UNDERSTANDING THE TEST · Web viewInternet Resources for Mathematics Content Review. SUBAREA...

M a t h e m a t i c s C o n t e n t S p e c i a l t y T e s t

INTERNET RESOURCES FORMATHEMATICS

CONTENT REVIEW

SUBAREA I-MATHEMATICAL REASONING AND COMMUNICATION; NUMBER THEORY AND CONCEPTS

0001 Understand the relationships and common themes that connect mathematics, science and technology.

For example: analyzing the use of mathematical methods and problem-solving

strategies in scientific inquiry and engineering design applying mathematical principles that are common to science and

technology (e.g., magnitude and scale, patterns of change, optimization)

applying the principles of measurement (e.g., conversion factors, dimensional analysis) and analyzing how uncertainty can influence the accuracy and precision of a mathematical model

using a variety of software (e.g., spreadsheets, graphing utilities, statistical packages, simulations) and information technologies to model and solve problems in mathematics, science, and technology

TOPIC URL ANNOTATIONUsing mathematics in scientific inquiry.

Applying mathematics common to technology

www.plus.maths.org

www.pass.maths.org.uk/issue2/dar

An on-line mathematical magazine dedicated to the applicability of mathematics. Interesting topics include the applicability of mathematical modeling in disease and radioactive decay. To access these links, scroll to the link issue 14: Mar 01, located on the left hand of the screen, then select the link ‘mathematics of diseases.’

A web page describing the use of mathematics in the modeling of telephone network systems.

K A P L A N 119

http://www.pass.maths.org.uk/issue2/dar

http://www.pass.maths.org.uk/issue2/dar

http://www.plus.maths.org/

N e w Y o r k S t a t e T e a c h e r C e r t i f i c a t i o n E x a m s

Applying mathematics common to science.

www.bio.brandeis.edu/biomath/menu.html

An excellent web page devoted to describing the mathematics involved in scientific processes, such as exponential growth and diffusion. To access these links, scroll down to ‘Dixon’s population pages’, select ‘exponential growth, pages 1-4’ and work through pages 1-18 (page 18 is matrix models). Then, return to the main page and find and select the sub-heading ‘diffusion simulation’ (under the heading Grey stuff dissolves into white stuff). Another interesting link is ‘gradient’, found under the sub-heading ‘a bug seeking nutrients.’ It is also worthwhile to select and read through ‘A Mathematical Look at Synaptic Junctions.

Units

Dimensional Analysis

www.2.ncsu.edu/unity/lockers/users/f/felder/public/kenny/papers/units.html

www.2.ncsu.edu/unity/lockers/users/f/felder/public/kenny/papers/units.html

A web page devoted to reviewing the importance and applications of units in mathematics.

A web page devoted to reviewing the importance and applications of units (including dimensional analysis) in mathematics.

Using software in mathematics

www.neufeldmath.com Neufeld is a company dedicated to producing mathematics software. On this web-page you will find software demonstrations that you can download and sample. This will give you an excellent idea of

120 K A P L A N

http://www.neufeldmath.com/

http://www.2.ncsu.edu/unity/lockers/users/f/felder/public/kenny/papers/units.html






http://www.bio.brandeis.edu/biomath/menu.html

http://www.bio.brandeis.edu/biomath/menu.html


available mathematical software and the applications of this software.

K A P L A N 121


0002Understand reasoning processes, including inductive and deductive logic and symbolic logic.For example:

analyzing mathematical situations by gathering evidence, making conjectures, formulating counterexamples, and constructing and evaluating arguments

analyzing the nature and purpose of axiomatic systems (including those of the various geometries)

analyzing and interpreting the truth value of simple and compound statements (e.g., negations, disjunctions, conditionals) in truth tables and Venn diagrams

applying laws of inference to draw conclusions and demonstrating the relationship between the laws of formal logic and mathematical proof

TOPIC URL ANNOTATIONBasic Proofs (Axiomatic Systems)

Truth Tables

Venn Diagrams

Mathematical Induction

www.math.csusb.edu/notes/proofs/bpf/bpf.html


www.math.csusb.edu/notes/sets/node5.html


A web-site designed to review the use of Proofs in mathematics. To review the types of proofs, select ‘Introduction’ then ‘Methods of Proofs’ then ‘Types of Proofs’; work through each link (in blue) found on this page.

For ‘truth tables,’ select Introduction, then Logic, then Statements, Truth Values and Truth Tables.

For ‘ Venn diagrams’ select Introduction then Venn Diagrams.

Select Mathematical Induction.

122 K A P L A N

http://www.math.csusb.edu/notes/proofs/bpf/bpf.html



http://www.math.csusb.edu/notes/sets/node5.html









0003Understand and communicate the meaning of mathematical concepts and symbols.

For example:

translating between algebraic, graphic, pictorial, and other modes of presenting mathematical ideas

translating mathematical language, notation, and symbols into everyday language

deducing the assumptions inherent in a given mathematical statement, expression, or definition

evaluating the precision or accuracy of a mathematical statement

TOPIC URL ANNOTATIONGraphic, pictorial, and other modes of presenting mathematical ideas

Mathematical Symbols

www.math2.org/index.xml

www.sellipi.com/science/math/symbols.html

This page provides advanced explanations for algebraic and geometric topics – many links provide both pictorial, graphical, and algebraic or geometric mathematical expressions.

A web page devoted to mathematical symbols and notations. A great review.

K A P L A N 123

http://www.sellipi.com/science/math/symbols.html



http://www.math2.org/index.xml

http://www.math2.org/index.xml


0004Understand principles and properties of the complex number system and its subsystems.For example:

applying knowledge of real numbers to arithmetic and algebraic operations

justifying the need for the extension of a given number system using multiple representations of the complex numbers and their

operations (e.g., polar form; algebraic and geometric interpretations of the sum, difference, and product of complex numbers)

analyzing and applying the properties of vectors, groups, and fields to the complex numbers and its subsystems

TOPIC URL ANNOTATIONReal Number Properties

Complex Numbers

Number Systems

Rules of Complex Numbers

Applying the Properties of Vectors,

www.regentsprep.org/Regents/math/realnum/properties.htm

www.math.toronto.edu/mathnet/questionCorner

www.math.toronto.edu/mathnet/questionCorner

www.sosmath.com/complex/number/basic/soscv.html

www.whyslopes.com/etc/ComplexNumbers

A listing of the properties of real numbers

The Toronto University Mathematics Question Corner providing detailed explanations of complex numbers. Scroll to the heading marked ‘Complex Numbers’ and work through each link in blue underneath this heading.

