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Summary of Pre-Calculus course at Coursera.Org
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Coursera-PreCalculus.md

Pre-Calculus

Description

This course is designed to prepare you for a college-level Calculus course. Through this course you will acquire a solid foundation in algebra and trigonometry. Emphasis is placed on understanding the properties of linear, polynomial, rational, radical, piece-wise, exponential, logarithmic, and trigonometric functions. You will learn to work with various types of functions in symbolic, graphical, numerical and verbal form.

This course will be taught over ten weeks, with materials released on a weekly basis. Each week will consist of a series of short lecture videos, quizzes every 3-5 lectures, readings and homework assignments through which you can practice your mastery of the material.

A prerequisite background in Introductory Algebra and Basic Geometry is necessary for this course.

Topics Outline

Week 0: Prerequisite Algebra Review.

  • Real numbers -- distributive, associative, inverse, commutative properties
  • Polynomials -- adding, subtracting, multiplication
  • Simplified Radical Form
  • Square Root -- addition, subtraction, multiplication
  • Rationalizing a Denominator

Week 1: Linear Equations and Inequalities. Absolute Value Equations and Inequalities.

  • Linear Equations -- solving, word problems, percentage problems
  • Linear Inequality -- solving, compound inequalities, word problems
  • Absolute Value -- equations, inequalities, radicals

Week 2: Quadratic Equations. Rational Equations. Additional Equation Solving Techniques.

  • Solving quadratic equations -- discriminant, quadratic formula
  • Difference of Two Squares
  • Perfect Square
  • Sum of Two Cubes
  • Square Root Property
  • Simplifying ration of polynomials
  • Rational Expressions -- add, subtract, multiply

Week 3: Functions. Graphing Functions. Transformations of Functions.

  • Vertical Line test, Domain and Range of Functions
  • Intercepts, Difference Quotient
  • Piecewise-defined Functions
  • Graph Transformations -- translations, vertically/horizontally stretch and shrink, reflect over x or y axis
  • Odd and Even Functions, tests for even, odd or neither

Week 4: Quadratic Functions. Inverse Functions. Polynomials.

  • Equation of Quadratic Function, vertex form and standard form
  • Graphing a parabola
  • Quadratic Inequalities
  • Finding the Inverse of Function, its domain and range
  • Verifying inverse functions
  • Polynomial Long Division, Synthetic Division (only with degree 1 polynomial)
  • Properties of Polynomials
  • Remainder Theorem and Factor Theorem

Week 5: Exponential and Logarithmic Equations.

  • Solving, Change of Base Formula for Logarithms, Converting between equations
  • Properties of Logarithms
  • Evaluating and Solving Logarithmic Equations
  • Exponential and Logarithmic Graphs, x- and y- intercepts

Week 6: Angles and their Measure. Trigonometric Functions: A Unit Circle. Solving Right Triangles.

  • Converting between degrees-minutes-seconds and degrees
  • Converting between degrees and radians
  • Coterminal and Reference (acute angle) Angles
  • Angle in Standard Position, Special Angles
  • Right Triangle

Week 7: Properties of Trigonometric Functions. Inverse Trigonometric Functions.

Week 8: Basic Trigonometric Identities: Sum, Difference, Cofunctions, Double-Angle and Half-Angle.

Week 9: Trigonometric Equations. Law of Sines. Law of Cosines

Week 10: Review and Final Exam.

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