Discipline: Mathematics Degree Credit  [X]
Non Credit  [ ]
Nondegree Credit  [ ]
Comm Service  [ ]
 

Riverside Community College District
Integrated Course Outline of Record

Mathematics 10


COURSE DESCRIPTION
10 Precalculus Units: 4.00
 
Prerequisite(s): MAT 36: Trigonometry
An integrated treatment of algebra and trigonometry at the college level, with major emphasis on polynomial, rational, exponential, logarithmic, trigonometric and inverse functions, sequences and series, mathematical induction, analytic geometry, partial fractions, polar coordinates and parametric equations. The course is designed to prepare students for the study of calculus. 72 hours lecture.
 
SHORT DESCRIPTION FOR CLASS SCHEDULE
The college level algebra and trigonometry preparation for calculus.
 
ADVISORY ENTRY SKILLS
Before entering the course, students will be able to:
  1. Apply the basic operations of algebra on the set of real and complex numbers.

  2. Solve equations in one or two variables.

  3. Graph equations.

  4. Identify special triangles and their related angle and side measures.

  5. Apply degree and radian measurements on trigonometric expressions.
STUDENT LEARNING OUTCOMES
 Upon successful completion of the course, students should be able to:

Solve polynomial, radical, exponential, logarithmic, trigonometric, parametric and absolute value equations.

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  3. Application of Knowledge - Maintain and transfer academic and technical skills to workplace

Graph polynomial, radical, exponential, logarithmic, trigonometric, parametric, absolute value equations, conics and their translations.

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  3. Application of Knowledge - Maintain and transfer academic and technical skills to workplace

Describe the behavior of the graph of the function from its equation.

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Critical Thinking - Integrate knowledge across a range of contexts
  3. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  4. Application of Knowledge - Maintain and transfer academic and technical skills to workplace

Analyze the patterns found in geometric and arithmetic sequences to find terms and evaluate series.

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Critical Thinking - Integrate knowledge across a range of contexts
  3. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  4. Application of Knowledge - Maintain and transfer academic and technical skills to workplace

Apply the Binomial Theorem to higher order polynomials.

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Critical Thinking - Generalize appropriately from specific contexts
  3. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  4. Application of Knowledge - Maintain and transfer academic and technical skills to workplace

Prove algebraic conjectures by using Mathematical Induction.
  

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Critical Thinking - Construct sound arguments and evaluate arguments of others
  3. Application of Knowledge - Maintain and transfer academic and technical skills to workplace
 
COURSE CONTENT
  TOPICS
 

1.   Review of number systems
      a.   Simple inequalities, exponents, absolute value and roots
      b.   Factoring, reducing, simplifying, and the quadratic formula
2.   Coordinate Plane 
      a.   Rectangular coordinates
      b.   Distance and midpoint formulas
3.   Function Concept
      a.   Domain and range, translations and transformations of graphs
            of basic functions
      b.   Function operations, inverse functions
4.   Sequences & Series
      a.   Sigma notion
      b.   Arithmetic and geometric progressions
5.   Polynomial and Rational Functions
      a.   Lines, slope, quadratic functions, zeros of polynomial functions
      b.   Graphs of polynomial and rational functions, partial fraction 
            decomposition
6.   Transcendental Functions
      a.   Exponential and logarithmic functions with their graphs
      b.   Properties of logarithms
      c.   Solving logarithmic and exponential equations, applications
7.   Trigonometric Functions
      a.   Graphs of trigonometric functions, including translations and
            phase shifts
      b.   Inverse trigonometric functions, trigonometric identities
      c.   Solving trigonometric equations
8.   Analytic Geometry
      a.   Conic sections, parametric equations
      b.   Polar coordinates
9.   Binomial Theorem and Mathematical Induction
 
METHODS OF INSTRUCTION
 Methods of instruction used to achieve student learning outcomes may include, but are not limited to:

  • Present class lectures/discussions/demonstrations in order to familiarize students with the elements of mathematics.
  • Create small group activities in order to provide an opportunity for students to the practice skills of mathematics with group interaction and support.
  • Develop and assign class exercises that build mathematical and reasoning skills.
  • Design class handouts to demonstrate mathematical principles for both visual and verbal learning styles.
  • Show videos/films/computer programs that demonstrate or perform mathematical operations.
  • Conduct individual conferences in order to identify strengths, weaknesses, and learning styles.
  • Develop and assign web-enhanced/online/distance learning tasks such as further reading and the investigation of Precalculus websites to deepen understanding of mathematics.
 
METHODS OF EVALUATION
 Students will be evaluated for progress in and/or mastery of learning outcomes by methods of evaluation which may include, but are not limited to:

  • Oral reports/presentations aimed to demonstrate knowledge of mathematical principles.
  • Quizzes, examinations, and written assignments designed to assess the progress and ability to define key concepts, translate statements, evaluate, and formulate solutions in Algebra, Trigonometry, and Geometry.
  • Group and individual projects designed to demonstrate ability to solve problems in formal reasoning cooperatively with others and to appreciate different approaches to solving such problems.
  • Final examination
ASSIGNMENTS

Required Reading Assignments


Required Writing Assignments


Other Outside-of-Class Assignments
 
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:

  • Larson and Hostetler. Precalculus . 7th ed. Houghton Mifflin Publishing Company, 2007.
  • Sullivan, Michael. Precalculus. 6th ed. Prentice Hall Publishing Company , 2002.
  • Stewart, Redlin & Watson. Precalculus . 4th ed. Brooks/Cole Publishing Company , 2002.
  • Aufmann, Baker, & Nation. Precalculus with Limits . Houghton Mifflin Publishing Company , 2000.
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