Detailed explanations of number systems. Scroll to the heading ‘Number Systems’ and work through each topic under this heading.

The SOS math explanation of complex number rules (division, addition, etc.)

Detailed explanations of applying properties of vectors,

124 K A P L A N

http://www.whyslopes.com/etc/ComplexNumbers

http://www.whyslopes.com/etc/ComplexNumbers

http://www.sosmath.com/complex/number/basic/soscv.html

http://www.sosmath.com/complex/number/basic/soscv.html

http://www.math.toronto.edu/mathnet/questionCorner/




http://www.regentsprep.org/Regents/math/realnum/properties.htm




Groups, and Fields

groups and fields to complex numbers.

0005Understand mathematical modeling and apply multiple mathematical representations to explore mathematical ideas and solve problems.For example:

analyzing the appropriateness and accuracy of various approaches to given problems

evaluating types and characteristics of mathematical models (e.g., graphs, equations, physical and pictorial representations, scattergrams, stem and leaf plots, box and whisker diagrams) in relation to a given mathematical problem and interpreting these models

analyzing techniques of estimation and identifying situations in which estimation is appropriate

TOPIC URL ANNOTATIONProblem Solving

Null graphs

Isomorphism

Complete Graphs, Subgraphs

Regular Graphs

Platonic Graphs

Adjacency

www.jersey.uoregon.edu/~chuckp

www.utc.edu/~cpmawata/petersen/index.htm



www.utc.edu/~cpmawata/petersen/

This page provides five different methods for mathematical problem solving. Scroll to ‘Daily Problems’ and work through each section (‘guess and check’, ‘look for a pattern’, etc.)

A lesson on null graphs. Select lesson 1.

A lesson on isomorphism. Select lesson 3.

A lesson on complete graphs and subgraphs. Select lesson 4.

A lesson on regular graphs. Select lesson 5.

A lesson on platonic graphs. Select lesson 6.

A lesson on adjacency matrices.

K A P L A N 125

http://www.utc.edu/~cpmawata/petersen/index.htm











http://www.jersey.uoregon.edu/~chuckp

http://www.jersey.uoregon.edu/~chuckp


Matrices

Bipartite Graphs

Stars and Tripartite Graphs

Circuits and Wheel

Trees and Searches

Unions and Sums

Complements

Line Graphs

Grids

Spanning Trees

Planar Graphs

Dual Graphs

Weighted Graphs, Shortest Paths, and Minimal

index.htm











Select lesson 7.

A lesson on bipartite graphs. Select lesson 9.

A lesson on stars and tripartite graphs. Select lesson 10.

A lesson on circuits and wheels. Select lesson 11.

A lesson on trees and searches. Select lesson 13.

A lesson on unions and sums. Select lesson 14.

A lesson on complements. Select lesson 15.

A lesson on line graphs. Select lesson 18.

A lesson on grids. Select lesson 19.

A lesson on spanning trees. Select lesson 20.

A lesson on planar graphs. Select lesson 21.

A lesson on dual graphs. Select lesson 22.

A lesson on weighted graphs. Select lesson 23.

126 K A P L A N

































Spanning Trees





K A P L A N 127














SUBAREA II-ALGEBRA, ANALYTIC GEOMETRY, AND CALCULUS

0006Understand the principles and properties of algebraic operations and relations.For example:

determining algebraic expressions that best represent patterns among data presented in tabular, graphic, and pictorial form

performing and analyzing basic operations on numbers and algebraic expressions

distinguishing the algebraic model that best represents a given situation and analyzing the strengths and weaknesses of that model

applying algebraic concepts of relation and function (e.g., range, domain, roots) to analyze mathematical relationships

TOPIC URL ANNOTATIONStraight Lines

Absolute ValuesQuadratics

Polynomials

Radical Functions

Rational Functions

Piecewise Functions

Basic Operations On Algebraic

www.purplemath.com/modules/graphing.htm






www.algebrahelp.com/lessons/equationbasics/

Represents data in tabular, graphic, and pictorial form.






A tutorial that walks you through the basics of algebraic operations. At the end of each page, select the blue link ‘next

128 K A P L A N

http://www.algebrahelp.com/lessons/equationbasics/

http://www.algebrahelp.com/lessons/equationbasics/

http://www.purplemath.com/modules/graphing.htm













Expression

Range

Domain

www.purplemath.com/modules/fcns.htm#domain


page.’

The application of range in functions.

The application of the domain in functions.

0007Apply principles and techniques of algebra to model and solve problems involving linear, quadratic, and higher-degree relations.For example:

modeling and solving real-world problems involving linear or quadratic equations and inequalities

diagnosing logical errors in the solution of problems involving linear or quadratic equations or inequalities

evaluating techniques for modeling and solving problems involving higher-degree polynomials

representing and solving systems of linear equations using various algebraic techniques (e.g., vectors, matrices)

TOPIC URL ANNOTATIONQuadratic Equations

Factorization and Roots of Polynomials

Solving Equations

Systems of Equations

Inequalities

www.sosmath.com/algebra/algebra.html





A good website encompassing most of the principles in this section.

K A P L A N 129

http://www.sosmath.com/algebra/algebra.html










http://www.purplemath.com/modules/fcns.htm#domain







Inverse Functions

Logarithms and Exponential Functions

4th Degree Polynomials

Matrix Algebra

Vector Spaces



www.exploremath.com/activities_activitylist.cfm?categoryID=5

www.math.unl.edu/~tshores/linalgtext.html

www.math.unl.edu/~tshores/linalgtext.html

Select 4th degree polynomials.

Scroll to table of contents, work through the section labeled matrix algebra.

Scroll through Table of Contents to Vector Spaces, work through each link under this heading.

0008Understand and apply methods for using graphic representations to analyze, interpret, and communicate linear, quadratic, and higher-order relations.For example:

applying graphing techniques to model and solve problems involving systems of equations and inequalities

analyzing graphic, tabular, or pictorial representations of given linear, quadratic, or higher-order relations

applying algebraic principles to determine the properties associated with curves presented in graphic form (e.g., symmetries, turning points, intercepts) and analyzing the results of changing parameters on the graphs of functions and relations

modeling and solving real-world problems using linear programming and difference equations

TOPIC URL ANNOTATION2x2 Linear Systems

www.exploremath.com/activities/

“Define a 2 x 2 linear system and view the corresponding

130 K A P L A N

http://www.exploremath.com/activities/activity_list.cfm?categoryID=7


http://www.math.unl.edu/~tshores/linalgtext.html




http://www.exploremath.com/activities_activitylist.cfm?categoryID=5








Systems of Linear Inequalitiesin Slope-Intercept Form

Systems of Linear Inequalities in Normal Form

Systems of Two Quadratic Linear Inequalities

Slope Calculation

Slope-Intercept Form

Quadratics: Polynomial Form

Quadratics: Vertex Form

activity_list.cfm?categoryID=7

www.exploremath.com/activities/activity_list.cfm?categoryID=7






lines and their intersection. Examine the value of the determinant.”

