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.
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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
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available mathematical software and the applications of this software.
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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/proofs/bpf/bpf.html
www.math.csusb.edu/notes/sets/node5.html
www.math.csusb.edu/notes/proofs/bpf/bpf.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.
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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.
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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,
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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/index.htm
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.
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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
www.utc.edu/~cpmawata/petersen/index.htm
www.utc.edu/~cpmawata/petersen/index.htm
www.utc.edu/~cpmawata/petersen/index.htm
www.utc.edu/~cpmawata/petersen/index.htm
www.utc.edu/~cpmawata/petersen/index.htm
www.utc.edu/~cpmawata/petersen/index.htm
www.utc.edu/~cpmawata/petersen/index.htm
www.utc.edu/~cpmawata/petersen/index.htm
www.utc.edu/~cpmawata/petersen/index.htm
www.utc.edu/~cpmawata/petersen/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.
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Spanning Trees
www.utc.edu/~cpmawata/petersen/index.htm
www.utc.edu/~cpmawata/petersen/index.htm
www.utc.edu/~cpmawata/petersen/index.htm
www.utc.edu/~cpmawata/petersen/index.htm
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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.purplemath.com/modules/graphing.htm
www.purplemath.com/modules/graphing.htm
www.purplemath.com/modules/graphing.htm
www.purplemath.com/modules/graphing.htm
www.purplemath.com/modules/graphing.htm
www.algebrahelp.com/lessons/equationbasics/
Represents data in tabular, graphic, and pictorial form.
Represents data in tabular, graphic, and pictorial form.
Represents data in tabular, graphic, and pictorial form.
Represents data in tabular, graphic, and pictorial form.
Represents data in tabular, graphic, and pictorial form.
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
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Expression
Range
Domain
www.purplemath.com/modules/fcns.htm#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
www.sosmath.com/algebra/algebra.html
www.sosmath.com/algebra/algebra.html
www.sosmath.com/algebra/algebra.html
www.sosmath.com/algebra/algebra.html
A good website encompassing most of the principles in this section.
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Inverse Functions
Logarithms and Exponential Functions
4th Degree Polynomials
Matrix Algebra
Vector Spaces
www.sosmath.com/algebra/algebra.html
www.sosmath.com/algebra/algebra.html
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
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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
www.exploremath.com/activities/activity_list.cfm?categoryID=7
www.exploremath.com/activities/activity_list.cfm?categoryID=7
www.exploremath.com/activities/activity_list.cfm?categoryID=3
www.exploremath.com/activities/activity_list.cfm?categoryID=3
www.exploremath.com/activities/activity_list.cfm?categoryID=5
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
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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
www.exploremath.com/activities/activity_list.cfm?categoryID=5
home.earthlink.net/~djbach/precalc.html
home.earthlink.net/~djbach/precalc.html
home.earthlink.net/~djbach/precalc.html
home.earthlink.net/~djbach/precalc.html
home.earthlink.net/~djbach/precalc.html
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,
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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
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Functions
Rational Functions
Algebra of Functions
Exponential Functions
Inverses of Functions
index.html
www.archives.math.utk.edu/visual.calculus/0/index.html
www.archives.math.utk.edu/visual.calculus/0/index.html
www.archives.math.utk.edu/visual.calculus/0/index.html
www.archives.math.utk.edu/visual.calculus/0/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,
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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.exploremath.com/activities/Activity_page.cfm?ActivityID=7
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.
