Discipline: Mathematics
Originator: Mary Margarita Legner
Riverside Community College District
Integrated Course Outline of Record
Mathematics
10
MAT10 : Precalculus 
College:
Lecture Hours:
90.000 OutsideofClass Hours: 180.000 Units: 5.00 Grading Methods: Pass/No Pass Letter Grade 
Course Description
Prerequisite:
MAT36 or appropriate placement
Course Credit Recommendation:
Degree Credit
Preparation for calculus: Polynomial, absolute value, radical, rational, exponential, logarithmic, and trigonometric functions and their graphs; analytic geometry, polar coordinates, sequences, and series. Students cannot receive credit for MAT 10 if they have already received credit for MAT 23. 90 hours lecture. (Letter Grade or Pass/No Pass option)
Short Description for Class Schedule
College level algebra and trigonometry preparation for calculus.
Entrance Skills:
Before entering the course, students should be able to demonstrate the following skills:
Sketch trigonometric functions
 MAT36  Graph trigonometric functions.

Verify trigonometric identities.
 MAT36  Prove trigonometric identities.

Identify special triangles and their related angle and side measures.
 MAT36  Solve applications involving triangles and trigonometric functions.

Solve trigonometric equations.
 MAT36  Solve trigonometric equations.
Course Objectives:
Upon successful completion of the course, students should be able to demonstrate the following activities: Graph functions and relations in rectangular and polar coordinates.
 Synthesize results from the graphs and/or equations of functions and relations.
 Apply transformations to the graphs of functions and relations.
 Recognize the relationship between functions and their inverses graphically and algebraically.
 Solve and apply equations including rational, linear, polynomial, exponential, absolute value, radical, and logarithmic, and solve linear, nonlinear, and absolute value inequalities.
 Apply functions to model real world applications.
 Solve systems of equations and inequalities.
 Identify special triangles and their related angle and side measures.
 Evaluate the trigonometric function of an angle given in degree and radian measure.
 Manipulate and simplify a trigonometric expression.
 Prove trigonometric identities.
 Solve trigonometric equations, triangles, and applications.
 Graph the basic trigonometric functions and apply changes in period, phase shift and amplitude to generate new graphs.
 Find the terms of a sequence and the partial sums of a series.
 Use the Binomial Theorem to expand expressions.
 Prove statements using induction.
 Graph relations in parametric form.
Student Learning Outcomes:
Upon successful completion of the course, students should be able to demonstrate the following skills: Solve algebraic, exponential, logarithmic, and trigonometric equations and algebraic inequalities.
 Critical Thinking: Students will be able to demonstrate higherorder thinking skills about issues, problems, and explanations for which multiple solutions are possible. Students will be able to explore problems and, where possible, solve them. Students will be able to develop, test, and evaluate rival hypotheses. Students will be able to construct sound arguments and evaluate the arguments of others.
 Graph translations of algebraic, exponential, logarithmic, and trigonometric functions and identify the graph of a function from its equation.
 Communication Skills: Students will be able to communicate effectively in diverse situations. They will be able to create, express, and interpret meaning in oral, visual, and written forms. They will also be able to demonstrate quantitative literacy and the ability to use graphical, symbolic, and numerical methods to analyze, organize, and interpret data.
 Apply functions and relations to model real world applications.
 Communication Skills: Students will be able to communicate effectively in diverse situations. They will be able to create, express, and interpret meaning in oral, visual, and written forms. They will also be able to demonstrate quantitative literacy and the ability to use graphical, symbolic, and numerical methods to analyze, organize, and interpret data.
 Manipulate and simplify algebraic, exponential, logarithmic, and trigonometric expressions.
 Critical Thinking: Students will be able to demonstrate higherorder thinking skills about issues, problems, and explanations for which multiple solutions are possible. Students will be able to explore problems and, where possible, solve them. Students will be able to develop, test, and evaluate rival hypotheses. Students will be able to construct sound arguments and evaluate the arguments of others.
Course Content:
 Functions
 Domain and range
 Evaluation of linear, quadratic, polynomial, absolute value, radical, rational, logarithmic, exponential, and trigonometric functions