“Experiment with and visualize solution sets for a system of up to sixLinear inequalities in slope-intercept form.”

“Experiment with and visualize solution sets for a system of up to sixlinear inequalities in standard form.”

“Experiment with the graphical solution of a system of two quadratic inequalities in polynomial form.”

Determining the slope using two data points.

Review how to calculate the slope of a line and experiment with slope and intercept.

“Experiment with the graph of a quadratic of the form y = ax2 + bx + c. Calculate the location of the vertex and y-intercepts. Trace the motion of the vertex as a, b, and c are changed.”

Experiment with the graph of a

K A P L A N 131






















Factoring Polynomials

Solving Quadratic Equations

Graphing Functions

Moving Function Graphs Around

Exponential and Logarithmic Functions

Applications Of Functions

Modeling Using Differential Equations

First Order Differential Equations


home.earthlink.net/~djbach/precalc.html






www.sosmath.com/diffeq/modeling/modeling.html

www.sosmath.com/diffeq/diffeq.html

quadratic of the form y = a(x - h)2 + k. Calculatethe location of the vertex and y-intercepts. View the function in polynomial form.

Provides a quick lesson in factoring polynomials, including examples and explanations.

Three methods for solving quadratic equations are explained, including factoring, completing the square, and the quadratic formula.

This lesson starts with the basics of functions and then details ways to graph a number of different functions.

This page provides an explanation for how to move a function on a graph.

A brief explanation of exponential and logarithmic functions.

A real-world example of functions: simple and compound interest.

Explains how to translate physical phenomenon into sets of equations which describes it.

A great explanation of first order differential equations,

132 K A P L A N

http://www.sosmath.com/diffeq/diffeq.html


http://www.sosmath.com/diffeq/modeling/modeling.html



http://home.earthlink.net/~djbach/precalc.html
















Second Order Differential Equations

www.sosmath.com/diffeq/diffeq.html

including linear and separable equations, the qualitative technique and some applications of differential equations. Explore each link under the heading ‘First Order Differential Equations.’

A great explanation of second order differential equations, including nonlinear, linear, and homogenous linear equations, reduction or order and series solutions. Explore the links under the heading ‘Second Order Differential Equations.’

0009Understand the principles and properties of rational, radical, absolute value, exponential, and logarithmic functions; and apply algebraic techniques to problem-solving situations involving these functions.For example:

applying the properties of rational, radical, absolute value, exponential, and logarithmic functions to model and solve problems in mathematics, science, and technology

solving problems involving rational, radical, absolute value, exponential, and logarithmic functions using various algebraic techniques

diagnosing logical errors in the solution of problems involving rational, radical, absolute value, exponential, and logarithmic functions

TOPIC URL ANNOTATIONFunctions

Even and Odd

www.archives.math.utk.edu/visual.calculus/0/index.html

www.archives.math.utk.edu/visual.calculus/0/

Provides a tutorial on functions, including drills and a computer program to assist in visualization of functions. Select the link ‘Introduction to Functions.’

A tutorial on even and odd

K A P L A N 133

http://www.archives.math.utk.edu/visual.calculus/0/index.html








Functions

Rational Functions

Algebra of Functions

Exponential Functions

Inverses of Functions

index.html





functions, including a LiveMath notebook to assist in visualization of functions with respect to the y-axis or origin. Includes quiz and computer programs designed to determine graphically whether a function is even or odd or neither.

A tutorial designed to explain rational functions. Select the link ‘Rational Functions.’

A Live Math Notebook on the graphing of the sum of two functions as well on how to use a graphing calculator. Select the link ‘Algebra of Functions.’

A tutorial on exponential functions including animation, computer programs and applets to assist in visualization of these functions. Select the link ‘Exponential Functions.’

A tutorial on the inverses of functions including quizzes, animation, computer programs and applets to assist in visualization of these functions. Select the link ‘ Inverses of Functions.’

0010Understand and apply methods for using graphic representations to analyze, interpret, and present rational, radical, absolute value, exponential, and logarithmic relations.For example:

converting between algebraic and graphic representations of rational,

134 K A P L A N















radical, absolute value, exponential, and logarithmic relations interpreting and analyzing relationships involving graphic and

algebraic representations (e.g., the relationship between the functions and the effects of algebraic transformations on the graph of a function)

applying algebraic principles to determine the properties associated with rational, radical, absolute value, logarithmic, and exponential relations presented in graphic form

modeling and solving problems graphically using systems of equations and inequalities involving rational, radical, absolute value, exponential, and logarithmic relationships.

TOPIC URL ANNOTATIONFunction Basics

Exponential Functions

Logarithms

Absolute Value

Linear Equations

Radical Equations

Inequalities

www.library.thinkquest.org/2647/algebra/algebra.htm

www.exploremath.com/activities/Activity_page.cfm?ActivityID=4


www.purplemath.com/modules/graphabs.htm

www.purplemath.com/modules/graphlin.htm

www.purplemath.com/modules/graphrad.htm

www.purplemath.com/modules/ineqgrph.htm

A great introduction to graphing basic functions. A nice review.

An interactive tutorial in graphing exponential functions.

An interactive tutorial in graphing logarithms.

Algebraic, graphical and tabular representations of absolute values.

Algebraic, graphical and tabular representations of linear equations.

Algebraic, graphical, and tabular representations of radical equations.

Algebraic, graphical, and tabular representations of inequalities.

