Discipline: Mathematics
Originator: Mary Margarita Legner

Riverside Community College District
Integrated Course Outline of Record

Mathematics 10
MAT-10 : Precalculus
College:
Lecture Hours: 90.000
Outside-of-Class Hours: 180.000
Units: 5.00
Grading Methods: Pass/No Pass
Letter Grade
Course Description
Prerequisite: MAT-36 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:
  1. Sketch trigonometric functions
    • MAT-36 - Graph trigonometric functions.
  2. Verify trigonometric identities.
    • MAT-36 - Prove trigonometric identities.
  3. Identify special triangles and their related angle and side measures.
    • MAT-36 - Solve applications involving triangles and trigonometric functions.
  4. Solve trigonometric equations.
    • MAT-36 - Solve trigonometric equations.
Course Objectives:
Upon successful completion of the course, students should be able to demonstrate the following activities:
  1. Graph functions and relations in rectangular and polar coordinates.
  2. Synthesize results from the graphs and/or equations of functions and relations.
  3. Apply transformations to the graphs of functions and relations.
  4. Recognize the relationship between functions and their inverses graphically and algebraically.
  5. Solve and apply equations including rational, linear, polynomial, exponential, absolute value, radical, and logarithmic, and solve linear, nonlinear, and absolute value inequalities.
  6. Apply functions to model real world applications.
  7. Solve systems of equations and inequalities.
  8. Identify special triangles and their related angle and side measures.
  9. Evaluate the trigonometric function of an angle given in degree and radian measure.
  10. Manipulate and simplify a trigonometric expression.
  11. Prove trigonometric identities.
  12. Solve trigonometric equations, triangles, and applications.
  13. Graph the basic trigonometric functions and apply changes in period, phase shift and amplitude to generate new graphs.
  14. Find the terms of a sequence and the partial sums of a series.
  15. Use the Binomial Theorem to expand expressions.
  16. Prove statements using induction.
  17. Graph relations in parametric form.
Student Learning Outcomes:
Upon successful completion of the course, students should be able to demonstrate the following skills:
  1. Solve algebraic, exponential, logarithmic, and trigonometric equations and algebraic inequalities.
    • Critical Thinking: Students will be able to demonstrate higher-order 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.
  2. 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.
  3. 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.
  4. Manipulate and simplify algebraic, exponential, logarithmic, and trigonometric expressions.
    • Critical Thinking: Students will be able to demonstrate higher-order 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:
  1. Functions
    1. Domain and range
    2. Evaluation of linear, quadratic, polynomial, absolute value, radical, rational, logarithmic, exponential, and trigonometric functions
    3. Transformations of graphs of quadratic, absolute value, radical, rational, logarithmic, exponential, and trigonometric functions
    4. Algebra of functions
    5. Inverse functions
  2. Equations and Inequalities
    1. Rational, linear, radical, polynomial, exponential, logarithmic, absolute value, and trigonometric equations
    2. Linear, nonlinear, and absolute value inequalities
  3. Systems of Equations and Inequalities
  4. Linear, Polynomial, Rational, Radical, Absolute Value Functions
    1. Real and complex zeros of polynomial functions
    2. Graphs of functions including asymptotic behavior, intercepts, and vertices
    3. Partial fraction decomposition
  5. Exponential and Logarithmic Functions
    1. Graphs
    2. Properties of logarithms
    3. Applications to exponential and logarithmic functions and equations
  6. Trigonometric Functions
    1. Unit circle and right triangle trigonometry
    2. Graphs of trigonometric functions, including periods, translations and phase shifts
    3. Inverse trigonometric functions and their graphs
    4. Trigonometric and inverse trigonometric identities and formulas
  7. Sequences and series
  8. Binomial Theorem
  9. Mathematical induction
  10. Polar coordinate system
  11. Conic sections
  12. 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:
Outside-of-Class 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.
Outside-of-Class Writing Assignments
  • Use the symbols of algebra and trigonometry to manipulate and simplify trigonometric expressions and solve trigonometric equations, triangles, and applications.
Other Outside-of-Class 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)
C-ID#: MATH 155
Board of Trustees Approval Date: 11/13/2018
COR Rev Date: 11/13/2018