 Transformations of graphs of quadratic, absolute value, radical, rational, logarithmic, exponential, and trigonometric functions
 Algebra of functions
 Inverse functions
 Equations and Inequalities
 Rational, linear, radical, polynomial, exponential, logarithmic, absolute value, and trigonometric equations
 Linear, nonlinear, and absolute value inequalities
 Systems of Equations and Inequalities
 Linear, Polynomial, Rational, Radical, Absolute Value Functions
 Real and complex zeros of polynomial functions
 Graphs of functions including asymptotic behavior, intercepts, and vertices
 Partial fraction decomposition
 Exponential and Logarithmic Functions
 Graphs
 Properties of logarithms
 Applications to exponential and logarithmic functions and equations
 Trigonometric Functions
 Unit circle and right triangle trigonometry
 Graphs of trigonometric functions, including periods, translations and phase shifts
 Inverse trigonometric functions and their graphs
 Trigonometric and inverse trigonometric identities and formulas
 Sequences and series
 Binomial Theorem
 Mathematical induction
 Polar coordinate system
 Conic sections
 Parametric equations
Methods of Instruction:
Methods of instruction used to achieve student learning outcomes may include, but are not limited to, the following activities:
 Lectures, discussions, and demonstrations on graphing polynomial and rational functions, applying functions to model real world applications, and manipulating and simplifying trigonometric expressions.
 Create small group activities in order to provide an opportunity for students to the practice verifying trigonometric identities, solving trigonometric equations, triangles, and applications, and recognizing the relationship between functions and their inverses graphically and algebraically with group interaction and support.
 Develop and assign class exercises that build the students abilities to solve systems of equations and inequalities, and graph functions and relations in rectangular coordinates and polar coordinates.
 Design class handouts on the unit circle and basic trigonometric graphs, and applying transformations to the graphs of functions and relations for both visual and verbal learning styles.
 Show videos, films, and computer programs that demonstrate the properties of logarithms, how to graph basic trigonometric functions, and how to synthesize results for the graphs and/or equations of functions and relations.
Methods of Evaluation:
Students will be evaluated for progress in and/or mastery of student learning outcomes using methods of evaluation which may include, but are not limited to, the following activities:
 Written assignments designed to ensure the students abilities to solve rational, radical, and polynomial equations, and graph functions and relations in rectangular coordinates and polar coordinates.
 Quizzes and examinations designed to assess the ability to find inverse functions, prove trigonometric identities, and synthesize results from the graphs and/or equations of functions and relations.
 Cumulative Final examination.
Sample Assignments:
OutsideofClass Reading Assignments
 Read and analyze text, examples and notes covering topics such as the algebra of functions, inverses of functions, and solving systems of equations and inequalities.
OutsideofClass Writing Assignments
 Use the symbols of algebra and trigonometry to manipulate and simplify trigonometric expressions and solve trigonometric equations, triangles, and applications.
Other OutsideofClass Assignments
 Problem sets that require students to graph the basic trigonometric functions and apply changes in period, phase shifts and amplitude to generate new graphs.
 Problem sets that require students to apply functions to model real world applications.
Course Materials:
All materials used in this course will be periodically reviewed to ensure that they are appropriate for college level instruction. Possible texts include the following:
 Stitz & Zeager. Precalculus. 3rd Open Educational Resources, 2013.
 Stewart, Redlin & Watson. Precalculus Mathematics for Calculus. 7th Cengage Learning, 2017.
 Sullivan. Precalculus . 10th Pearson, 2015.
 Zill & Dewar. Precalculus with Calculus Previews. 10th Jones & Bartlett, 2017.
Codes/Dates:
CB03 TOP Code:
1701.00  Mathematics, General
CB05 MOV Transfer Status: Transfers to Both UC/CSU (A)
CB05 NOR Transfer Status: Transfers to Both UC/CSU (A)
CB05 RIV Transfer Status: Transfers to Both UC/CSU (A)
CID#: MATH 155
CB05 MOV Transfer Status: Transfers to Both UC/CSU (A)
CB05 NOR Transfer Status: Transfers to Both UC/CSU (A)
CB05 RIV Transfer Status: Transfers to Both UC/CSU (A)
CID#: MATH 155
Board of Trustees Approval Date:
11/13/2018
COR Rev Date:
11/13/2018