K A P L A N 135

http://www.purplemath.com/modules/ineqgrph.htm

http://www.purplemath.com/modules/ineqgrph.htm

http://www.purplemath.com/modules/graphrad.htm

http://www.purplemath.com/modules/graphrad.htm

http://www.purplemath.com/modules/graphlin.htm

http://www.purplemath.com/modules/graphlin.htm

http://www.purplemath.com/modules/graphabs.htm

http://www.purplemath.com/modules/graphabs.htm

http://www.exploremath.com/activities/Activity_page.cfm?ActivityID=7






http://www.library.thinkquest.org/2647/algebra/algebra.htm




0011Understand how the techniques of analytic geometry can be used to model and solve problems.For example:

applying the concepts of range, domain, symmetry, intercepts, and asymptotes to the graphic or algebraic representations of given relations (e.g., finding the equation of a conic section given its parameters, determining the directrix of a conic section presented in algebraic or graphic form)

using the equations of transformations to find new representations of a given relation (e.g., translations, rotations, parametric equations)

recognizing the relationships between multiple representations of equivalent geometric, algebraic, and calculus concepts (e.g., the turning points on the graph of a function and the local maximum value of the function)

modeling and solving problems using conic sections and the principles of analytic geometry (e.g., modeling satellite orbits, optical properties)

TOPIC URL ANNOTATIONDomain and Range

Translations

Reflections

Rotations


www.utc.edu/~cpmawata/transformations/translations/index.html



A basic explanation of the domain and range of functions.

Interactive explanation of translations. Don’t ignore the applets as you work through this tutorial. Select the link ‘Translations’ and work through the entire section.

Interactive explanation of reflections. Don’t ignore the applets as you work through this tutorial. Select the link ‘Reflections’ and work through the entire section.

Interactive explanation of reflections. Don’t ignore the applets as you work through this tutorial. Select the link ‘Rotations’ and work through

136 K A P L A N

http://www.utc.edu/~cpmawata/transformations/translations/index.html













Parabola

Parabola with Horizontal Direction

Ellipse

Hyperbola





the entire section.

“Experiment with parabolas from a conic-sections perspective in standard form by manipulating the focus, directrix, and vertex. Visualize the string property.” Select the link ‘Parabola.’

“Experiment with parabolas from a conic-sections perspective in standard form by manipulating the focus, directrix, and vertex. Visualize the string property.” Select the ‘Parabola with Horizontal Direction’ link.

“Experiment with an ellipse in standard form. Manipulate vertices and foci, show their Pythagorean relationship, and visualize the string property.” Select the ‘Ellipse’ link.

“Experiment with a hyperbola in standard form. View asymptotes, manipulate vertices and foci, and visualize the string property.” Select the link marked ‘Hyperbola.’

0012Demonstrate an understanding of the fundamental concepts of calculus.For example:

analyzing limiting processes in infinite series and sequences and in areas under curves

K A P L A N 137














applying concepts of derivatives to interpret gradients, tangents, and slopes

applying concepts of limits to analyze and interpret the properties of functions (e.g., continuity, asymptotes)

analyzing the relationships among limiting processes, integration, and differentiation

TOPIC URL ANNOTATIONLimits - Numerical

Limits -Graphically

Limits -Symbolically

Continuous Functions

Properties of Continuous Functions

Horizontal Asymptotes

Vertical Asymptotes








An introduction to limits from a numerical point of view. Select links under the Heading ‘Limits - Numerical.’

An introduction to limits from a graphical point of view. Select links under the heading ‘Limits - Graphically.’

An introduction to limits from a symbolical point of view. Select links under the heading ‘Limits - Symbolically.’

A tutorial to continuous functions, including interactive notebooks and computer programs. Select links under ‘Continuous Functions.’

Tutorial on the Intermediate Value Theorem, the Bisection Method and the Extreme Value Theorem. Select links under ‘Properties of Continuous Functions.’

A great, interactive tutorial on horizontal asymptotes. Select link under ‘Horizontal Asymptotes.’

An interactive tutorial on

138 K A P L A N























Tangent Lines

Definition of Derivative at a Point

Definition of Derivative

Differential Formulas

Applications of Differentiation

Applications of Integration

Limits

Tangent Lines and Derivatives

Differential







www.home.earthlink.net/~djbach/calc.html



www.home.earthlink.net/

vertical asymptotes. Scroll to heading ‘Vertical Asymptotes’ and select links.

Tutorial on tangent lines as an introduction to the derivative.

Tutorial on the definition of derivative at a point. Select links under ‘Definition of Derivative at a Point.’

Using various interactive techniques, define and understand the derivative. Select links under the heading ‘Definition of a Derivative.’

Tutorial on elementary differentiation formulas, their derivation and use. Includes the Power Formula.

A number of applications for differentiation, including graphing, tangent lines, parametric curves, maxima and minima, etc.

A number of applications for integration are presented, including area between two curves, arc length, volume, work, moments and center of mass.

A basic definition of limits is provided.

A clear, easy description of tangent lines and derivatives.

K A P L A N 139

http://home.earthlink.net/~djbach/calc.html


























Calculus

Applications of Differential Calculus

~djbach/calc.html

An introduction to differential calculus.

Real-world applications of differential calculus.

0013Apply the principles and techniques of calculus to model and solve problems.For example:

using derivatives to model and solve problems (e.g., rates of change, maxima, minima, concavity)

using integration to model and solve problems (e.g., the area under a curve, applications of antiderivatives)

modeling and solving problems involving first order differential equations (e.g., separation of variables, initial value problems)

TOPIC URL ANNOTATIONApplications of Differentiation

Applications of Integration

Concavity

Maxima and Minima



www.sosmath.com/calculus/diff/der15/der15.html

www.sosmath.com/calculus/diff/der14/der14.html

A number of applications for differentiation, including graphing, tangent lines, parametric curves, maxima and minima, etc.

A number of applications for integration are presented, including area between two curves, arc length, volume, work, moments and center of mass.

Refresher on concavity, including graphical representations.

Graphical and tabular representations of global extrema.

140 K A P L A N

http://www.sosmath.com/calculus/diff/der14/der14.html














Rates

Area under a curve - Beginning

Area Under a Curve - Advanced

Modeling using Differential Equations

Applications of Differential Equations in Real Life

home.earthlink.net/~djbach/calc.html#anchor169988

www.sosmath.com/calculus/integ/integ01/integ01.html

www.sosmath.com/calculus/integ/integ02/more.html

www.sosmath.com/diffeq/modeling/modeling.html

www.sosmath.com/diffeq/first/application/application.html

An example of rates of change using diff. eq.’s

A very clear and concise introduction to the area problem.

Advanced topics on finding the area under the curve.

A great description of basic modeling using first order differential equations.

Every day applications of differential equations, including Radioactive Decay, Newton’s Law of Cooling, Orthogonal Trajectories and Population Dynamics. Select links of interest.

