5. Pre-Calculus

 
  1. Functions (P1)
  2. Exponential and Logarithmic Functions (P2)
  3. Quadratic Functions (P3)
  4. Polynomial Functions (P4)
  5. Rational Functions and Difference Quotients (P5)
  6. Trigonometric Functions (P6)
  7. Vectors, Matrices, and Systems of Equations (P7)
  8. Sequences, Series, and Mathematical Induction (P8)
  9. Polar Coordinates, Parameterizations, and Conic Sections (P9)

 

Additional Links to General Mathematics Sites

Pre-Calculus Topics

High School

  1. P1 Functions
    1. Chapter 4 Functions!
      A function is a rule that assigns to every element in a set D (domain) exactly one element in the set R (range).
    2. Concept Map for Calculus Graphing New
      This concept map shows procedure for using calculus to locate absolute extream of a function,f(x), on an interval I
    3. Exploring PreCalculus
      This site provides an introduction to PreCalculus and explains how functions are used in everyday applications.
    4. Families of Functions
      When we wish to describe a particular function, we specify its input-output rule.
    5. Finite Mathematics
      Outstanding!       This site provides students with interactive tutorials concerning functions and linear models. Specifically, functions from the numerical and algebraic viewpoints, functions from the graphical viewpoint, linear functions and models, linear regression, families of functions, and fitting functions to data. The site provides other on-line resources and the necessary math tools.
    6. Introduction to Functions
      The basic object of study in calculus is a function. We will start with the definition of a function and examine the representation in four modes: symbolic, numerical, graphical and verbal. The domain and range of a function are also defined; exercises on finding the domain of a function are provided.
    7. Precalculus Problems Website
      This site provides a series of sample problems that can be used to teach precalculus.
    8. Precalculus Tutorial
      This tutorial is designed for students enrolled in a Precalculus Course, or a course in College Algebra and Trigonometry.
    9. Topics in PRECALCULUS - Functions
      This site has a section on What is a Function? as well as material on many PreCalculus topics.
  2. P2 Exponential and Logarithmic
    1. Exponential Functions
      Exponential functions have made their way into the popular vernacular. Often, news reports will marvel at the exponential growth of something or other: Populations, stock prices, grocery bills, etc. When referring to growth rates, the word exponential has become synonymous with explosive.
    2. Exponential Growth
      In this lesson we will consider exponential growth problems. Exponential growth occurs when some quantity regularly increases by a fixed percentage.
    3. Exponential and Logarithmic functions
      This site has lessons on Exponential and Logarithmic functions.
    4. LOGARITHMS
      A good introduction to logarithms with many sample problems.
    5. Logarithmic Functions
      Logarithmic functions are just the inverses of exponentials. Where an exponential function may start slowly and then grow explosively, a logarithm can grow explosively and then turn a corner, making further accumulations at an excrutiatingly gradual pace.
    6. LOGARITHMIC AND EXPONENTIAL FUNCTIONS
      This site has a number of good sample problems dealing with Logarithmic and Exponential Functions.
    7. The Normal Distribution
      This is an interactive site that allows students to change the standard deviation on a normal curve to see how it affects the graph.  It will also display a variety of histograms that could fit that curve.
  3. P3 Quadratic Functions
    1. Exploring Linear Functions: Representational Relationships
      This interactive web site explores linear functons.  An interactive model is included.  This interactive diagram shows the graph of f(x) = mx + b. Use the sliders to change the values of m and b, and observe how the graph changes.  Student interactive.
    2. Exponentials/Logarithms
      Students can experiment with exponential or logarithmic graphs and compare them to each other. A lesson plan is provided for each activity.
    3. Finite Mathematics
      Outstanding! This site provides students with interactive tutorials concerning functions and linear models. Specifically, functions from the numerical and algebraic viewpoints, functions from the graphical viewpoint, linear functions and models, linear regression, families of functions, and fitting functions to data. The site provides other on-line resources and the necessary math tools.
    4. Function Evaluator and Grapher
      Use of this system is pretty intuitive. Enter your function f(x) in graphing calculator format (press the "example" button to see some examples). Then specify some values of x, and press "Evaluate". To see a graph, enter a range of x-values (Xmin and xMax) and press "Graph." The graph will appear in a little window called "Your Graph."
    5. Chapter 1 Linear & Quadratic Functions!
      This section is a basic review of lines and points and their relationship to graphing.
    6. Loan Calculator
      Students can set the amount of the loan, the interest rate and the number of years to see how variations in these numbers can change amount of payment and interest paid over the course of the loan. They also can set the amount of the monthly payment and calculate the amount of time required to pay off the loan.
    7. Pascal's Triangle
      Outstanding - This site gives Standards, Lessons, and Links for students in K-4, 5-8, and 9-12 and references for Pascal's Triangle. It emphasizes the concept of patterns and this site is for all grade levels. If you have geometer sketchpad there are some interactive activities to do.
    8. Quadratic Functions
      Quadratic functions and the properties of their graphs such as vertex and x and y intercepts are explored interactively using applets.
    9. QUADRATICS Polynomials of the 2nd degree
      This site has a number of lessons on solving Quadratic equations.
    10. Savings Calculator
      Students can use the savings calculator and see how changing the amount deposited, frequency of deposits, interest rate, time, and method of compounding interest affects their total.
  4. P4 Polynomial Functions
    1. Chapter 2 Polynomials!
      This site provides a series of lessons on Polynomial Functions.
    2. Polynomial Functions
      In this tutorial, we define polynomial functions. We investigate some properties of polynomials including the domain, range, roots and symmetry.
