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Free mathematics tutorials to help you explore and gain deep understanding of math topics. The site includes several java applets to investigate Graphs of Functions, Equations, and Algebra. Topics explored are: equations of line, ellipse, circle, parabola, hyperbola, polynomials; graphs of quadratic, rational, hyperbolic, exponential and logarithmic functions; one-to-one and inverse functions and inverse trigonometric functions; systems of linear equations; determinants and Cramer's rule; inverse matrix and matrix multiplication; vectors, complex numbers, polar equations; absolute value function; slope of a line; angle in trigonometry, unit circle, solutions to trigonometric equations; graph shifting, stretching, compression and reflection. Applets used as Online Math Calculators and Solvers and Online Geometry Calculators and Solvers are also included.
Calculus Tutorials and Problems and Questions with answers on topics such as limits, derivatives, integrals, natural logarithm, runge kutta method in differential equations, the mean value theorem and the use of differentiation and integration rules are also included.
Trigonometry Tutorials and Problems for Self Tests on sine, cosine, tangent, secant functions, trigonometric identities and formulas are also included. Free trigonometry worksheets to download are in this site. Interactive Geometry Tutorials and Problems on topics such as reflection across a line, sine and cosine laws, central and inscribed angles, perpendicular bisector, medians and circumcircle of a triangle are also included. Each math topic is explored interactively and graphically through tutorials .
Math problems for self tests and free math worksheets to download, analytical tutorials with examples and detailed solutions on: algebra; solving equation and inequalities; domain and range; composition of functions; solving exponential, logarithmic and trigonometric equations; graphs of trigonometric and exponential functions; equations of line, parabola, circle, hyperbola and graphing of linear, quadratic, rational, sine, logarithmic, exponential and absolute value functions are included.
Elementary statistics and probability tutorials are also included.
All applets used to explore topics in mathematics in this site are grouped as online math software.
Examples related to the applications of mathematics in physics and engineering such as the projectile problem, distance-time-rate problems and cycloid are included.
Several java applets to describe the mathematical properties ofAntennas are also included.
If needed, Free graph paper is available.
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Table Of Contents
1- Interactive Exploring and Tutorials in Precalculus
Java applets are used to explore interactively important topics in precalculus. These tutorials can be
used either as complements to topics already studied or to learn a new
topic through exploration.
Equations in Two Variables
- Slope of a Line
- General Equation of a Line: ax + by = c
- Slope Intercept Form Of The Equation Of a Line: y = mx + b
- Find Equation of a Line - applet
- Construct a Parabola
- Equation of Parabola
- Find Equation of Parabola - applet
- Equation of Hyperbola
- Equation of a Circle
- Find Equation of Circle - applet
- Equation of an Ellipse
Functions and Graphs
- Graph, Domain and Range of Common Functions
- Quadratic Functions (general form)
- Quadratic Functions in Standard Form
- Horizontal Shift of Graphs
- Vertical Shifting or translation of Graphs
- Horizontal Stretching and Compression of Graphs
- Vertical Stretching and Compression(scaling) of Graphs
- Definition of the Absolute Value
- Absolute Value Function
- Reflection of Graphs In x-axis
- Reflection of Graphs In y-axis
Inverse of a Function and One to One Functions
- Inverse Function Definition
- One-To-One function
- Inverse Function
Explore Other Functions
- Explore graphs of functions
Exponential and Logarithmic Functions
- Exponential Functions
- Logarithmic Functions
Hyperbolic Functions
- Graphs of Hyperbolic Functions
Trigonometry
- Graphs of Basic Trigonometric Functions.
- Trigonometric Equations and the Unit Circle.
- Angle in Trigonometry
- Unit Circle And The Trigonometric Functions sin(x), cos(x) and tan(x)
- Inverse Trigonometric Functions
- Sine Function
- Cosine Function
- Tangent Function
- Secant Function
Applications Of Trigonometry
- Sine Law - Ambiguous Case - applet
Systems Of Equations
- Systems of Linear Equations - Graphical Approach
Polar Coordinates And Equations
- Polar Coordinates and Equations
Polynomials
- Multiplicity of Zeros and Graphs Polynomials
- Polynomial Functions
Rational Functions
- Rational Functions
Matrix Multiplication
- Matrix Multiplication
Geometry
- Medians of Triangle - Interactive applet
- Perpendicular Bisector- Interactive applet
- Central and Inscribed Angles - Interactive applet
- Reflection Across a Line
- Triangles, Bisectors and Circumcircles - interactive applet
2- Online Algebra and Trigonometry Tutorials
Tutorials using step by step approach with examples and matched exercises are presented here. Detailed solutions to the examples are also included. Several tutorials have been designed so that they can be used with the applet tutorials in this site.
- Graphs of Rational Functions - Tutorials
- Identify Graphs of Functions - Tutorials
- Domain and Range of Functions
- Ellipse Problems
- Hyperbola Problems
- Solve Linear Inequalities
- Solve Polynomial Inequalities
- Solve Inequalities With Absolute Value - Tutorials
- Solve Rational Inequalities
- Solve Equations of the Quadratic Form
- Solve Equations with Absolute Value
- Slope of a line
- Tutorial on Equation of Line
- Find inverse function
- Tutorial on equation of circle
- Tutorial on equation of circle (2)
- Solve Systems of Linear Equations
- Solve Equations Graphically
- Algebra Tutorial
- Tutorial on Inequalities
- Composition of Functions
- Equations with Rational Expressions - Tutorials
- Solve Exponential and Logarithmic Equations
- Solve Trigonometric Equations
3 - Graphing of Functions
Tutorials on graphing functions, with examples and matched problems. Detailed solutions to the examples are included. Tutorials have been designed so that they can be used with the applet tutorials in this site.
- Graphing Linear Functions
- Graphing Quadratic Functions
- Graph of Rational Functions - Sketching
- Graph of Sine, a*sin(bx+c), Function
- Graphs of Logarithmic Functions
- Graphs of Exponential Functions
4 - Online Problems and self tests with Answers
Several precalculus problems are included in these pages. The applets are easy to use and answers are provided once the test is finished.
- Equations And Inequalities with Absolute Value - Problems
- Polynomial and Rational Inequalities - Questions and Answers
- Solve Trigonometric Equations
- Domain of a Function
- Composition of Functions
- Solve Exponential and Logarithmic Equations
- Graphs of Functions - Questions
- Graphs of Polynomial Functions - Questions
- Graphs of Rational Functions - Questions
- Graphs of Logarithmic and Exponential Functions - Questions
- Find Inverse Functions - Questions
- Graphs of Trigonometric Functions - Questions
- Solve Quadratic Equations With Rational Expressions - Problems
- Algebra Problems
5 - Calculus Tutorials
Topics in calculus are explored interactively using java applets. These tutorials can be used to explore a new topic or as a complement to what have been learnt already.
- Mean Value Theorem
- Differential Equations - Runge Kutta Method
- Definition of the Derivative of a Function
- Definition of Definite Integrals - Riemann Sums
- Integral Form of the Definition of Natural Logarithm ln(x)
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