0014Understand techniques of numerical methods used to model and solve problems and to explore relationships.For example:

analyzing procedures for partitioning finite portions of a curve to investigate changes in the slope or the area under the curve

using graphing utilities and graphing calculators to explore roots, critical points, asymptotes, limits, and concavity

using statistical packages to model data using linear, logarithmic, exponential, and power regression models

applying simplex method procedures to solve problems involving linear programming models

K A P L A N 141

http://www.sosmath.com/diffeq/first/application/application.html






http://www.sosmath.com/calculus/integ/integ02/more.html



http://www.sosmath.com/calculus/integ/integ01/integ01.html



http://home.earthlink.net/~djbach/calc.html#anchor169988




TOPIC URL ANNOTATIONCalculus of Areas

Changes in Slope

Graphing Utilities and Graphing Calculators to Explore Roots, Critical Points, Etc.

On-line Utilities and Software for:

Finite Math

home.earthlink.net/~djbach/intcalc.html#anchor1428555

home.earthlink.net/~djbach/calc.html

www.graphcalc.com/index.shtml

147.4.150.5/~matscw/RealWorld/utilsindex.html

147.4.150.5/~matscw/RealWorld/utilsindex.html

A great explanation of how to find the area under the curve using calculus.

A nice graphical representation of finding the change in slope using the tangent.

Download GraphCalc! Easy to Use! “GraphCalc is a powerful calculatoryou can use for a variety of purposes,including the production of 2D and 3D Euclidean and Polar graphs. You can use it for simple arithmetic,statistical analysis, unit conversion, and expression evaluation -- all from a single interface. Follow the prompts for downloading.

A page devoted to links for on-line graphing resources.

A page devoted to links for on-line graphing resources.

SUBAREA III-GEOMETRY AND TRIGONOMETRY

0015Understand the principles and properties of axiomatic (synthetic) geometries and the relationship of axiomatic geometries to other mathematical models.For example:

142 K A P L A N

http://www.graphcalc.com/index.shtml

http://www.graphcalc.com/index.shtml



http://home.earthlink.net/~djbach/intcalc.html#anchor1428555




using the properties of lines and their associated angles (including parallelism, perpendicularity, skew, supplementary angles, vertical angles) to characterize geometric relationships

using the concepts of similarity and congruence and the properties of geometric figures (e.g., triangle, parallelogram, rhombus, circle) to build arguments within an axiomatic system

comparing procedures used in geometric construction (e.g., constructing the perpendicular bisector of a given line segment) and contrasting the axiomatic approach with a coordinate or algebraic approach

analyzing, comparing, and contrasting the axiomatic structure and properties of various geometries (e.g., Euclidean, non-Euclidean, projective)

TOPIC URL ANNOTATIONAngles and their Measures

Parallel lines

Perpendicular Lines

Constructions

Congruence of Triangles

www.library.thinkquest.org/2647/geometry/angle/measure.htm

www.library.thinkquest.org/2647/geometry/angle/parallel.htm

www.library.thinkquest.org/2647/geometry/angle/perpen.htm

www.library.thinkquest.org/2647/geometry/construc.htm#perpen

www.library.thinkquest.org/2647/geometry/construc.htm

www.mcn.net/~jimloy/math.html

Everything you need to know about angles, including angle measure postulates and theorems.

Postulates and theorems of parallel lines

Theorems of perpendicular lines

Constructions of perpendicular lines

A page designed to teach you how to make constructions.

Introduction to the SAS, ASA, and SSS theorems. Scroll to Geometry heading, then select ‘Congruence of Triangles I’ link.

K A P L A N 143

http://www.mcn.net/~jimloy/congruen.html


http://www.library.thinkquest.org/2647/geometry/construc.htm



http://www.library.thinkquest.org/2647/geometry/construc.htm#perpen



http://www.library.thinkquest.org/2647/geometry/angle/perpen.htm



http://www.library.thinkquest.org/2647/geometry/angle/parallel.htm



http://library.thinkquest.org/2647/geometry/angle/measure.htm




Geometric Constructions

Euclidean v. Non-Euclidean Geometry

Euclidean v. Non-Euclidean Geometry



www.cvu.strath.ac.uk/courseware/msc/jgraves/

A more in-depth view of constructions, including theorems. Scroll to Geometry heading and select the link ‘Geometric Constructions.’

A good source for geometric theorems, as well as some non-Euclidean geometry. Scroll to the Geometry heading and peruse links under Euclidean and Non-Euclidean geometry sub-headings.

A verbal description of Euclidean v. Non-Euclidean Geometry.

0016Understand the principles and properties of coordinate geometry.For example:

applying the principles of distance, midpoint, slope, parallelism, and perpendicularity to characterize coordinate geometric relationships

using the properties of geometric figures and their relationships (e.g., triangle, parallelogram, circle, parabola, hyperbola) to build formal arguments

representing two- and three-dimensional geometric figures in various coordinate systems (e.g., Cartesian, polar)

analyzing and applying transformations in the coordinate plane

TOPIC URL ANNOTATIONCoordinate Geometry

Introduction to Proofs

www.Library.thinkquest.org/16284/a_coordinate_1.htm#The Basics

www.library.thinkquest.org/2609/lessons/htm

A great tutorial working through the basics of coordinate geometry, including graphs and generalizations.

Select lesson 2, Introduction to Proofs, and work through all sections select lesson 3,

144 K A P L A N

http://www.library.thinkquest.org/2609/lessons/htm

http://www.library.thinkquest.org/2609/lessons/htm






Cartesian coordinate system

2D Cartesian coordinate system

3D Cartesian coordinate system

Higher dimension coordinate system

Polar coordinate system

Non-Cartesian coordinate system

Spherical coordinate system

Geographic coordinate

www.ai.mit.edu/extra/tools/iue-docs/docs/AAI/IUE/spec/coordsys/coordsys-classes.html







www.ai.mit.edu/extra/tools/iue-docs/docs/AAI/

Triangles, and work through all sections.

This site provides basic descriptions for a number of coordinate systems, including Cartesian and Non-Cartesian. Programming information is also supplied. Select appropriate links as listed to review these systems.

K A P L A N 145

http://www.ai.mit.edu/extra/tools/iue-docs/docs/AAI/IUE/spec/coordsys/coordsys-classes.html
























systems

Color coordinate systems

Transformations

IUE/spec/coordsys/coordsys-classes.html



An excellent tutorial on transformations, including rotations, reflections and rotations. Provides graphical representations and applets for user interaction.

