course ID: 2603