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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.purplemath.com/modules/fcns.htm#domain
www.utc.edu/~cpmawata/transformations/translations/index.html
www.utc.edu/~cpmawata/transformations/translations/index.html
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
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Parabola
Parabola with Horizontal Direction
Ellipse
Hyperbola
www.exploremath.com/activities/activity_list.cfm?categoryID=1
www.exploremath.com/activities/activity_list.cfm?categoryID=1
www.exploremath.com/activities/activity_list.cfm?categoryID=1
www.exploremath.com/activities/activity_list.cfm?categoryID=1
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
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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
www.archives.math.utk.edu/visual.calculus/1/index.html
www.archives.math.utk.edu/visual.calculus/1/index.html
www.archives.math.utk.edu/visual.calculus/1/index.html
www.archives.math.utk.edu/visual.calculus/1/index.html
www.archives.math.utk.edu/visual.calculus/1/index.html
www.archives.math.utk.edu/visual.calculus/1/index.html
www.archives.math.utk.edu/visual.calculus/1/index.html
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
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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.archives.math.utk.edu/visual.calculus/2/index.html
www.archives.math.utk.edu/visual.calculus/2/index.html
www.archives.math.utk.edu/visual.calculus/2/index.html
www.archives.math.utk.edu/visual.calculus/2/index.html
www.archives.math.utk.edu/visual.calculus/3/index.html
www.archives.math.utk.edu/visual.calculus/5/index.html
www.home.earthlink.net/~djbach/calc.html
www.home.earthlink.net/~djbach/calc.html
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.
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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.archives.math.utk.edu/visual.calculus/3/index.html
www.archives.math.utk.edu/visual.calculus/5/index.html
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
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
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
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
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
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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
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
Geometric Constructions
Euclidean v. Non-Euclidean Geometry
Euclidean v. Non-Euclidean Geometry
www.mcn.net/~jimloy/math.html
www.mcn.net/~jimloy/math.html
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
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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/IUE/spec/coordsys/coordsys-classes.html
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/IUE/spec/coordsys/coordsys-classes.html
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/IUE/spec/coordsys/coordsys-classes.html
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
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
systems
Color coordinate systems
Transformations
IUE/spec/coordsys/coordsys-classes.html
www.ai.mit.edu/extra/tools/iue-docs/docs/AAI/IUE/spec/coordsys/coordsys-classes.html
www.utc.edu/~cpmawata/transformations/translations/index.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
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
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
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
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
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
Tesselations
Introduction to Transformations
Translations
Scaling
Rotations
Shears
Projections
www.homepage.mac.com/efithian/Geometry/Activity-10.html
www.homepage.mac.com/efithian/Geometry/Activity-11.html
www.homepage.mac.com/efithian/Geometry/Activity-12.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
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
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.mathtv.com/Trig/pages/ch02/ch02.htm
www.mathtv.com/Trig/pages/ch03/ch03.htm
www.mathtv.com/Trig/pages/ch04/ch04.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
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
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.mathforum.com/dr.math/faq/formulas/faq.circle.html
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
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
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
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
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.exploremath.com/activities/Activity_page.cfm?ActivityID=23
www.exploremath.com/activities/Activity_page.cfm?ActivityID=23
www.exploremath.com/activities/Activity_page.cfm?ActivityID=23
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
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
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
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
Permutation
Permutations on a Circle
Combination
Counting: Binomial CoefficientsCounting: The Binomial Theorem
www.andrews.edu/~calkins/math/webtexts/prod02.htm
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
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
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/Elaine.Young-1/math3213_frames.html
www.faculty-staff.ou.edu/Y/Elaine.Young-1/math3213_frames.html
www.faculty-staff.ou.edu/Y/Elaine.Young-1/math3213_frames.html
www.faculty-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
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
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.andrews.edu/~calkins/math/webtexts/prod02.htm
www.math.uah.edu/stat/prob/prob6.html
www.math.uah.edu/stat/prob/prob7.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
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
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.math.uah.edu/stat/special/special3.html
Www.math.uah.edu/stat/special/special4.html
Www.math.uah.edu/stat/special/special5.html
Www.math.uah.edu/stat/special/special9.html
Www.math.uah.edu/stat/special/special11.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.
Basic definition and graphical representation.
Basic definition and graphical representation.
Basic definition and graphical representation.
Basic definition and graphical representation.
Basic definition and graphical representation.
Basic definition and graphical representation.
Basic definition and graphical representation.
Basic definition and graphical representation.
Basic definition and graphical representation.
158 K A P L A N
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
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/
Basic definition and graphical representation.
Basic definition and graphical representation.
Basic definition and graphical representation.
Basic definition and graphical representation.
Basic definition and graphical representation.
Basic definition and graphical representation.
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
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
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
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
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
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
NOTES
162 K A P L A N
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
K A P L A N 163