146 K A P L A N










0017Understand and apply the principles and techniques of axiomatic (synthetic) and coordinate geometries.For example:

applying geometric theorems and postulates to model and solve problems in mathematics, science, and technology involving linear, planar, and solid figures (e.g., properties of angles, similarity, surface area, volume)

determining the validity of a formal argument within a given axiomatic system

comparing the techniques used in solving problems involving linear, planar, and solid figures

using learning technologies to make and investigate geometric conjectures

TOPIC URL ANNOTATIONAxioms

Twenty Conjectures in Geometry

Www.ou.edu/oumathed/Non-Egeometry/NEG_frames.html

Www.geom.umn.edu/~dwiggins/mainpage.html

A great tutorial on axioms and postulates. Select the ‘Intro’ button on the left hand side of the page, then continue through to the end

Interactive site dedicated to teaching geometric conjectures. Scroll to the Twenty Conjectures, select each one, and use the Sketchpads to investigate geometric conjectures.

K A P L A N 147

http://www.geom.umn.edu/~dwiggins/mainpage.html



http://www.ou.edu/oumathed/Non-Egeometry/NEG_frames.html




0018Apply mathematical principles and techniques to model and solve problems involving vector and transformational geometries.For example:

modeling and solving problems in mathematics, science, and technology involving vector addition and scalar multiplication (e.g., force)

applying principles of geometry to model and solve problems involving the composition of transformations (e.g., translations, reflections, dilations, expansions, contractions, rotations)

analyzing how transformational geometry and symmetry is used in art and architecture (e.g., tessellations, tilings, frieze patterns, fractals)

using multiple representations of geometric transformations (e.g., coordinate, matrix)

TOPIC URL ANNOTATIONScalars and Vectors

Vectors and Direction

Vector Addition

Force

Acceleration

Transformation Matrices

www.glenbrook.k12.il.us/gbssci/phys/Class/1DKin/U1L1b.html

www.glenbrook.k12.il.us/gbssci/phys/Class/vectors/u3l1a.html

www.glenbrook.k12.il.us/gbssci/phys/Class/vectors/u3l1b.html

www.glenbrook.k12.il.us/gbssci/phys/Class/newtlaws/u2l2a.html

www.glenbrook.k12.il.us/gbssci/phys/Class/newtlaws/u2l3c.html www.silcom.com/~barnowl/HTransf.htm#III. TRANSFORMATION MATRICES

A basic definition of scalar and vector quantities. Includes an on-line quiz to test understanding.

A great explanation of vectors, including vector diagrams and free body diagrams.

A fantastic explanation of vector addition, including Pythagorean theorem.

Using scalar and vector quantities to calculate force.

Using scalar and vector quantities to calculate acceleration.

A very mathematical approach to transformation matrices, including translation, dilation

148 K A P L A N

http://www.silcom.com/~barnowl/HTransf.htm#III

http://www.silcom.com/~barnowl/HTransf.htm#III

http://www.glenbrook.k12.il.us/gbssci/phys/Class/newtlaws/u2l3c.html



http://www.glenbrook.k12.il.us/gbssci/phys/Class/newtlaws/u2l2a.html



http://www.glenbrook.k12.il.us/gbssci/phys/Class/vectors/u3l1b.html



http://www.glenbrook.k12.il.us/gbssci/phys/Class/vectors/u3l1a.html



http://www.glenbrook.k12.il.us/gbssci/phys/Class/1DKin/U1L1b.html




Tesselations

Introduction to Transformations

Translations

Scaling

Rotations

Shears

Projections

www.homepage.mac.com/efithian/Geometry/Activity-10.html



www.cs.fit.edu/wds/classes/cse5255/thesis/transformation/transformation.html#intro

www.cs.fit.edu/wds/classes/cse5255/thesis/translate/translate.html

www.cs.fit.edu/wds/classes/cse5255/thesis/scale/scale.html

www.cs.fit.edu/wds/classes/cse5255/thesis/rot/rot.html

www.cs.fit.edu/wds/classes/cse5255/thesis/shear/shear.html

and reflection, and strain and shear.

Three great introductions to tesselations, including Escher and kaleidoscope tesselations.

A basic definition of transformation.

A fantastic explanation of translations, including graphical and matrical representations.

A great site on scaling.

A wonderful look at rotations, including 2D and 3D rotation.

A great explanation of shears in the x and y direction, including graphical and matrical representations.

An introduction and taxonomy of projections is given.

K A P L A N 149

http://www.cs.fit.edu/wds/classes/cse5255/thesis/shear/shear.htm



http://www.cs.fit.edu/wds/classes/cse5255/thesis/rot/rot.html



http://www.cs.fit.edu/wds/classes/cse5255/thesis/scale/scale.html



http://www.cs.fit.edu/wds/classes/cse5255/thesis/translate/translate.html



http://www.cs.fit.edu/wds/classes/cse5255/thesis/transformation/transformation.html#intro



http://www.homepage.mac.com/efithian/Geometry/Activity-12.html










0019Understand principles, properties, and relationships involving trigonometric and circular functions and their associated geometric representations.For example:

analyzing connections among right triangle ratios, trigonometric functions, circular functions, and their inverses

determining methods to explore properties of trigonometric functions and their geometric representations and to arrive at conjectures about relationships (e.g., computer-based, calculator-based)

determining methods to explore the relationship between trigonometric functions and power series

analyzing the role of graphing utilities in exploring the relationships between vector and transformational geometries and trigonometric functions

TOPIC URL ANNOTATIONThe Six Trigonometric Functions

Right Triangle Trigonometry

Radian Measure(Circular Functions)

Graphing and Inverse Functions

Power Series, Trigonometr

www.mathtv.com/Trig/pages/ch01/ch01.htm




www.cl.cam.ac.uk/Teaching/2000/ContMaths/JGD-notes/node3.html

Problems and video lesson on the six trigonometric functions.

An interactive video lesson on right triangle trig, including definitions, problem solving and vector applications.

A great lesson on radian measure, including radians and degrees, circular functions, arc length and velocities.

A video lesson describing graphing, including inverse trig functions.

A basic definition of the power series of transcendental functions.

150 K A P L A N

http://www.cl.cam.ac.uk/Teaching/2000/ContMaths/JGD-notes/node3.html



http://www.mathtv.com/Trig/pages/ch04/ch04.htm









ic Functions

Expansions and Basis Functions

www.cl.cam.ac.uk/Teaching/2000/ContMaths/JGD-notes/node4.html

A very mathematical explanation of expansions and basis functions.

