Free analytical 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 applets tutorials in this site.

Questions on one to one Functions. Several questions with detailed solutions as well as exercises with answers on how to prove that a given function is a one to one function.

Slopes of Two Perpendicular Lines. A detailed tutorial on the proof of the fact that two perpendicular lines have slopes such that one is the negative of the reciprocal of the other.

Add Fractions. Add fractions with same denominator or different denominator. Several examples with detailed solutions and exercises.

Multiply Fractions. Multiply a fraction by another fraction or a number by a fraction. Examples with solutions and exercises.

Divide Fractions. Divide a fraction by a fraction, a fraction by a number of a number by a fraction. Several examples with solutions and exercises with answers.

Percent Math Problems Several word problems on percentage with detailed solutions are presented.

Percent Math Questions Several questions on percentages, with detailed solutions are presented.

Convert Percentages, Fractions and Decimals Tutorial on how to convert percentages, fractions and decimals. Questions with detailed solutions as well as exercises with answers are presented.

Vector Addition and Scalar Multiplication. A tutorial on how to find components of a vector , add two vectors, multiply a vector by a scalar. Examples, solutions, exercises and answers are included.

Matrix Addition and Multiplication. A tutorial on how to add, multiply by a scalar and multiply matrices with examples, solutions, exercises and answers.

The Inverse of a Square Matrix. A tutorial on how to find the inverse of any square matrix. The proof of a formula that gives the inverse of an invertible 2 x 2 matrix is also included.

Complex Numbers - Basic Operations. A tutorial on how to find the conjugate of a complex number and add, subtract, multiply, divide complex numbers supported by online calculators.

Cramer's Rule to Solve Systems of Equations. A tutorial on proving Cramer's rule for a 2 by 2 systems of linear equations. Presentation of the rule for a 3 by 3 systems of equations. An example on using Cramer's rule is presented.