    3. Polynomial Functions
      Polynomial functions are nothing more than a sum of power functions. As a result, certain properties of polynomials are very "power-like." When many different power functions are added together, however, polynomials begin to take on unique behaviors.
    4. THE VOCABULARY OF POLYNOMIAL FUNCTIONS
      Functions can be categorized, and the simplest type is a polynomial function.
  5. P5 Rational Functions and Difference Quaotatients
    1. RATIONAL FUNCTIONS
      A rational function is a quotient of polynomials. This site has a series of lessons on rational functions.
    2. Rational Functions
      In this tutorial, we define rational functions. They discuss the domain and range of rational functions. The graph of a rational function is compared to the graph of the rational function k(x) = c xp for some particluar c and p. The graphs of f(x) = x- n and g(x) = x- m are also compared.
    3. Rational Functions
      Just as polynomials are composed of power functions, rational functions are the ratio of polynomials. A rational function is just one polynomial divided by another.
  6. P6 Trigonometric Functions
    1. Chapter 7 Trigonometric Functions
      This site provides a series of lessons on Trigonometric Functions.
    2. Direct and Partial Variations - Variability and Change (I.2.HS.5)
      This site contains teacher lessons plans for direct and partial variations. The concepts of direct and partial variation are introduced and compared to each other.
    3. Function Evaluator and Grapher - Variability and Change (I.2.HS.2,3,4&5)
      Use of this system is pretty intuitive. Enter your function f(x) in graphing calculator format (press the "example" button to see some examples). Then specify some values of x, and press "Evaluate". To see a graph, enter a range of x-values (Xmin and xMax) and press "Graph." The graph will appear in a little window called "Your Graph."
    4. Finite Mathematics - Variability and Change (I.2.HS.1,2,3,4,5&6)
      Outstanding! This site provides students with interactive tutorials concerning functions and linear models. Specifically, functions from the numerical and algebraic viewpoints, functions from the graphical viewpoint, linear functions and models, linear regression, families of functions, and fitting functions to data. The site provides other on-line resources and the necessary math tools.
    5. Maths Online Gallery: Functions 2 - Variability and Change (I.2.HS.4,5&6)
      Students match graphs to the functions they represent using and interactive applet. Types of functions include power, rational and trigonometric.
    6. Trigonometric Functions
      This site provides a listing of rigonometric identities and Computer programs that draw the graphs of trigonometric functions, sine and cosine, considered as circular functions.
    7. Trigonometric Functions
      Trigonometric functions are sometimes called circular functions. This is because the two fundamental trigonometric functions – the sine and the cosine – are defined as the coordinates of a point P travelling around on the unit circle of radius 1 .
  7. P7 Vectors, Matrices, and Systems of Equations
    1. Finite Mathematics
      Outstanding! This site provides students with interactive tutorials concerning functions and linear models. Specifically, functions from the numerical and algebraic viewpoints, functions from the graphical viewpoint, linear functions and models, linear regression, families of functions, and fitting functions to data. The site provides other on-line resources and the necessary math tools.
    2. Function Evaluator and Grapher
      Use of this system is pretty intuitive. Enter your function f(x) in graphing calculator format (press the "example" button to see some examples). Then specify some values of x, and press "Evaluate". To see a graph, enter a range of x-values (Xmin and xMax) and press "Graph." The graph will appear in a little window called "Your Graph."
    3. Function Notation; f(x)
      This site allows students to work problems in the f(x) notation step by step.
    4. Functions of Several Variables
      To expand our thinking from scalar quantities to the quantities described by vectors and matricies, we must also expand our notion of function.
    5. Maths Online Gallery: Functions 2
      Students match graphs to the functions they represent using and interactive applet. Types of functions include power, rational and trigonometric.
    6. Vectors & Matricies
      Individual numbers, real or complex, describe a wide range of things
  8. P8 Sequences, Series, and Mathematical Inductions
    1. Fibonacci Numbers and the Golden Section
      Outstanding - Fibonacci: Patterns shown in different areas i.e. Nature, Golden section (art, architecture and music) figures, puzzles. Leads to many hypertext links, and references.
    2. Mission Sequential (Geometric Sequences)
      The Applet requires the user to use general terms of Geometric Sequences to calculate the actual sequences. It does this through the use of a game.
    3. Pascal's Triangle
      Outstanding - This site gives Standards, Lessons, and Links for students in K-4, 5-8, and 9-12 and references for Pascal's Triangle. It emphasizes the concept of patterns and this site is for all grade levels. If you have geometer sketchpad there are some interactive activities to do.
    4. Series
      In this site students can read about and study arithmetic, geometric, infinite, biniomial, Taylor and species series. At the end, they can take an on-line quiz.
  9. P9 Polar Coordinates, Parameterizations, and Conic Sections
    1. Complex Numbers & Polar Coordinates
      Complex numbers: The very name sounds difficult. However, these numbers are based on just one very simple idea. Or, rather, they are based on one very simple need : To describe the things for which real numbers are inadequate.
    2. Conic Sections
      Review the concept of eccentricity through examining the effects of changing the value of the variable e in the following equation.This site provides a number of computer programs that draw the graphs of various conic sections.
    3. Polar Coordinates
      In this tutorial, we define polar coordinates. We convert from polar coordinates to rectangular coordinates and from rectangular coordinates to polar coordinates. We graph some of the basic functions in polar coordinates using LiveMath and a graphing calculator.

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