0020Apply the principles and techniques of trigonometry to model and solve problems.For example:

applying trigonometric functions to solve problems involving length or area (e.g., arcs, sectors, unknown sides of polygons, vectors)

applying trigonometric functions to solve problems involving angle measures (e.g., angles in a circle, unknown angles in polygons)

using circular functions to model periodic phenomena in mathematics, science, and technology

TOPIC URL ANNOTATIONArc of a Circle

Segment of a Circle

Sector of a Circle

Angle Measure

Problem solving using Trigonometric functions

Unit Circle

www.mathforum.com/dr.math/faq/formulas/faq.circle.html



www.sosmath.com/trig/Trig1/trig1/trig1.html www.sosmath.com/trig/Trig2/trig2/trig2.html

www.exploremath.com/activities/

A basic mathematical definition for determining the arc of a circle.

How to determine a segment of a circle using trig. Functions.

A basic description of defining a sector of a circle using trig. Functions.

Using trig. to find the measure of an angle.

Explanations and exercises for problem solving using the trig. functions.

K A P L A N 151



http://www.sosmath.com/trig/Trig2/trig2/trig2.html




http://www.mathforum.com/dr.math/faq/formulas/faq.circle.html













Activity_page.cfm?ActivityID=19

“Explore the relationship between the unit circle and the graphs of the sine, cosine, and tangent functions.”

152 K A P L A N




0021Understand and apply methods for using graphic representations to analyze, interpret, and present trigonometric functions.For example:

using rectangular coordinates to analyze the characteristics of the graph of trigonometric function (e.g., frequency, period, amplitude, phase angle)

using polar coordinates to analyze trigonometric functions (e.g., r, , periodicity, parametric representation)

comparing rectangular and polar representations applying graphing techniques to model and solve problems involving

trigonometric functions and systems of trigonometric equations and inequalities

TOPIC URL ANNOTATIONAmplitude

Period

Frequency

Solving Trigonometric Functions

Cartesian coordinates




www.sosmath.com/algebra/solve/solve0/solvtrig.html

“Experiment with the graphs of trigonometric functions of the form y = a sin[b (x - c)] + d. Relate the equation and graph to amplitude, period, and frequency.”

This section illustrates the process of solving trigonometric equations of various forms. It also shows you how to check your answer three different ways: algebraically, graphically, and using the concept of equivalence.

An interactive web page

K A P L A N 153

http://www.sosmath.com/algebra/solve/solve0/solvtrig.html













www.univie.ac.at/future.media/moe/galerie/zeich/zeich.html

designed to familiarize users with each coordinate system. Be sure to select each applet (in RED box), and utilize the graphs provided.

SUBAREA IV-DATA ANALYSIS, PROBABILITY, STATISTICS, AND DISCRETE MATHEMATICS

0022Understand the principles, properties, and techniques related to sequence, series, summation, and counting strategies and their applications to problem solving.For example:

analyzing the principle of mathematical induction in proving or disproving arguments

modeling and solving problems using the properties of arithmetic, geometric, and Fibonacci sequences or series

demonstrating an understanding of various counting strategies (e.g., permutations, combinations, binomial expansion)

TOPIC URL ANNOTATIONMathematical Induction

Fibonacci Numbers

Counting Rules

www.otal.umd.edu/drweb/induction

www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fib.html

www.andrews.edu/~calkins/math/webtexts/prod02.htm

Tutorial on mathematical induction, starting with the basics and working up to complex mathematics. Open the small window by clicking on the underlined word here. (This is also given in the web page instructions).

Click on links to find Fibonacci numbers in nature, the geometry of the golden section, continued fractions, the golden string, etc. Over 200 pages of information!

A great overview on counting

154 K A P L A N

http://www.andrews.edu/~calkins/math/webtexts/prod02.htm



http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fib.html



http://www.otal.umd.edu/drweb/induction

http://www.otal.umd.edu/drweb/induction

http://www.univie.ac.at/future.media/moe/galerie/zeich/zeich.html




Permutation

Permutations on a Circle

Combination

Counting: Binomial CoefficientsCounting: The Binomial Theorem


www.andrews.edu/~calkins/math/webtexts/prod02.htmwww.andrews.edu/~calkins/math/webtexts/prod02.htm

www.lklnd.usf.edu/~ejnioui/discrete/chap4_3.html

www.lklnd.usf.edu/~ejnioui/discrete/chap4_3.html

rules, including the multiplication and addition rules.

A basic definition of permutations.

A basic overview of permutations on a circle.

A brief description and the mathematical representation of combination.

A mathematical explanation of binomial coefficients in counting.

A mathematical explanation of the binomial theorem.

0023Understand the principles, properties, and techniques of probability and their applications.For example:

evaluating descriptions of probabilistic events (e.g., joint, conditional, or independent events; mutual exclusivity; exhaustiveness)

interpreting graphic representations of probabilities, including tables, charts, Venn diagrams, tree diagrams, frequency graphs, and the normal curve

modeling and solving problems involving uncertainty using the techniques of probability (e.g., addition and multiplication rules, random variables, discrete and continuous probability distributions)

comparing and contrasting the assumptions inherent in theoretical and empirical probability, using simulations to estimate probabilities, and analyzing the relationships between probability and statistics

K A P L A N 155

http://www.lklnd.usf.edu/~ejnioui/discrete/chap4_3.html
















TOPIC URL ANNOTATIONSets and Events

Introduction to Probability

The Vocabulary of ProbabilitySimple Probability

Conditional Probability

Joint Probability

Tree Diagrams

Odds

Permutations

www.math.uah.edu/stat/prob/prob2.html

www.faculty-staff.ou.edu/Y/Elaine.Young-1/math3213_frames.html

www.faculty-staff.ou.edu/Y/Elaine.Young-1/math3213_frames.htmlfaculty-staff.ou.edu/Y/Elaine.Young-1/math3213_frames.html





www.faculty-staff.ou.edu/Y/

A great explanation of events and the use of sets in probability.

A basic introduction to probability. A menu is on the left hand side of the screen, a frame on the right. Select the appropriate link and view in the frame.

The vocabulary of probability - an important review.

The basics of probability. A nice refresher course. Select the Simple Probability link on the left hand side of the page.

An introduction to conditional probability. Select the link on the left hand side of the page.

A basic definition of joint probability. Select link on the left hand side of the page.

A nice pictorial representation of a tree diagram. Select link on the left.

An introduction to odds. The link is on the left hand side of the page.

A great overview of permutations. Select the ‘Permutations’ link on the left hand side of the page.

