Mathematics Tutorials and Problems
(with applets)

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.

How to enable ( if it is not already ) your browser to view java applets?

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

1. Slope of a Line
2. General Equation of a Line: ax + by = c
3. Slope Intercept Form Of The Equation Of a Line: y = mx + b
4. Find Equation of a Line - applet
5. Construct a Parabola
6. Equation of Parabola
7. Find Equation of Parabola - applet
8. Equation of Hyperbola
9. Equation of a Circle
10. Find Equation of Circle - applet
11. Equation of an Ellipse




Functions and Graphs

12. Graph, Domain and Range of Common Functions
13. Quadratic Functions (general form)
14. Quadratic Functions in Standard Form
15. Horizontal Shift of Graphs
16. Vertical Shifting or translation of Graphs
17. Horizontal Stretching and Compression of Graphs
18. Vertical Stretching and Compression(scaling) of Graphs
19. Definition of the Absolute Value
20. Absolute Value Function
21. Reflection of Graphs In x-axis
22. Reflection of Graphs In y-axis




Inverse of a Function and One to One Functions

23. Inverse Function Definition
24. One-To-One function
25. Inverse Function




Explore Other Functions

26. Explore graphs of functions




Exponential and Logarithmic Functions

27. Exponential Functions
28. Logarithmic Functions




Hyperbolic Functions

29. Graphs of Hyperbolic Functions




Trigonometry

30. Graphs of Basic Trigonometric Functions.
31. Trigonometric Equations and the Unit Circle.
32. Angle in Trigonometry
33. Unit Circle And The Trigonometric Functions sin(x), cos(x) and tan(x)
34. Inverse Trigonometric Functions
35. Sine Function
36. Cosine Function
37. Tangent Function
38. Secant Function




Applications Of Trigonometry

39. Sine Law - Ambiguous Case - applet




Systems Of Equations

40. Systems of Linear Equations - Graphical Approach




Polar Coordinates And Equations

41. Polar Coordinates and Equations




Polynomials

42. Multiplicity of Zeros and Graphs Polynomials
43. Polynomial Functions




Rational Functions

44. Rational Functions




Matrix Multiplication

45. Matrix Multiplication




Geometry

46. Medians of Triangle - Interactive applet
47. Perpendicular Bisector- Interactive applet
48. Central and Inscribed Angles - Interactive applet
49. Reflection Across a Line
50. Triangles, Bisectors and Circumcircles - interactive applet

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.

1. Graphs of Rational Functions - Tutorials
2. Identify Graphs of Functions - Tutorials
3. Domain and Range of Functions
4. Ellipse Problems
5. Hyperbola Problems
6. Solve Linear Inequalities
7. Solve Polynomial Inequalities
8. Solve Inequalities With Absolute Value - Tutorials
9. Solve Rational Inequalities
10. Solve Equations of the Quadratic Form
11. Solve Equations with Absolute Value
12. Slope of a line
13. Tutorial on Equation of Line
14. Find inverse function
15. Tutorial on equation of circle
16. Tutorial on equation of circle (2)
17. Solve Systems of Linear Equations
18. Solve Equations Graphically
19. Algebra Tutorial
20. Tutorial on Inequalities
21. Composition of Functions
22. Equations with Rational Expressions - Tutorials
23. Solve Exponential and Logarithmic Equations
24. Solve Trigonometric Equations

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.

1. Graphing Linear Functions
2. Graphing Quadratic Functions
3. Graph of Rational Functions - Sketching
4. Graph of Sine, a*sin(bx+c), Function
5. Graphs of Logarithmic Functions
6. Graphs of Exponential Functions

Several precalculus problems are included in these pages. The applets are easy to use and answers are provided once the test is finished.

1. Equations And Inequalities with Absolute Value - Problems
2. Polynomial and Rational Inequalities - Questions and Answers
3. Solve Trigonometric Equations
4. Domain of a Function
5. Composition of Functions
6. Solve Exponential and Logarithmic Equations
7. Graphs of Functions - Questions
8. Graphs of Polynomial Functions - Questions
9. Graphs of Rational Functions - Questions
10. Graphs of Logarithmic and Exponential Functions - Questions
11. Find Inverse Functions - Questions
12. Graphs of Trigonometric Functions - Questions
13. Solve Quadratic Equations With Rational Expressions - Problems
14. Algebra Problems

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.

1. Mean Value Theorem
2. Differential Equations - Runge Kutta Method
3. Definition of the Derivative of a Function
4. Definition of Definite Integrals - Riemann Sums
5. Integral Form of the Definition of Natural Logarithm ln(x)