156 K A P L A N

http://faculty-staff.ou.edu/Y/Elaine.Young-1/math3213_frames.html











http://www.faculty-staff.ou.edu/Y/Elaine.Young-1/math3213_frames.html






http://www.math.uah.edu/stat/prob/prob2.html



Venn Diagrams

Counting Rules

Independence

Convergence

Combinatorics

Relationship between Probability and Statistics

Elaine.Young-1/math3213_frames.html

www.math.csusb.edu/notes/sets/node5.html




www.math.uah.edu/stat/comb/index.html

www.math.uah.edu/stat/

A nice representation of Venn Diagrams.

A great overview on counting rules, including the multiplication and addition rules

Describes the concept of independence in probability, including the independence of two events and the independence of random variables.

A more advanced topic in probability, including the properties of distribution functions, the weak law of large numbers, and the strong law of large numbers.An excellent explanation of combinatorics, focusing on basic principles, permutations, combinations and multinomial coefficients.

A great website devoted to probability and statistics. Surfing the set will allow the user to see the similarities of the two subjects.

0024Understand the principles, properties, and techniques of statistics and their applications.For example:

applying the measures of central tendency, dispersion, and skewness to summarize and interpret data presented in graphic, tabular, or pictorial form

evaluating the statistical claims made for a given set of data (e.g.,

K A P L A N 157

http://www.math.uah.edu/stat/

http://www.math.uah.edu/stat/comb/index.html

http://www.math.uah.edu/stat/comb/index.html













analyzing assumptions made in the sampling, analysis, and testing of statistical hypotheses)

interpreting the outcomes of a given statistical test (e.g., t-test, chi-square analysis, correlation, simple regression)

using computers and graphing calculators to analyze and interpret data from a variety of disciplines (e.g., sciences, social sciences, technology)

TOPIC URL ANNOTATIONNormal Distribution

Gamma Distribution

Chi-Square Distribution

The Student t Distribution

The Beta Distribution

The Zeta Distribution

Dispersion: Variance

Standard Deviation

Sampling Distribution

Central Limit Theorem

Z Score

Www.math.uah.edu/stat/special/special2.html






Www.animatedsoftware.com/statglos/sgvarian.htm

Www.animatedsoftware.com/statglos/sgstdev.htm

Www.animatedsoftware.

Definition of the normal distribution.

Basic definition and graphical representation.










158 K A P L A N

http://www.animatedsoftware.com/statglos/sgsampds.htm

http://www.animatedsoftware.com/statglos/sgstdev.htm



http://www.animatedsoftware.com/statglos/sgvarian.htm



http://www.math.uah.edu/stat/special/special11.html



















Null Hypothesis

Statistical Significance

Degrees of Freedom

The t Test

Chi Square

ANOVA

Statistical Graphs

Using Computers to Analyze and Interpret Data From a Variety of Disciplines (e.g., Sciences, Social Sciences, Technology)

Hypothesis testing using Statistics

com/statglos/sgsampds.htm

Www.animatedsoftware.com/statglos/sgcltheo.htm

Www.animatedsoftware.com/statglos/sgzscore.htm

Www.animatedsoftware.com/statglos/sgnullhy.htm

Www.animatedsoftware.com/statglos/sgsignif.htm

Www.animatedsoftware.com/statglos/sgdegree.htm

Www.animatedsoftware.com/statglos/sgstat_t.htm

Www.animatedsoftware.com/statglos/sgchi_sq.htm

Www.animatedsoftware.com/statglos/sg_anova.htm

www.Faculty-staff.ou.edu/Y/Elaine.Young-1/math3213_frames.html

www.learner.org/







An important look at statistical graphs, including frequency tables, pictographs, histograms, scatterplots and boxplots. Select link on left hand menu termed ‘Statistical Graphs’

Answer the survey and then proceed through the exhibit. A great example of computer and statistical use in the real world

A very important site teaching the user how to apply statistics to test a hypothesis.

Reference site for all the different types of calculators

K A P L A N 159

http://www.learner.org/exhibits/statistics

http://www.animatedsoftware.com/statglos/sg_anova.htm



http://www.animatedsoftware.com/statglos/sgchi_sq.htm



http://www.animatedsoftware.com/statglos/sgstat_t.htm



http://www.animatedsoftware.com/statglos/sgdegree.htm



http://www.animatedsoftware.com/statglos/sgsignif.htm



http://www.animatedsoftware.com/statglos/sgnullhy.htm



http://www.animatedsoftware.com/statglos/sgzscore.htm



http://www.animatedsoftware.com/statglos/sgcltheo.htm






Calculators On-Line

exhibits/statistics

www.math.uah.edu/stat/hypothesis/index.html

www-sci.lib.uci.edu/HSG/RefCalculators.html

and which discipline they are used for. Some are available on the net.

0025Understand how techniques of discrete mathematics (e.g., diagrams, graphs, matrices, propositional statements) are applied in the analysis, interpretation, communication, and solution of problems.For example:

representing finite data using a variety of techniques representing real-world situations and relationships using sequences

and recurrence relations modeling and solving problems in mathematics, science, and

technology using techniques of discrete mathematics evaluating the use of computers and calculators to solve problems

(e.g., developing and analyzing algorithms)

TOPIC URL ANNOTATIONFitting Functions to Data

Sampling

147.4.150.5/~matscw/RealWorld/calctopic1/regression.html

147.4.150.5/~matscw/

A page explaining how to obtain a linear or exponential model from two data points

An introduction to sample

160 K A P L A N

http://www.math.uah.edu/stat/hypothesis/index.html

http://www.math.uah.edu/stat/hypothesis/index.html

http://www.learner.org/exhibits/statistics


Distributions & The Central Limit Theorem

Confidence Intervals

Introduction to Logic

Mathematics and CalculusApplied to the Real World

Calculators On-Line

RealWorld/finitetopic1/sampldistr.html

147.4.150.5/~matscw/RealWorld/finitetopic1/confint.html

147.4.150.5/~matscw/RealWorld/logic/logicintro.html

147.4.150.5/~matscw/RealWorld/textindex.html

www.sci.lib.uci.edu/HSG/RefCalculators2.html

statistics--descriptive measurements of a sample

Introduction to the central limit theorem.

A relatively simple, but greatly explained introduction to logic.

Each link under Finite Mathematics provides every day examples for the use of finite math.

A great on-line resource for finding a calculator applicable to anyone’s needs. Peruse the selection!

K A P L A N 161


NOTES

162 K A P L A N


K A P L A N 163

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